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GAMS — A User's Guide

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1. 98 GAMS Output The coefficient of x is determined by first differentiating the equation above with respect to x This results in 2 2 x 1 power y 1 3 5 which evaluates to 221 Similarly the coefficient of y is obtained by differenti ating the equation above with respect to y which results in 2 sqr x 1 3 sqr y 1 1 5 sqr y 1 giving 216 1667 Notice that the coefficient of y could not have been determined if its level had been left at zero The attempted division by zero would have produced an error and premature termination The result of evaluating the left hand side of the equation at the initial point is shown at the end of each individual equation listing In the example above it is 225 5 and the three asterisks are a warning that the constraint is infeasible at the starting point t The order in which the equations are listed depends on how the model was defined If it was defined with a list of equation names then the listing will be in the order in that list If it was defined as al11 then the list will be in the order of declaration of the equations The order of the entries for the individual constraints is determined by the label entry order 10 5 2 The Column Listing The next section of the listing file is the Column Listing This is a list of the individual coefficients sorted by column rather than by row Once again the default is to show the first three entries for each variable along with their bound
2. i i15 countries s0051 whereas the following identifiers are incorrect 25 currency food amp drink 4 2 3 Set Elements The name of each set element can be up to 63 characters long and can be used in quoted or unquoted form The unquoted form is simpler to use but places restrictions on characters used in that any unquoted label must start with a letter or digit and can only be followed by letters digits or the sign characters and Examples of legal unquoted labels are Phos Acid 1986 1952 53 A September H2504 Line 1 In quoted labels quotes are used to delimit the label which may begin with and or include any legal character Either single or double quotes can be used but the closing quote has to match the opening one A label quoted with double quotes can contain a single quote and vice versa Most experienced users avoid quoted labels because they can be tedious to enter and confusing to read There are a couple of special circumstances If one wants to make a label stand out then to put asterisks in it and indent it as below is common A more subtle example is that it is possible to use GAMS keywords as labels if they are quoted If one need to use labels like no ne or sum then they will have to be quoted Examples of quoted labels are gt TOTAL Match 10 incr 12 foot Line 1 t Labels do not have a value The label 1986 does not have the numerical value 1986 and the label 101 is different f
3. 9 4 3 Iterative Implementation of Non Standard Algorithms 9 5 Making New Solvers Available with GAMS 10 GAMS Output IGI a IIA 10 2 The Mlustrative Model i ce cee a bean Pe as e a a a 10 3 Compilation Output lt c se i osa eae e A ee 10 3 1 Echo Print of the Input File aa oo sua ee a a wa 10 3 2 The Symbol Reference Map 10 3 3 The Symbol Listing Map 2 ao ravet aavet a 10 3 4 The Unique Element Listing Map 10 3 5 Useful Dollar Control Directives IMA Execution Qatput e m s acs ee ora e a ee Qe ae 10 5 Output Produced by a Solve Statement 10 5 1 The Equation Listing gt ooo cs 9 10 5 2 The Column Listing o eaa ya neado a aiee cs 10 5 3 The Model Statistics lt lt ceci e 10 5 4 The Solve Summary ses scra o seresa rrian WS Solver Report eest odara agi ba kee os ai nus da 10 5 6 The Solution Listing 44 064 ecb ua ee ee eas Ia eto II 105 8 Flo SUMMAY o ea ia a a a a T06 Error Reporting o 0 ee mora e es 10 6 0 Compilation Errofs e lt o ese aci ba Se rar 10 6 2 Compilation Time Errors 10 6 3 Execution Errors 22 ee ee ee A WGA Salve EITO ccs ee kk ee a Oe eee A IOT Summ o be a oe Oe eh ee Re ed A 11 Conditional Expressions Assignments and Equations 11 1 Introdueti n ociosos Bowe eh eee aD hee 112 Logical Conditio s 2 sosa awas PRR HE eee a 11 2 1 Numerical Expressions as Logical Conditions
4. TARGET target mean annual return on portfolio 7 V variance covariance array squared annual return VARIABLES VARIANCE variance of portfolio X fraction of portfolio invested in asset i EQUATIONS DMEAN definition of mean return on portfolio DVAR definition of variance FSUM fractions must add to 1 0 MODELS PORTFOLIO 10 3 4 The Unique Element Listing Map The following map is called the Unique Element Listing All unique elements are first grouped in entry order and then in sorted order with their explanatory texts The unique element listing map can be turned on by entering a line containing onuelxref at the beginning of the program Unique Element Listing Unique Elements in Entry Order 1 hardware software show biz t bills Unique Elements in Sorted Order 1 hardware show biz software t bills ELEMENT REFERENCES hardware DECLARED 11 REF 19 26 28 show biz DECLARED 11 REF 21 26 30 software DECLARED 11 REF 20 26 29 t bills DECLARED 11 REF 22 26 31 10 3 5 Useful Dollar Control Directives This sub section reviews the most useful of the Dollar Control Directives These must not be confused with the dollar exception handling operators that will be introduced later the similarity of terminology is unfortunate 96 GAMS Output The dollar control directives are compiler directives that can be put in the input file to control the appearance and amount of detail in the output produced by the GAMS compiler offlisting
5. The second put statement illustrates the updating of the cursor control suffixes by writing the letters x y and z On three different lines Each is preceded by the cursor being moved to the out cc value Initially the value for the cursor control suffice is 20 Since a single put statement is used for these three items the out cc value remains constant and consequently the letters end up in the same column Following this put statement the out cc value is updated to 23 which is the location of the cursor at the end of the second put statement note the additional blank spaces displayed with the letter z 15 13 2 Current Cursor Row These suffixes have numeric values corresponding to coordinates in the window of the page Because of this they can be used in conjunction with cursor control characters to manipulate the position of the cursor in the output file cr current cursor row in window hdcr header current row tler title current row The convention for updating the values stored for the cr suffix is that it are updated at the conclusion of a put statement Consequently the cr value remains constant throughout the writing of items for the next put statement even if multiple items are displayed It s behavior is similar to that of cl 15 13 3 Last Line Control These suffixes control the last line used in a writing area 11 last line used in window hd11 header last line t111 title last line Unlike the row and colum
6. scalar z 11 geval x sqrt 1 clearerror log x display z Without the use of clearerror s the programm would not continue with the execution comment This option changes the start of line comment to a single character which follows immediately the comment keyword This should be used with great care and one should reset it quickly to the default symbol ts The case of the start of line comment character does not matter when being used Consider the following example comment c c now we use a FORTRAN style comment symbol comment now we are back how it should be compress Causes a file to be compressed into a packed file The syntax is compress source target where source is the name of the source file to be compressed and target is the name for the resultant compressed file Consider the following example where the model library file TRNSPORT is used call gamslib trnsport compress trnsport gms t2 gms include t2 gms The first command retrieves the transport file and the second command compresses it Then later the compressed file can be solved as it is treated like any other GAMS input file decompress Causes a compressed file to be decompressed into an unpacked file The syntax is decompress source target where source is the name of the compressed file to be decompressed and target is the name for the resultant decompressed file Consider the following example where the model library file TRN
7. CK 160 In this case the GAMS compiler indicates that something is wrong with the set element sum At the bottom of the echo print we see the interpretation of error code 160 20 A GAMS Tutorial by Richard E Rosenthal Error Message 160 UNIQUE ELEMENT EXPECTED The problem is that sum is a reserved word denoting summation so our set element must have a unique name like summer This is a common beginner s error The complete list of reserved words is shown in the next chapter Example 2 Another common error is the omission of a semicolon preceding a direct assignment or equation definition In our transportation example suppose we omit the semicolon prior to the assignment of c i j as follows parameter c i j transport cost in 1000s of dollars per case c i j f d i j 1000 Here is the resulting output 16 parameter c i j transport cost in 1000s of dollars per case 17 c i j f d i j 1000 OK 97 195 96 194 1 Error Message 1 REAL NUMBER EXPECTED 96 BLANK NEEDED BETWEEN IDENTIFIER AND TEXT OR ILLEGAL CHARACTER IN IDENTIFIER OR CHECK FOR MISSING ON PREVIOUS LINE 97 EXPLANATORY TEXT CAN NOT START WITH or OR CHECK FOR MISSING ON PREVIOUS LINE 194 SYMBOL REDEFINED 195 SYMBOL REDEFINED WITH A DIFFERENT TYPE It is not uncommon for one little offense like our missing semicolon to generate five intimidating error messages The lesson here is concentrate on fix
8. migcp default This option controls the solver used to solve miqcp models For details cf option cns nlp default This option controls the solver used to solve nlp models For details cf option cns optca 0 0 This option is only used with problems containing discrete variables i e the GAMS model type mip General mixed integer problems are often extremely difficult to solve and proving that a solution found is the best possible can use enormous amounts of resources This option sets an absolute termination tolerance which means that the solver will stop and report on the first solution found whose objective value is within optca of the best possible solution opter 0 1 This option sets a relative termination tolerance for problems containing discrete variables which means that the solver will stop and report on the first solution found whose objective value is within 100 optcr of the best possible solution profile 0 This option is used to generate more information on program execution profiles This option is equivalent in function to the profile command line parameter 0 No execution profile is generated in listing file 1 The listing file reports execution times for each statement and the number of set elements over which the particular statement is executed 2 Specific times for statements inside control structures like loops profiletol 0 0 This option sets profile tolerance in seconds All statements that take less t
9. report cr p two z l cr p report sulfur limit two qs upper fuel oil sulfur display report This example shows not only how simply sensitivity analysis can be done but also how the associated multi case reporting can be handled The parameter qs is used to set the upper bound on the sulfur content in the fuel oil and the value is retrieved for the report 88 Model and Solve Statements The output from the display is shown below Notice that there is no production at all if the permissible sulfur content is lowered The case attributes have been listed in the row SULFUR LIMIT The wild card domain is useful when generating reports otherwise it would be necessary to provide special sets containing the labels used in the report Any mistakes made in spelling labels used only in the report should be immediately apparent and their effects should be limited to the report Section 14 5 1 page 136 contains more detail on how to arrange reports in a variety of ways So 205 PARAMETER REPORT PROCESS LEVEL REPORT BASE ONE TWO MID C A DIST 89 718 35 139 MID C N REFORM 20 000 6 772 MID C CC DIST 7 805 3 057 W TEX CC GAS OIL 5 902 W TEX A DIST 64 861 W TEX N REFORM 12 713 W TEX CC DIST 4 735 W TEX HYDRO 28 733 SULFUR LIMIT 3 500 3 400 5 000 9 4 3 Iterative Implementation of Non Standard Algorithms Another use of multiple solve statements is to permit iterative solution of
10. table upgradex strat size tech alternative way of writing table techi tech2 strategy 1 small medium 05 strategy 2 strategy 3 small medium 2 trategy 4 medium 25 display attrib attribx Here we encounter the display statement again It causes the data associated with upgrade and upgradex to be listed on the output file 5 4 6 Handling Long Row Labels It is possible to continue the row labels in a table on a second or even third line in order to accommodate a reasonable number of columns The break must come after a dot and the rest of each line containing an incomplete row label tuple must be blank The following example adapted from INDUS is used to illustrate As written this table actually has nine columns and many rows we have just reproduced a small part to show continued row label tuples table yield c t s w z crop yield metric tons per acre nwfp pmw wheat bullock semi mech la plant heavy january 385 338 wheat bullock semi mech la plant light 506 446 wheat bullock semi mech la plant standard 592 524 wheat bullock semi mech qk harv standard heavy january 439 387 5 5 Acronyms An acronym is a special data type that allows the use of strings as values 5 5 1 The Syntax The declaration for an acronymis similar to a set or parameter declaration in that several of them can be declared in one statement Acronym s acronym_name acronym_name Acronym_name is
11. 0 does not default outside of IDE input i text input file name Completing the input file name with the current directory composes the final name If such a file does not exist and the extension was not specified the standard input extension is attached and a second attempt is made to open an input file inputdir idir input search path In general GAMS searches for input and include files in the current working directory only This option allows the user to specify additional directories for GAMS to search for the input files A maximum of 40 separate directories can be included with the directories separated by Operating System specific symbols On a PC the separator is a semicolon character and under Unix it is the colon character Note that libinclude and sysinclude files are handled differently and their paths are specified by libincdir and sysincdir Consider the following illustration gams myfile idir mydir mydir2 The search order for the file myfile or myfile gms and all included files in PC systems is as follows 1 current directory 2 directories specified by inputdir mydir and mydir2 directories in order Under Unix the corresponding command is gams myfile idir mydir mydir2 inputdirl to inputdir40 idirl tezt idir40 tezt input search path The same information as in inputdir can be transferred to GAMS by entering the individual directories separately A maximum of 40 directories can be pas
12. 42 supply i sum j x i j 1 a i 43 44 demand j sum i x i j g b j 45 46 Model transport all 47 48 Solve transport using lp minimizing z 49 50 Display x l x m 51 The reason this echo print starts with line number 3 rather than line number 1 is because the input file contains two dollar print control statements This type of instruction controls the output printing but since it has nothing to do with defining the optimization model it is omitted from the echo The dollar print controls must start in column 1 title a transportation model offuppper The title statement causes the subsequent text to be printed at the top of each page of output The offupper statement is needed for the echo to contain mixed upper and lowercase Other available instructions are given in Appendix D page 203 2 11 2 Error Messages When the GAMS compiler encounters an error in the input file it inserts a coded error message inside the echo print on the line immediately following the scene of the offense These messages always start with and contain a directly below the point at which the compiler thinks the error occurred The is followed by a numerical error code which is explained after the echo print Several examples follow Example 1 Entering the statement set q quarterly time periods spring sum fall wtr results in the echo 1 set q quarterly time periods spring sum fall wtr
13. Controls multiple data statements or tables By default GAMS does not allow data statements to be redefined If this option is enabled the second or subsequent data statements are merged with entries of the previous ones Note that all multiple data statements are executed before any other statement is executed Consider running the following slice of code eolcom set i 1 10 parameter x i 1 3 1 1 1 2 1 3 1 onmulti parameter x i 7 9 parameter x i 2 6 parameter x i 3 5 display x This would have been illegal without the presence of the onmulti option The result of the display statement in the listing file is as follows 8 PARAMETER X 7 2 8 2 9 2 OWN NN PRP ow ou BRR NNN nono wwe Oww nono wwe NAN C O N UN an C O N UN om oO no NWN 1 1 000 2 3 000 6 3 000 7 2 000 8 2 000 9 2 000 Note that x 1 has a value of 1 after the first data statement since none of the subsequent data statements affect it x 2 on the other hand is reset to 3 by the third data statement t The two pass processing of a GAMS file can lead to seemingly unexpected results Both the dollar control options and the data initialization is done in the first pass and assignments in the second irrespective of their relative locations This is an issue particularly with onmulti since it allows data initializations to be performed more than once Consider the following example D 3 Detailed Descript
14. Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j Keep in mind that the word Equation has a broad meaning in GAMS It encompasses both equality and inequality relationships and a GAMS equation with a single name can refer to one or several of these relationships For example cost has no domain so it is a single equation but supply refers to a set of inequalities defined over the domain i 2 6 2 GAMS Summation and Product Notation Before going into equation definition we describe the summation notation in GAMS Remember that GAMS is designed for standard keyboards and line by line input readers so it is not possible nor would it be convenient for the user to employ the standard mathematical notation for summations The summation notation in GAMS can be used for simple and complex expressions The format is based on the idea of always thinking of a summation as an operator with two arguments Sum index of summation summand A comma separates the two arguments and if the first argument requires a comma then it should be in parentheses The second argument can be any mathematical expression including another summation As a simple example the transportation problem contains the expression Sum j x i j that is equivalent to gt xij A slightly more complex summation is used in the following example Sum i j c i j x i j that is equivalent to 7 g
15. RMPEC 80 model generation 171 model list 171 model status error unknown 100 feasible solution 100 integer infeasible 100 intermediate noninteger 100 intermediate infeasible 100 locally optimal 100 optimal 100 unbounded 100 mpec GAMS call parameter 192 MPEC model type 16 80 multipass GAMS call parameter 192 multiple solves 87 na extended range value 32 65 INDEX 309 ncpCM function 58 ncpF function 58 ncp VUpow function 58 ncpVUsin function 58 ne relational operator 109 negBinomial distribution 282 284 nlp GAMS call parameter 192 GAMS option 248 NLP model type 15 80 nodlim GAMS call parameter 192 nonbasic 171 nonlinear equations 97 programming 69 80 nonlinear nonzero 171 nonoptimal 171 nonsmooth 171 nonzero element 171 nopt solution marker 104 normal completion a solver status 102 normal distribution 281 283 normal function 58 not relational operator 121 number of rows and columns in display 135 objective row or function 171 objective value 172 objective variable 172 on offDelim dollar control option 224 on offDigit dollar control option 225 on offDollar dollar control option 225 on offDotL dollar control option 225 on offEcho dollar control option 225 on offEmbedded dollar control option 226 on offEmpty dollar control option 226 on offEnd dollar control option 227 on offEolCom dollar control option
16. The call to this file in the parent file could look like batinclude inclproc bch fili inc fil2 inc fil3 inc fil4 inc The ifE dollar control option does the same as if but allows constant expression evaluation There are two different forms of that statement D 3 Detailed Description of Dollar Control Options 217 ife expri expr2 true if expri expr2 1 abs expr2 lt 1e 12 ife expr true if expri lt gt 0 Consider the following example scalar a ife log2 16 2 16 a 0 display a ife log2 16 72 16 a 1 display a ife NOT round log2 16 2 16 a 2 display a ife round log2 16 2 16 a 3 display a ife round log2 16 72 17 a 4 display a This will create the following ouput SS 2 PARAMETER a 1 000 Jasa 3 PARAMETER a 2 000 TERS 5 PARAMETER a 4 000 The ifI statement is working like the if statement The only difference is that if makes comparisons involving text in a case sensitive fashion while ifI is case insensitive ifThen ifThen is a form of an if that controls whether a number of statements are active The syntax for the condition is generally the same as for the if statement The ifthen and elseif have a few variants and attributes that should be mentioned ifThen is used to do case sensitive comparisons It must be matched with an endIf ifThenE is used to do numerical comparisons It must be matched with an endIf ifThenI is used to do case insensitive comparisons It mu
17. This option initializes the modelname optfile parameter to the value set Modelname is the name of the model specified in the model statement For example the file myfile contains the slice of GAMS code model m all solve m using nlp maximizing dollars Consider the following call gams myfile optfile 1 The option file that is being used after this assignment is solvername opt where solvername is the name of the solver that is specified For CONOPT the option file is called conopt opt for MINOS it is minos opt The names that you can use are listed in the Solver Manual ts Setting modelname optfile in the GAMS input file overrides the value of the optfile parameter passed through the command line To allow different option file names for the same solver the optfile parameter can take other values as well Formally the rule is optfile n will use solvename opt if n 1 and solvername opX solvername oXX or solvername XXX where X s are the characters representing the value of n for n gt 1 and will use no option file at all for n 0 For example the following optfile values profile the option file names for the CONOPT solver O no option file used 1 conopt opt 2 conopt op2 26 conopt o26 345 conopt 345 1234 conopt 1234 194 The GAMS Call output o tewt output file name If no name is given the input file name is combined with the current directory and the standard output file extension LST is applied If the outpu
18. e 2 if a model associated with the HANDLE is not known to the system e 3 the completion signal could not be removed e 4 the resubmit procedure could not be found e 5 the resubmit process could not be started In case of a nonzero return an execution error is triggered allocated memory which is no more in use but not freed yet interrogates the current heap limit maximum allowable mem ory use in Mb and allows it to be reset returns the current heap size in Mb returns the Process ID PID of the last job started sends a kill signal to the running job with Process ID PID the return value is one if this was succesful otherwise it is zero 6 3 Expressions 63 jobStatus PID none checks for the status of the job with the Process ID PID pos sible return values are e 0 error input is not a valid PID or access is denied e 1 process is still running e 2 process is finished with return code which could be accessed by errorlevel e 3 process not running anymore or was never running no return code available jobTerminate PID none sends an interrupt signal to the running job with Process ID PID the return value is one if this was succesful otherwise it is zero licenseLevel any returns an indicator of type of license 0 demo license limited to small models 1 full unlimited developer license 2 run time license no new variables or equations can be introduced besides those inherited in a work file 3 applic
19. eq2 3xy1 4 y2 g 6 t The user may have to perform a combination of equation and variable scaling until a well scaled model is obtained Consider the following example positive variables x1 x2 equation eqi eq2 eqi 100 x1 5 x2 g 20 eq2 50 x1 10 x2 1l 5 x1 up 0 2 x2 up 1 5 166 Special Language Features Setting the following scale values x1 scale 0 1 eqi scale Buy eq2 scale 53 will result in the solver seeing the following well scaled model positive variables xprime1 x2 equation eqprimel eqprime2 eqprimel 2 xprimei x2 g 4 eqprime2 xprimel 2 xprime2 1 1 xprimel up 2 x2 up 1 5 17 3 4 Scaling of Derivatives For nonlinear models the derivatives also need to be well scaled The derivatives in the scaled model seen by the algorithm i e d Ga d Va are related to the derivatives in the user s model d G d V through the formula d Ga d Va d Gu d Va V Gs The user can affect the scaling of derivatives by scaling both the equation and variable involved Appendix A Glossary acronym A GAMS data type used to give logical classifications to data points alias An alternative name for a set algorithm This term may be used in two ways It is either a prescription for how to solve a problem or a particular solver system assignment The statement used to change values associated with an identifier basic A classification of a row or c
20. recognize macros for expansion hide objects from user protect objects from user modification remove the objects and all associated data DCO Dollar Control Option Table D 1 Dollar control options 206 Dollar Control Options D 3 Detailed Description of Dollar Control Options This section describes each of the dollar control options in detail The dollar control options are listed in alpha betical order for easy reference In each of the following dollar control options the default value if available is bracketed abort This option will issue a compilation error and abort the compilation Consider the following example if not system filesys UNIX abort We only do UNIX This attempts to stop compilation if the operating system is not Unix Running the above example on a non Unix platform results in the compilation being aborted and the following listing file 2 abort We only do UNIX HA 343 Error Messages 343 Abort triggered by above statement batinclude The batinclude facility performs the same task as the include facility in that it inserts the contents of the specified text file at the location of the call In addition however it also passes on arguments which can be used inside the include file batinclude file argl arg2 The batinclude option can appear in any place the include option can appear The name of the batch include file may be quoted or unquoted while arg1 arg2 are argument
21. 139 local item formatting 148 numeric items 147 output items 145 page format 142 page sections 143 paging 144 paging control 152 positioning the cursor on a page 144 set value items 147 syntax 139 system suffices 145 text items 146 put current cursor control cc 150 cr 151 hder 151 tlcr 151 put cursor control hdec 150 tlec 150 put local item formatting 148 put paging control lp 152 ws 152 putdir GAMS call parameter 196 pwpFunc function 280 qep GAMS call parameter 196 GAMS option 248 QCP model type 15 80 quoted labels 31 INDEX 311 names of sets 36 text 31 quotes 31 36 RAMSEY example from GAMSLIB 67 76 randBinomial function 58 randLinear function 58 randTriangle function 58 range of numbers 32 rayleigh distribution 281 reall to real 5 GAMS option 248 ref reference type 94 reference GAMS call parameter 196 rel eq function 60 rel_ge function 60 rel_gt function 60 rel_le function 60 rel_lt function 60 rel_ne function 60 relational operator 172 remark dollar control option 236 report summary 104 reporting format 106 reserved words 30 reslim GAMS call parameter 196 GAMS option 248 resource interrupt 102 restart GAMS call parameter 196 right hand side 172 rminlp GAMS call parameter 197 GAMS option 248 RMINLP model type 16 80 rmip GAMS call parameter 197 GAMS option 248 RMIP model type 15 80 rmiqcp GAMS
22. 16 80 mip GAMS call parameter 192 GAMS option 248 MIP model type 15 80 miqcp GAMS call parameter 192 GAMS option 248 MIQCP model type 15 80 mod function 58 model library 175 statistics 98 status 100 styles 29 syntax of statement 79 308 INDEX types 80 model status error no solution 100 infeasible 100 integer solution 100 model attributes bRatio 81 cheat 81 cutoff 81 dictFile 81 domLim 81 domUsd 84 etAlg 84 etSolve 84 etSolver 84 handle 84 holdFixed 81 integerl 81 integer2 81 integer3 81 integer4 81 integerd 81 iterLim 81 iterUsd 84 limCol 81 limRow 81 line 84 linkUsed 84 modelStat 84 nodLim 81 nodUsd 84 number 84 numDepnd 84 numDVar 84 numEqu 84 numInfes 84 numNLIns 84 numNLNZ 84 numNOpt 84 numNZ 84 numRedef 84 numVar 84 numVarProj 84 objEst 84 objVal 84 optCA 81 optCR 81 optFile 81 priorOpt 81 procUsed 84 reall 81 real2 81 real3 81 real4 81 real5 81 reform 81 resGen 84 resLim 81 resUsd 84 rObj 84 savePoint 81 scaleOpt 81 solPrint 81 solveLink 81 solveOpt 81 solveStat 84 sumInfes 84 sysOut 81 threads 81 tolInfeas 81 tollnfRep 81 tolProj 81 tryInt 81 tryLinear 81 workF actor 81 workSpace 81 model classification CNS 80 DNLP 80 EMP 80 LP 80 MCP 80 MINLP 80 MIP 80 MIQCP 80 MPEC 80 NLP 80 QCP 80 RMINLP 80 RMIP 80 RMIQCP 80
23. 3 The key word using 4 An available solution procedure The complete list is lp for linear programming qcp for quadratic constraint programming nlp for nonlinear programming dnlp for nonlinear programming with discontinuous derivatives mip for mixed integer programming rmip for relaxed mixed integer programming miqcp for mixed integer quadratic constraint programming 16 A GAMS Tutorial by Richard E Rosenthal rmigcp for relaxed mixed integer quadratic constraint programming minlp for mixed integer nonlinear programming rminlp for relaxed mixed integer nonlinear programming mcp for mixed complementarity problems mpec for mathematical programs with equilibrium constraints rmpec for relaxed mathematical program with equilibrium constraints cns for constrained nonlinear systems emp for extended mathematical programming 5 The keyword minimizing or maximizing 6 The name of the variable to be optimized 2 9 Display Statements The solve statement will cause several things to happen when executed The specific instance of interest of the model will be generated the appropriate data structures for inputting this problem to the solver will be created the solver will be invoked and the output from the solver will be printed to a file To get the optimal values of the primal and or dual variables we can look at the solver output or if we wish we can request a display of these results from GAMS Our example contai
24. 47 condensing 49 continued 48 example 48 long row labels 50 more than two dimensions 49 statement 47 48 syntax 47 tan function 58 tanh function 58 terminate dollar control option 241 terminated by solver 102 text 172 tformat GAMS call parameter 201 The GAMS Grid Computing Facility 269 threads GAMS call parameter 201 GAMS option 250 timeClose function 61 timeComp function 61 timeElapsed function 61 timeExec function 61 timer GAMS call parameter 201 timeStart function 61 title dollar control option 241 trace GAMS call parameter 201 traceopt GAMS call parameter 201 triangular distribution 281 283 trunc function 58 type 173 of discrete variables 161 unbounded 100 104 undf extended range value 65 uniform distribution 281 283 uniform function 58 uniformInt distribution 282 uniformInt function 58 union of sets 123 unique element 173 UNIX Installation Notes 292 unknown error 102 unload dollar control option 241 use205 dollar control option 242 use225 dollar control option 242 use999 dollar control option 242 userl to user GAMS call parameter 201 314 INDEX using 86 variable binary 68 free 68 integer 68 negative 68 positive 68 statement 67 68 styles for declaration 68 suffix 69 syntax of declaration 67 types 68 variable attributes activity level 1 69 branching priority value prior 69 fixed val
25. 5 As you can see from the list of input components above the creation of GAMS entities involves two steps a declaration and an assignment or definition Declaration means declaring the existence of something and giving it a name Assignment or definition means giving something a specific value or form In the case of equations you must make the declaration and definition in separate GAMS statements For all other GAMS entities however you have the option of making declarations and assignments in the same statement or separately 6 The names given to the entities of the model must start with a letter and can be followed by up to thirty more letters or digits 2 3 Sets Sets are the basic building blocks of a GAMS model corresponding exactly to the indices in the algebraic representations of models The Transportation example above contains just one Set statement Sets i canning plants seattle san diego j markets new york chicago topeka The effect of this statement is probably self evident We declared two sets and gave them the names i and j We also assigned members to the sets as follows i Seattle San Diego j New York Chicago Topeka You should note the typographical differences between the GAMS format and the usual mathematical format for listing the elements of a set GAMS uses slashes rather than curly braces to delineate the set simply 2 4 Data 9 because not all computer keyboard
26. Classification of functions with endogenous arguments soosoo e a eee ee eee 76 Subfield definitions for equations 0 ee 77 Model Attributes mainly used before solve a oa aaa e 84 Model Attributes mainly used after solve 2 0 ee 85 List of GAMS data tyes 55 foe eee pea eed ee FR eee waa aw ER ee ees 94 Truth table of logical operators 2 c o o a a ee RA we os 110 Operator precedente osas a ae ee PEA a A E 111 Examples of logical conditions 0006 6 ee ee 112 Default values for lo and up subtypes e 134 Default layout of display GU DUE soea soea manaa u odad ak ekak ea Die a 134 GAMS command line pardmeters 0 4 20s ee eee ke ee DE ee ee AS 179 Dollar control Options 1 2 4 0 seseo adii droa wepi cadu ea rhaa meaa a abaa 205 GAMS IOUS a s uca da O e e AA AA 246 Fitpeee uDENODS lt 2 4 as eae A rn a a ew ee ere RR 279 Piecewise polynomial functions lt o e cocos asia a 280 Random number generators sen ee he 282 Distribution Tene ss soa a ae a pe KR AeA ERR AA A A 282 Normal distribution MACTONS cosida a Re a ke Re a Ee ee ea 283 LINDO sampling fanetions ss coi 64 06 nae PA ee Ee ESE EA SEY OE Re 285 Trigonometrie Tiichioms o ae eg es ek Re ee a eS ale os ER a we er E A 286 GAMS Parameter File reading Scsi oe ee we OR a A ce ee ds 287 12 LIST OF TABLES J 9 CPP Library functions Introduction 1 1 Motivation Substantial progress was made in the 1950s and 1960s with the
27. Default value is 0 holdFixed This attribute can reduce the problem size by treating fixed variables as x constants Allowable values are e 0 fixed variables are not treated as constants default e 1 fixed variables are treated as constants integer1 Integer communication cell that can contain any integer number x x integer2 Integer communication cell that can contain any integer number x x integer3 Integer communication cell that can contain any integer number x x integer4 Integer communication cell that can contain any integer number x x integer5 Integer communication cell that can contain any integer number x x iterLim Iteration limit The solvers will interrupt the solution process when the x x iteration count reaches that limit The default value is 2 billion limCol Maximum number of cases written to the LST file for each named variable xX xX in a model The default value is 3 limRow Maximum number of cases written to the LST file for each named equation x x in a model The default value is 3 nodLim Node limit This attribute specifies the maximum number of nodes to x process in the branch and bound tree for a MIP problem The default value is 0 and is interpreted as not set 82 Model and Solve Statements optCA Absolute optimality criterion This attribute specifies an absolute termi nation tolerance for use in solving all mixed integer models The default
28. For a as expected the values 1987 1988 up to 1991 are obtained corresponding to the labels y 1987 y 1988 and so on b is initialized to 1 For b the assignment is done over all members of t and for each the value of a from the previous period is assigned to the current member of b If no previous period as with y 1987 zero is used and b y 1987 becomes zero replacing the previous value of 1 13 5 2 Linear Lag and Lead Operators Assignment Consider the following example where two parameters a and c are used to illustrate the assignment of linear lag and lead operators set t time sequence y 1987 y 1991 parameter a t c t a t 1986 ord t c t 1 c t 2 a t 0 display a c The results are shown below a5 6 PARAMETER A Y 1987 1987 Y 1988 1988 Y 1989 1989 Y 1990 1990 Y 1991 1991 6 PARAMETER C Y 1987 1 Y 1988 1 Y 1989 1987 Y 1990 1988 Y 1991 1989 The assignment to a is explained in Section 13 5 1 The assignment to c is different It is best to spell it out in words For each member of t in sequence find the member of c associated with t 2 If it exists replace its value with that of a t If not as with y 1990 and y 1991 make no assignment The first member of t is y 1987 13 6 Lags and Leads in Equations 129 and therefore the first assignment is made to c y 1989 which takes the value of a y 1987 viz 1987 No assignments at all are made to c y 1987 o
29. LOCAL SCOPED 1 GLOBAL what GLOBAL The resulting listing file looks as follows 1 set i 1 2 2 scalar a 1 4 set j 10 15 5 scalar b 2 7 set k 5 10 8 scalar c 3 Note that lines between the double and single options are listed double spaced while the lines after the single option revert back to being listed singly spaced Dollar Control Options D 3 Detailed Description of Dollar Control Options 241 stars This option is used to redefine the marker in the GAMS listing file By default important lines like those denote errors and the solver model status are prefixed with Consider the following example stars garbage The resulting listing file looks as follows 2 garbage HHHH 140 36 299 UNEXPECTED END OF FILE 1 Error Messages 36 or or or operator expected rest of statement ignored 140 Unknown symbol 299 Unexpected end of file stitle This option sets the subtitle in the page header of the listing file to text which follows immediately the keyword stitle The next output line will appear on a new page in the listing file Consider the following example stitle data tables for input output stop Stops program compilation without creating an error But there is a difference to exit If you have only one input file stop and exit will do the same thing If you are in an include file exit acts like an en
30. Moreover the design of GAMS incorporates the following features that specifically address the user s documentation needs gt A GAMS model representation is concise and makes full use of the elegance of the mathematical representation gt All data transformations are specified concisely and algebraically This means that all data can be entered in their most elemental form and that all transformations made in constructing the model and in reporting are available for inspection gt Explanatory text can be made part of the definition of all symbols and is reproduced whenever associated values are displayed gt All information needed to understand the model is in one document Of course some discipline is needed to take full advantage of these design features but the aim is to make models more accessible more understandable more verifiable and hence more credible 1 2 3 Portability The GAMS system is designed so that models can be solved on different types of computers with no change A model developed on a small personal computer can later be solved on a large mainframe One person can develop a model that is later used by others who may be physically distant from the original developer In contrast to previous approaches only one document need be moved the GAMS statement of the model It contains all the data and logical specifications needed to solve the model 1 2 4 User Interface Portability concerns also have implic
31. Normal completion Job trnsport gms Stop 11 30 11 05 42 55 elapsed 0 00 00 097 Comparing this output to the one shown in the example of option logfile one can see that the line numbers are absent from the log file logoption lo 1 log file option This option controls the location of the output log of a GAMS run By default GAMS directs the log of the run to the screen console If 1o 2 the log is redirected to a file With 1o 3 all the output goes to the standard output If no file name is provided for the log through the 1f option the file name will be the input file name with the extension log Values no log output log output to screen console log output to file log output to stdout WNRo To illustrate the use of the 1o option run TRNSPORT with the options 10 2 The resulting log file trnsport 1og looks exactly as shown in the example of option logfile Ip lp tezt default LP solver maxprocdir maxprocdir 26 Maximum number of process directories This option controls the maximum number of workfile directories that can be generated by GAMS By default they are called 225a 225b 225aa 225ab 192 The GAMS Call mcp mcp text default MCP solver minlp minlp text default MINLP solver mip mip tezt default MIP solver miqcp miqcp tezt default MIQCP solver mpec mpec tezt default MPEC solver multipass mp 0 multipass facility This option allows slices of GAMS code to be independently checked
32. RMIP NLP MCP MPEC RMPEC CNS 9 DNLP 10 RMINLP 11 MINLP 12 QCP 13 MIQCP 14 RMIQCP 15 EMP A E srr resGen Time GAMS took to generate the model in CPU seconds resUsd Time the solver used to solve the model in CPU seconds r0bj The objective function value from the relaxed solve of a mixed integer model when the integer solver did not finish solveStat This model attribute indicates the solver termination condition Range from 1 to 13 For details check page 102 sumInfes Sum of infeasibilities Table 9 2 Model Attributes mainly used after solve 9 3 The Solve Statement Once the model has been put together through the model statement one can now attempt to solve it using the solve statement On seeing this statement GAMS calls one of the available solvers for the particular model type us It is important to remember that GAMS itself does not solve your problem but passes the problem definition to one of a number of separate solver programs The next few sub sections discuss the solve statement in detail 9 3 1 The Syntax In general the syntax in GAMS for a model declaration is solve model_name using model_type maximizing minimizing var_name solve model_name maximizing minimizing var_name using model_type 86 Model and Solve Statements Model_name is the name of the model as defined by a model statement Var_name is the name of the objective var
33. a i first one first two 2 93930 first three second one INF second two 14 5 3 Display Statement to Generate Data in List Format a four dimensional structure a ii b i b ii 5 63559 0 02873 10 34570 6 31610 1 00370 17 29948 INF 19 83500 This is a special use of the local display controls to generate data in list format using the display statement This is when all the labels are spelled out for each value as in the parameter style of data initialization The format of the option is option ident d value 0 c value and in this case the c value specifies the maximum number of items displayed on a line The actual number will depend on the page width and the number and length of your labels Using the same example as in the previous sections the following extension option x 5 0 1 display x changes the output to look like below 12 PARAMETER X first one b i 5 63559 first two a i 2 93930 first two a ii 0 02873 first two b ii 10 34570 first three b i 6 31610 second one a i INF second one a ii 1 00370 second one b ii 17 29948 second two a ii INF second two b i 19 83500 a four dimensional structure This output nicely illustrates the label order used The first index varies the slowest the last the fastest and each one runs from beginning to end before the next one to the left advances This ordering scheme is also used on equation and column lists and on the solution report al
34. among the solvers that allow their use the precise definition can vary from solver to solver Any model that contains these variables may not be transferable among solvers Please verify how the solver you are interested in handles SOS2 variables by checking the relevant section of the Solver Manual 17 2 4 Semi Continuous Variables Semi continuous variables are those whose values if non zero must be above a given minimum level This can be expressed algebraically as Either x O or L lt x lt U By default this lower bound L is 1 and the upper bound U is 00 The lower and upper bounds are set through lo and up In GAMS a semi continuous variable is declared using the reserved phrase semicont variable The following example illustrates its use semicont variable x x lo 1 5 x up 23 1 The above slice of code declares the variable x to be semi continuous variable that can either be 0 or can behave as a continuous variable between 1 5 and 23 1 ts Not all MIP solvers allow semi continuous variables Please verify that the solver you are interested in can handle semi continuous variables by checking the relevant section of the Solver Manual ts The lower bound has to be less than the upper bound and both bounds have to be greater than 0 GAMS will flag an error if it finds that this is not the case 17 2 5 Semi Integer Variables Semi integer variables are those whose values if non zero must be integral above a given m
35. gt gt strictly greater than The following example of a numerical relationship illustrates its use as a logical condition sqr a gt a This condition evaluates to False if 1 lt a lt 1 For all other values of a this condition evaluates to True Note that the same expression can also be written as sqr a gt a 11 2 3 Logical Operators The logical operators available in GAMS are listed below not not and and or inclusive or xor exclusive or The truth table generated by these logical operators is given in table 11 1 Operands Results a b aand b aor b a tor b not a 0 0 0 0 0 1 0 non zero 0 1 1 1 non zero 0 0 1 1 0 non zero non zero 1 1 0 0 Table 11 1 Truth table of logical operators 11 2 4 Set Membership Set membership can also be used as a logical condition The label results in a logical value of True if it is a member of the set in question and False if it is not This is used with subsets and dynamic sets Consider the following example for illustration set i 1 10 subi i 1 3 The set subi i results in a logical value of True for all elements that belong to subi and False for all elements of i that do not belong to subi The use of set membership as a logical condition is an extremely powerful feature of GAMS and while its use will be illustrated later on in this chapter its full power becomes clear when considered with the description of dynamic sets later 11 2 Logical Condit
36. inputdir GAMS call parameter 188 inputdirl to inputdir40 GAMS call parameter 188 integer infeasible 100 solution 100 variable 69 80 integerl to integer5 GAMS call parameter 189 GAMS option 247 intermediate infeasible 100 noninteger 100 intersection set operation 123 invGaussian distribution 281 iteration default limit 100 interrupt 102 iterlim GAMS call parameter 189 GAMS option 247 option 100 102 jdate function 61 jnow function 61 jobHandle function 61 jobKill function 61 jobStatus function 61 jobTerminate function 61 jobtrace GAMS call parameter 189 jstart function 61 jtime function 61 keep GAMS call parameter 189 kill dollar control option 219 KORPET example from GAMSLIB 48 label 29 31 41 dollar control option 219 order 137 order on displays 134 quoted 31 36 row and column 49 unquoted 31 using in equations 75 laplace distribution 281 283 le relational operator 30 109 legal characters 30 level 70 libincdir GAMS call parameter 189 INDEX 307 libinclude dollar control option 219 license GAMS call parameter 189 licenseLevel function 61 licenseStatus function 61 limcol GAMS call parameter 189 GAMS option 247 limrow GAMS call parameter 189 GAMS option 247 lines dollar control option 220 list 171 of labels using Asterisks 37 list format 171 load dollar control option 220 loadDC dollar con
37. node limit in branch and bound tree This option specifies the maximum number of nodes to process in the branch and bound tree for a MIP problem The default value 0 is interpreted as not set C 3 Detailed Description of Command Line Parameters 193 onl115 on115 0 generate certain errors Generate errors for unknown unique elements in an equation Values O no error messages 1 issue error messages optca optca 0 0 absolute optimalitty criterion This option is only used with problems containing discrete variables i e the GAMS model type mip General mixed integer problems are often extremely difficult to solve and proving that a solution found is the best possible can use enormous amounts of resources This option sets an absolute termination tolerance which means that the solver will stop and report on the first solution found whose objective value is within optca of the best possible solution optcr optcr 0 1 relative optimality criterion This option sets a relative termination tolerance for problems containing discrete variables which means that the solver will stop and report on the first solution found whose objective value is within 100 optcr of the best possible solution optdir optdir text option file directory This keyword gives the name of the directory to be used by GAMS for solver option files If not specified it will be set to the current working directory optfile optfile 0 option file indicator
38. notation where 1 3 Organization of the Book 3 denotes that the enclosed construct is optional denotes that the enclosed construct may be repeated zero or more times and denotes that there is an or operator across the arguments on both sides of the symbol 1 3 Organization of the Book Some introductions to software systems are like reference manuals they describe each command in detail Others take you step by step through a small number of examples This book uses elements of both approaches The text is divided into three parts The first part Chapters 1 and 2 is introductory Chapter 2 is a self contained tutorial that guides you through a single example a small transportation model in some detail you can quickly investigate the flavor of GAMS by reading it The second part Chapters 3 to 17 comprises the meat of the book The components of the GAMS language are introduced in an ordered way interspersed with detailed examples that are often drawn from the model library All models from the model library are enclosed in square parenthesis for example TRNSPORT Some specialized material has deliberately been omitted in this process because the primary aim is to make GAMS accessible to the widest possible audience especially those without extensive experience with computers or mathematical programming systems Some familiarity with quantitative methods and mathematical representations is assumed The third part consi
39. oorccrcsn seres a 267 I The GAMS Grid Computing Facility 269 Ll APOCO core A A A eG oe A A A A ee 269 10 TABLE OF CONTENTS 2 Basile Concepts lt occszicacuras o e a A a e aa eM 269 LA APUESTA ds a Ea ee Ow 270 14 Advanced use of Grid Features es 272 14 1 Very Long Job Durations o y ci oee sosa adoba a oras rss a 272 LS Summaty ol Grid Features o se s sa crause i a e ea a a a ee e ee a A 273 1 5 1 G d Handle Functions c i se 2 4344 22 bu su a ha aaie a eS 274 1 52 Grid Model Attributes cs Go a hb ee Re a a ls 274 1 5 3 Grid Solution Retrieval s saar 64 48a De ee a a ee eae 275 LSA Grid DISEASE 275 16 Architecture and Customization lt lt lt aau ss a a aa 275 LOT Grid Submision Teng re a Ta o A a Oe a RA A e a 276 L7 Glossary and Definitions 2 6 cc a aa w a ece eA a a a E a A a a a a 277 J Extrinsic Functions 279 Ad PUNO 2 45 a eee da a a ee ar Baw ee ee we DA ead a a 279 dia Pitperk LIDAD noce o o6 4 oe eas Deane bd Add bw wee dee Ey a A E a 279 J Piecewise Polynomial Library coo s sacred a caga e s BL ee eee ee aR 280 J St chastie LIBRETA ou s er EO we gs a ee ds Paw A ER 281 d LINDO Sampling Library a ecb 64 ee ae ede Ree De Be RE eee ea a aew eae 283 J 6 Build Your Own Trigonometric Library Example o 286 J 7 Build Your Own Reading the GAMS Parameter File in your Library 287 Je CPP UNAY AI AE 288 USA Automatic differentia
40. sqexp 58 griddir 178 sqlog10 58 gridscript 178 sqr 58 heaplimit 178 sqrec 58 holdfixed 178 sqrt 58 ide 178 tan 58 input 178 tanh 58 inputdir 178 timeClose 61 inputdirl 178 timeComp 61 iterlim 178 timeElapsed 61 jobtrace 178 timeExec 61 keep 178 timeStart 61 libincdir 178 trunc 58 license 178 uniform 58 logfile 178 uniformInt 58 logline 178 vcPower 58 logoption 178 Ip 178 g205 maxprocdir 178 GAMS call parameter 186 mcp 178 gamma distribution 281 283 minlp 178 gamma function 58 mip 178 gammaReg function 58 migcp 178 GAMS call parameter mpec 178 action 178 multipass 178 appendexpand 178 nlp 178 appendlog 178 nodlim 178 appendout 178 on115 178 bratio 178 case 178 cerr 178 charset 178 cns 178 curdir 178 dformat 178 dnlp 178 domlim 178 dumpopt 178 dumpparms 178 emp 178 eolonly 178 errmsg 178 errnam 178 error 178 errorlog 178 etlim 178 optca 100 178 opter 100 178 optdir 178 optfile 178 output 178 pagecontr 178 pagesize 178 pagewidth 178 parmfile 178 plincense 178 procdir 178 profile 178 profilefile 178 profiletol 178 putdir 178 acp 178 reference 178 reslim 178 INDEX 305 restart 178 rminlp 178 rmip 178 rmiqcp 178 rmpec 178 save 178 savepoint 178 serdir 178 scrext 178 scriptexit 178 scriptfrst 178 scriptnext 178 scrnam 178 seed 178 solprint 178 solvelink 178 solvercntr 178 so
41. sqr mysin x sqr mycos x e 1 model m e x lo 0 x 1 3 mypi solve m min x using nlp The following lines from the listing file describe the library loaded 6 3 Expressions 65 FUNCLIBIN trilib tridclib Function Library trilib Mod Function Description Type NLP Cosine x MODE Cosine mode 0 default gt rad mode 1 gt grad NLP Sine x MODE Sine mode 0 default gt rad mode 1 gt grad any Pi Pi A description of the libraries included in the GAMS sytem can be found in Appendix J Stateful Libraries While GAMS intrinsic function are stateless a user can implement stateful extrinsic functions meaning that the extrinsic libraries can have some memory This can be done in two ways 1 Library initialization see Piecewise Polynomial Library appendix J 3 At initialization time the function library reads some data to provide the necessary functions 2 Previous function calls see Trigonometric Library function setMode appendix J 6 Function calls that alter the execution of successive function calls The latter type of memory is problematic since different parts of the GAMS system potentially use different instances of the function library For example if one sets SetMode 1 before the solve statement and one uses GAMS option solvelink lt gt 5 see solvelink the solver runs in a separate process with a new instance of the function library and therefore uses the default mode which is 0 Eve
42. subsections Once again the example from Section 12 2 2 is used to illustrate each operation 12 4 1 Set Union The symbol performs the set union operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subitem3 is set equal to all the elements of subitem1 and all the elements of subitem2 The operation above is equivalent to the following longer way of representation subitem3 item no subitem3 subitem2 yes subitem3 subitem1 yes 12 4 2 Set Intersection The symbol performs the set intersection operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subitem3 is set equal to only those present in both subitem1 and subitem2 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem1i item and subitem2 item 12 4 3 Set Complement The operator not performs the set complement operation Consider the following example subitem3 item not subitemi item The membership of subitem3 is set equal to all those in item but not in subitem1 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem3 subitem1 no 124 Dynamic Sets 12 4 4 Set Difference The operator performs the set difference operation Consider the following example subitem3 item subitemi item subitem2 item The membership of subite
43. ts The user can in addition explicitly provide whatever convexity row that the problem may need through an equation that requires the members of the SOS set to be less than a certain value Any such convexity row would implicitly define bounds on each of the variables Consider the following example sosi Variable s1 i Equation defsoss1 defsoss1 sum i si i 1 3 5 The equation defsoss1 implicitly defines the non zero values that one of the elements of the SOS1 variable s1 can take A special case of SOS1 variables is when exactly one of the elements of the set have to be non zero In this case the defsoss1 equation will be defsoss1 sum i s1 i e 3 5 A common use of the use of this set is for the case where the non zero value is 1 In such cases the SOS1 variable behaves like a binary variable It is only treated differently by the solver at the level of the branch and bound algorithm For example consider the following example to model the case where at most one out of n options can be selected This is expressed as sosi variable x i equation defx defx sum i x i 1 1 The variable x can be made binary without any change in meaning and the solution provided by the solver will be indistinguishable from the SOS1 case The use of special ordered sets may not always improve the performance of the branch and bound algorithm If there is no natural order the use of binary variables may be a better choice A go
44. value is 0 optCR Relative optimality criterion This attribute specifies a relative termina tion tolerance for use in solving all mixed integer models The default value is 0 1 optFile Look for a solver options file if optFile gt 0 The value of optfile determines which option file is used e If Optfile 1 the option file solvername opt will be used If Optfile 2 the option file solvername op2 will be used If Optfile 3 the option file solvername op3 will be used If Optfile 15 the option file solvername o15 will be used If Optfile 222 the option file solvername 222 will be used If Optfile 1234 the option file solvername 1234 will be used If Optfile 0 no option file will be used default priorUOpt Priority option Variables in mixed integer programs can have a priority attribute One can use this parameter to specify an order for picking variables to branch on during a branch and bound search for MIP model solutions The default value is 0 in which case priorities will not be used reali Real communication cell that can contain any real number real2 Real communication cell that can contain any real number real3 Real communication cell that can contain any real number real4 Real communication cell that can contain any real number real5 Real communication cell that can contain any real number reform Reformulation level resLim Maximum time avai
45. 11 2 2 Numerical Relationship Operators 11 23 Logical Operators o ao ea be ee 11 2 4 Set Membership 2 sa ee A Soe moane ee a 11 2 5 Logical Conditions Involving Acronyms 11 2 6 Numerical Values of Logical Conditions 11 2 7 Mixed Logical Conditions Operator Precedence 11 2 8 Mixed Logical Conditions Examples 11 3 The Dollar Condition 2 246 444 04446080 be 44d 2 ee TIM A Bele eee ed Aaa 11 3 2 Nested Dollar Conditions 11 4 Conditional Assignments e e 1141 Dollar om the Left lt 2 00 ee ee 114 2 Dollar onthe Right acn rpad ao eieaa ye ew eS 11 4 3 Filtering Controlling Indices in Indexed Operations 11 4 4 Filtering Sets in Assignments 11 5 Conditional Indexed Operations 11 5 1 Filtering Controlling Indices in Indexed Operations 11 6 Conditional Equations lt s se c sesa acea ee ee e 11 6 1 Dollar Operators within the Algebra 11 6 2 Dollar Control over the Domain of Definition TABLE OF CONTENTS 7 11 6 3 Filtering the Domain of Definition lt lt 118 12 Dynamic Sets 119 2 0 ir a esa ssas eaud A ee m a a a RE A Rae A ae oe a 119 12 2 Assigning Membership to Dynamic Sets a a 119 lea DNS pease ese ks de A cd a BE EO Oe SO eG a SR ee pa 119 1222 Illustrative Example co 6 0242 e RRR EGR De Ee ee ea 119 1
46. 111 myfile2 222 myfile8 wrk myfile8 888 t On Unix platforms the character is a special character and may require a backslash character 1 in front of it in order to be interpreted correctly The name myfile should be written on this platform as myfile savepoint sp 0 save solver point in GDX file This option tells GAMS to save a point format GDX file that contains the information on the current solution point Values O no point GDX file is to be saved 1 a point gdx file from the last solve is to be saved 2 a point gdx file from every solve is to be saved scrdir sd text scratch directory This option sets the scratch directory where the intermediate files generated by GAMS and the various solvers are stored The files in the scratch directory are used by GAMS and the various solvers to communicate with each other The scratch directory and all its contents are usually deleted at the end of a GAMS run If not specified the scratch directory will be set to the default one generated by GAMS scrext se dat Scratch extension for temporary files This keyword gives the name of the extension for the GAMS temporary files generated during execution scriptexit scriptexit text program or script executed at the end of a GAMS run By default GAMS does not call an exit script anymore If this is required the GAMS parameter ScriptExit has to be set explicitly to the script that should be called after GAMS terminates An empty tem
47. 5 2 Grid Model Attributes mymodel solvelink specifies the solver linking conventions 0 automatic save restart wait for completion the default start the solution via a shell and wait start the solution via spawn and wait start the solution and continue start the solution and wait same submission process as 3 or WN start the solution via shared library and wait mymodel handle specifies the current instance handle This is used to identify a specific model instance and to provide additional information needed for the process signal management mymodel number specifies the current instance number Any time a solve is attempted for mymodel the instance number is incremented by one and the handle is update accordingly The instance number can be reset by the user which then resyncs the handle 1 6 Architecture and Customization 275 1 5 3 Grid Solution Retrieval Execute loadhandle mymodel This will update the GAMS data base with the status and solution for the current instance of mymodel The underlying mechanism is a gdx file and operates otherwise like the execute_loadpoint procedure Additional arguments can be used to retrieve information from the gdx solution file 1 5 4 Grid Directory The instantiated generated models and their corresponding solution are kept in unique directories reachable from your submitting system Each GAMS job can have only one Grid Directory By default the grid directory is assumed to
48. DICOPT CONOPT SBB CONOPT JAMS demo demo demo demo demo demo demo or or or or or or or student student student student student student student solved by license license license license license license license We are now prepared to set read and execute permissions on the GAMS system files we recommend option 3 You can set read and execute permission for 1 user only 2 user and group 3 user group and world If you are not sure which option to choose Enter your choice now The files gams gamslib etc are now executable K 7 Example 297 You can run these commands in a number of ways 1 Call them using an absolute path i e Applications GAMS gams24 3_osx_x64_64_sfx gams 2 Create your own aliases for them 3 Add the GAMS system directory Applications GAMS gams24 3_osx_x64_64_sfx to your path Method 3 is recommended doe mac Applications GAMS gams24 3_osx_x64_64_sfx cd doe mac Users doe Applications GAMS gams24 3_osx_x64_64_sfx gamslib trnsport Copy ASCII trnsport gms doe mac Users doe Applications GAMS gams24 3_osx_x64_64_sfx gams trnsport gms Job trnsport Start 06 26 14 11 24 56 24 3 1 r46409 DEX DEG Mac x86_64 Darwin GAMS 24 3 1 Copyright C 1987 2014 GAMS Development All rights reserved Licensee Starting compilation trnsport gms 69 3 Mb Starting execution elapsed 0 00 00 024 trnsport gms 45 4 Mb Ge
49. EA 46 Soc An Illustrative Examples 2 20055 506 eb SYR a RR RED ERR EM 46 5 3 3 Parameter Data for Higher Dimensions 00020 47 pa TEDE oee poca Ae Gk a e ee a aa RS PR eb ee ee i e eee ee a a ad 47 a41 The Synta II E a deo e Goie a a a a a 47 342 An lustratvs Example 4 giia a a E y a a eS 48 aio Continued Taes c so si bed wa rra Re aa ae a a eG 48 5 4 4 Tables with more than Two Dimensions e 0000 eee eee 49 odo Condensing Tables sc o sc gaie gaer tatki aoha a a AA 49 9 10 Handling Long Row Labels a0 coke bak ae a a aaa 50 Oo BAON lt i iv eee owe eth bate Pet been hd we eee en bd ee Eee a 50 Rael e nk kb ele Bk Ble GE ene Ea ay Ae BP eNO Ga 50 292 hetave Example srai 4 22 84 4 oh eee eee GaSe Ed be eA ee a a a 50 EO a ke be ee a A 51 Data Manipulations with Parameters 53 Dl bra o ssp sk eke ek ee DAS Ae Boe SLE OS aS WE be RR ER e Bee hs 53 D2 The Assignment Statement sepe fe e Re eee eh ee EGG a ee eS 53 021 o ee koe peder ea OR ee Pe ee oe ee a 53 TABLE OF CONTENTS 5 622 Indexed Assignments gt o ocras u car a Pw eee eee 53 6 2 3 Using Labels Explicitly in Assignments o a 54 6 24 Assignments Over Subsets s sss sssr rrara as ra Ew eee ee 54 6 2 5 Issues with Controlling Indices o oa iio 04 ee a 54 6 2 6 Extended Range Identifiers in Assignments 0000000 eae 55 G27 Acronyms in Assigmmente lt e ceas ee SR Ree ee ER RE See 55 Ga ESPESA se A A
50. ERG EE OHS POR Re ea 127 13 5 1 Linear Lag and Lead Operators Reference 02 000 ee eee 128 13 5 2 Linear Lag and Lead Operators Assignment 0 000002 eee 128 13 5 3 Cirenlar Lag and Lead Operators oce rea ee we ee ee ee o 129 13 6 Lags and Leads in Rquations o c eceso ee 64 de A ee A A we es 129 13 6 1 Linear Lag and Lead Operators Domain Control 220 130 13 6 2 Linear Lag and Lead Operators Reference o e 130 134 3 Circular Lag and Lead Operators cq poa ac wi miari A A 131 e osie eK a OE eat RO RE ee A EN e 131 14 The Display Statement 133 BAI ii A A A 133 14 2 The A So a ee we A A A EA A e a a 133 AS An Beeps rear ra Re ee eR da OE ee AS 133 144 The Label Order in Displays o so 04 5626 eee aR RE ee Ee ee ae a 134 Hal Examples oo osas Bk ewe Se ee eee oe be Lek neha de Fad EEE ae 135 145 Display Comirols s ie 4 a Ske le a a ae eG ek ee a PR ee oe ean 135 14 6 1 Global Display Controle ce cee ra eee eho eae ee ee aa 136 14 5 2 Local Display Control o seo saada sin ta rra ee a ee ee ead 136 14 5 3 Display Statement to Generate Data in List Format 2 137 15 The Put Writing Facility 139 ial oduct ooer torpa a A a A ee ee ee a eae ee ee Se 139 15 3 The Bye o ioi orii BS Dew ea ee ee a ad ee SEERA BA we REE HS 139 Us An Eres so oe oe AL eR A a A BR a GP OE EO 140 154 Qutput Files ae kde wae fh bbb ee ee a eee ee eM EEE eae Ae DES eee
51. Examples of logical conditions 11 3 The Dollar Condition This section introduces the dollar operator which is one of the most powerful features of GAMS The dollar operator operates with a logical condition The term condition can be read as such that condition is valid where condition is a logical condition t The dollar logical conditions cannot contain variables Variable attributes like 1 and m are permitted however The dollar operator is used to model conditional assignments expressions and equations The following subsection provides an example that will clarify its use The next section will deal individually with the topic of using dollar conditions to model conditional assignments expressions and equations respectively 11 3 1 An Example Consider the following simple condition if b gt 1 5 then a 2 This can be modeled in GAMS using the dollar condition as follows a b gt 1 5 2 If the condition is not satisfied no assignment is made Note that one can read the as such that to clarify the meaning a such that b is greater than 1 5 equals 2 11 3 2 Nested Dollar Conditions Dollar conditions can be also nested The term conditioni condition2 can be read as condition1 and condition2 t For nested dollar conditions all succeeding expressions after the dollar must be enclosed in parentheses 11 4 Conditional Assignments 113 Consider the following example u
52. Fortran and C that come with every GAMS system Using Function Libraries Function libraries are made available to a model using a compiler directive 64 Data Manipulations with Parameters FuncLibIn lt InternalLibName gt lt ExternalLibName gt Note that the Function Library Facility gives you complete control over naming so that potential name conflicts between libraries can be avoided The lt InternalLibName gt is a sort of handle and will be used to refer to the library inside your model source code The lt ExternalLibName gt is the file name for the shared library that implements the extrinsic functions To access libraries included with your GAMS distribution you use the library s name with no path prefix GAMS will look for the library in a standard place within the GAMS installation To access a library that does not reside in this standard place the external name should include a relative or absolute path to the library s location GAMS will search for the shared library you specify using the mechanisms specific to the host operating system When processing the FuncLibIn directive GAMS will validate the library make the included functions available for use and add a table of the included functions to the listing file Before using individual functions you must declare them Function lt InternalFuncName gt lt InternalLibName gt lt FuncName gt Note that the syntax is similar to that used for declaring Sets
53. HEAP SIZE Mb STEP SUMMARY 0 000 0 000 STARTUP 0 000 0 000 COMPILATION 0 000 0 000 EXECUTION 0 000 0 000 CLOSEDOWN 0 000 0 000 TOTAL SECONDS 0 089 0 096 ELAPSED SECONDS 2 884 3 949 MAX HEAP SIZE Mb The first step summary occurs before the model is sent to the solver and the second occurs after the solver completes its task and returns control back to GAMS The first column reports time for the individual section of the run while the second column reports accumulated times including previous sections strictsingleton strictsingleton 1 behavior of assignment to singleton set This option affects the behavior of a membership assignment to a singleton set With strictSingleton 0 GAMS does not complain about an assignment with more than one element on the right hand side but takes the first one With strictSingleton 1 such an assignment creates an error stringchk stringchk 0 string substitution check for xxx symbols This option affects the result of the check for xxx symbols Values O no substitution and no error if symbol is undefined 1 error if symbol undefined 2 remove entire symbol reference if undefined and no error subsys subsys text configuration file name This option is only to be used by advanced users attempting to override internal sub system information The file name is used as given The default sub systems file is GMSCMPNT TXT on Windows or GMSCMPUN TXT on Unix suppress suppress 0 compiler listing opti
54. Target Company Name Starting continued compilation T2 GMS 6 1 Mb Starting execution Status Normal completion The access control commands are activated by the use of the privacy GAMS license option PLICENSE This option specifies the name of the target user license file The save restart file t2 g00 can only be read with the target license file The three lines starting with are a recap of the content of the target license file From now on the source and the target licensees are burned into this file and all its descendants We are ready to send the restart file to the target user or system The target user can now run the model with new data add new GAMS statements and make new save restart files The only restrictions are that some of the symbols are hidden and that this model can only be executed using the target license file For example the target user may want to half the demand and compare the original solution with the new one We will call this program t3 gms and it will be executed on the target system gt type t3 gms parameter rep summary report rep i j base x 1 i j b j b j 0 5 solve transport minimizing z using lp rep i j half x 1 i j display rep gt gams t3 r t2 2When using the GAMS IDE interface the GAMS parameters are entered and mainened in the text window just right to the Run GAMS F9 button G 3 Secure Work Files 259 GAMS Rev 124 Copyri
55. The first job will then look a follows gt gams qsubmit s submit gdir c test grid The solution of all the model instances may take hours From time to time I can then run a quick inquiry job to learn about the stats The following program qcheck gms will list the current status parameter status pp scalar handle acronym BadHandle Waiting Ready loop pp handle handlestatus h pp if handle 0 handle BadHandle elseif handle 2 handle Ready minvar handle h pp execute_loadhandle minvar status pp solvestat minvar solvestat I 5 Summary of Grid Features 273 status pp modelstat minvar modelstat status pp seconds minvar resusd else handle Waiting status pp status handle display status To run the above program we will restart from the previous save file by using the restart or r parameter gt gams qcheck r submit gdir c test grid The output may then look like 2 173 PARAMETER status solvestat modelstat seconds status pl 1 000 1 000 0 328 Ready p2 1 000 1 000 0 171 Ready p3 Waiting p4 Waiting pd 1 000 1 000 0 046 Ready You may want to do some more detailed analysis on one of the solved model instances Then we may have a qanalyze gms program that may look like and be called using the double dash option which sets a GAMS environment variable if not set instance abort instance is missing if not handlestatus h instance abort yes
56. World arctan2 y x NLP four quadrant arctan function yielding arctangent y x which is the angle the vector x y makes with 1 0 in radians Beta x y DNLP beta function B x y A see Math World betaReg x y z NLP regularized beta function see Math World binomial n k NLP returns the generalized binomial coefficient for n k gt 0 ceil x DNLP returns the smallest integer number greater than or equal to x centropy x y Z NLP Centropy x 2 default setting Z 0 cos x NLP returns the cosine of the argument x where x must be in radi ans see MathWorld cosh x NLP returns the hyperbolic cosine of x where x must be in radians see MathWorld cvPower X y NLP returns XY for X gt 0 div dividend divisor NLP returns dividend undefined for divisor 0 div0 dividend divisor NLP returns dividend returns 102 for divisor 0 eDist x1 x2 x3 NLP Euclidean or L 2 Norm yz2i x2 default setting 12 73 0 entropy x NLP Entropy 2 ln x errorf x NLP calculates the integral of the standard normal distribution from x ae negative infinity to x error f 1 Tz f e dt o00 execSeed none reads or writes the seed for the random number generator exp x NLP returns the exponential function e of an expression or term x see Math World fact N any returns the factorial of N where N is an integer floor x DNLP returns the greatest integer number less than or equal to x frac x DNLP returns the fractional part of x co
57. a new model attribute handle which provides a unique identification of the submitted solution request We need to store those handle values in this case in the parameter h to be used later to collect the solutions once completed This is then done with a collection loop 13 A First Example 271 loop pp handlecollect h pp xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i The function handlecollect interrogates the solution process If the solution process has been completed the results will be retrieved and the function returns a value of 1 If the solution is not ready to be retrieved the value zero will be returned The above collection loop has one big flaw If a solution was not ready it will not be retrieved We need to call this loop several times until all solutions have been retrieved or we get tired of it and quit We will use a repeat until construct and the handle parameter h to control the loop to look only for the not yet loaded solutions as shown below Repeat loop pp handlecollect h pp xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 display sleep card h 0 2 sleep some time until card h O or timeelapsed gt 100 xres i pp h pp na Once we have extracted a solution we will set the handle parameter to zero In addition we want to remo
58. aeaa pa ass eee ee aoa e eae a e a a 32 oie DENOS e a e AA 32 A COMES oia a A a ARA eae 32 Oo SUMMA AI EAA Cee wh MY Eb ed ow oe 33 Set Definitions 35 Ll Titoduchon s ea s Se A ae ae A A Sk ae Ee a RE OR De eS ea A des 35 AD Simple Sets 2 4 40 2 eee eae beeen Shee ee eee ee ke ea Ge a 35 Ao THe SM cado ha ee eee ee ee ed we REE be Pe eg 35 ALL O Namn iris i Boots ea ea sae awe eb La ak bee em mane Bas 35 Ade DEL Elements oo c c 62h ee edd ad SRE a e e aa es 36 dad Associated Tet oia criada ia aa e AAA 36 4 2 5 Sequences as Set Elements e 37 426 Declarations for Multiple Sets lt o s a cocoes e ma eaa ess a a a 37 4 3 The Alias Statement Multiple Names for a Set naaa eee eee 38 44 Subsets and Domain Checking osos nica a OO Re Re i 38 45 Kult dimensional SeS o e A A a ee a SS 39 dol QOnetobne Mappi lt o o ee cc ae a We a ee we he ae Be Ge ew 39 4 5 2 Mamny to many Mapping ca e se nai iea e aa 40 45 3 Projection and Aggregation of Sete o oea oaea r ee ee ee a 41 de a nok ee ee De ae ae Oe Bee ee ee Be Ae he EE 42 Oy PUND fn 6 AA 42 Data Entry Parameters Scalars amp Tables 45 eh DUOMO a xs ae he eS Bae Bootie RUE Oe Oe Rae ee NN 45 G2 WOOT ca Re ee ke ee ee Phe ea hae ae be ed eae aa BAR 45 Sl Te a da a a RAR A AA 45 5 2 2 An Illustrative Example sa 2 454 e eea mot eoe a RED Re 46 Gas Parametar o i asm ee Ske ne he e ee Oe ba eel OE Rae ea a Ee 46 Dol Ie Ge ee A ie ee See a Ge Gy ee ae ew He ow By
59. and end of line comments are stripped out of the input file before processing for new_input_line If either of these forms of comments appears it will be treated as blanks Consider the following example parameter a a 10 eolcom inlinecom if exist myfile dat in line comments end of line comments a 4 display a The fourth line is ignored and the fifth line involving an assignment setting a to 4 will be treated as the result of the conditional So the result of the display statement would be the listing of a with a value of 4 if the file myfile dat exists and a value of 10 if the file does not exist is It is suggested that a label not appear as part of the conditional input line The result is that if the label appears on the if line a goto to this label will re scan the entire line thus causing a reevaluation of the conditional expression On the other hand if the label appears on the next line the condition will not be reevaluated on subsequent gotos to the label The following example illustrates how an unknown number of file specifications can be passed on to a batch include file that will include each of them if they exist The batch include file could look as follows Batch Include File inclproc bch Process and INCLUDE an unknown number of input files label nextfile if fla a goto end if exist 1 include 1 name might have blanks shift goto nextfile label end
60. and level values The format for the coefficients is exactly as in the equation listing with the nonlinear ones enclosed in parentheses and the trailing zeroes dropped The column listing section from our example follows A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a Column Listing SOLVE PORTFOLIO USING NLP FROM LINE 48 gt fraction of portfolio invested in asset 1 X hardware LO L UP 0 0 INF 1 FSUM 8 DMEAN 0 DVAR X software LO L UP 0 0 INF 1 FSUM 9 DMEAN 0 DVAR X show biz LO L UP 0 0 INF 1 FSUM 12 DMEAN 0 DVAR REMAINING ENTRY SKIPPED VARIANCE variance of portfolio VARIANCE LO L UP INF 0 INF 1 DVAR ts The order in which the variables appear is the order in which they were declared 10 5 3 The Model Statistics The final information generated while a model is being prepared for solution is the statistics block shown below Its most obvious use is to provide details on the size and nonlinearity of the model 10 5 Output Produced by a Solve Statement 99 Model Statistics SOLVE PORTFOLIO USING NLP FROM LINE 48 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 5 NON ZERO ELEMENTS 12 NON LINEAR N Z 3 DERIVATIVE POOL 10 CONSTANT POOL 10 CODE LENGTH 87 GENERATION TIME 0 020 SECONDS 0 1 Mb WAT 50 094 The BLOCK counts refer to GAMS equations and variables the SINGLE coun
61. and so on More elaborate reporting is required to accurately describe any problems found The solve statement is only checked if the model has been found to be error free up to this point This is not only because the check is comparatively expensive but also because many erroneous and confusing messages can be produced while checking a solve in a program containing other errors ts Solve error messages are reported in two places and in two formats First they are shown immediately below the solve statement with a short text including the name of any offending identifier and the type of model involved This will be sufficient in most cases Second a longer message with some hints appears with the rest of the error messages at the end of the compilation The example below illustrates how the general reporting format for compiler errors associated with a solve statement 1 variables x y Z 2 equations eqi eq2 3 4 eql x 2 y e Z 5 eq2 min x y 1 20 6 7 model silly all 8 solve silly using lp maximizing z kkk 54 51 256 x xx k THE FOLLOWING LP ERRORS WERE DETECTED IN MODEL SILLY xxx 54 IN EQUATION EQ1 ENDOG OPERANDS FOR xo 51 IN EQUATION EQ2 ENDOG ARGUMENT S IN FUNCTION 9 Error Messages 51 Endogenous function argument s not allowed in linear models 54 Endogenous operands for not allowed in linear models 256 Error s in analyzing solve statement More detail appears Below the solve s
62. and two dimensional spline interpolation This library has been repackaged to work with the GAMS Function Library Facility As it can be seen in the GAMS Test Library model fit1ib01 the function data needs to be stored in a GDX file fit gdx containing a three dimensional parameter fitdata The first argument of that parameter contains the function index the second argument is the index of the supporting point and the last one needs to be one of w weight x x value y y value or z z value Function Endogenous Description Classifica tion fitFunc FUNIND x y DNLP Evalute Spline fitParam FUNIND PARAM VALUE none Read or set parameters Table J 1 Fitpack functions Paul Dierckx Curve and Surface Fitting with Splines Oxford University Press 1993 http www netlib org dierckx 280 Extrinsic Functions The function FitParam can be used to change certain parameters used for the evaluation e 1 Smoothing factor S e 2 Degree of spline in direction x Kx Degree of spline in direction y Ky Lower bound of function in direction x LOx Lower bound of function in direction y LOy Upper bound of function in direction x UPx UPy Upper bound of function in direction y UPy e I Dn BR Y This library is made available by the following directive FuncLibIn lt InternalLibName gt fitfclib J 3 Piecewise Polynomial Library This library can be used to evaluate piecewise polynomial functions
63. as there may be with parameters or sets 8 2 2 An Illustrative Example The example is adapted from PRODSCH an inventory and production management problem The relevant set definitions are also shown sets q quarters summer fall winter spring s shifts first second equations cost total cost definition invb q inventory balance sbal q s shift employment balance R 74 Equations The declaration of the first equation follows the keyword equations This declaration begins with the name of the equation in this case cost and is followed by the text namely Total cost definition The equation cost above is a scalar equation which will produce at most one equation in the associated optimization problem By contrast the equation sbal is declared over the sets q 4 members and s 2 members and is thus likely to produce eight individual equations one for each unique combination of labels The circumstances under which less than eight equations might be produced will be discussed in later chapters It is certainly true however that no more than eight equations will be produced 8 3 Equation Definitions The definitions are the mathematical specification of the equations in the GAMS language The next sub section explain the syntax for an equation definition and this is followed by an illustrative example The rest of this section is devoted to discussions about some of the key components of equation
64. b j as the right hand side of the demand constraint the result is 2 11 GAMS Output 21 45 demand j sum i x i j g dem j AK 140 Error Message 140 UNKNOWN SYMBOL ENTERED AS PARAMETER Example 5 The next example is a mathematical error which is sometimes committed by novice modelers and which GAMS is adept at catching The following is mathematically inconsistent and hence is not an interpretable statement For alli XC zij 100 2 There are two errors in this equation both having to do with the control of indices Index 7 is over controlled and index 7 is under controlled You should see that index 7 is getting conflicting orders By appearing in the quantifier for all 7 it is supposed to remain fixed for each instance of the equation Yet by appearing as an index of summation it is supposed to vary It can t do both On the other hand index j is not controlled in any way so we have no way of knowing which of its possible values to use If we enter this meaningless equation into GAMS both errors are correctly diagnosed meaninglss i sum i x i j e 100 Ao 125 149 ERROR MESSAGES 125 SET IS UNDER CONTROL ALREADY This refers to set i 149 uncontrolled set entered as constant This refers to set j A great deal more information about error reporting is given in Section 10 6 page 105 Comprehensive error detection and well designed error messages are a big help in getting models implemented qu
65. bool_or 60 bool_xor 60 cdf BVN 288 cdfTVN 288 cdfUVN 288 ceil 58 centropy 58 cos 58 cosh 58 cosine 286 cvPower 58 div 58 div0 58 eDist 58 entropy 58 errorf 58 errorLevel 61 execError 61 execSeed 58 exp 58 fact 58 fitFunc 279 fitParam 279 floor 58 frac 58 gamma 58 gammaReg 58 gamsRelease 61 gamsVersion 61 eday 61 gdow 61 ghour 61 gleap 61 gmillisec 61 gminute 61 gmonth 61 gsecond 61 gyear 61 handleCollect 61 handleDelete 61 handleStatus 61 handleSubmit 61 heapFree 61 heapLimit 61 heapSize 61 ifThen 60 jdate 61 jnow 61 jobHandle 61 jobKill 61 jobStatus 61 jobTerminate 61 jstart 61 jtime 61 licenseLevel 61 licenseStatus 61 log 58 log10 58 log2 58 logBeta 58 logGamma 58 LogOption 287 mapVal 58 max 58 maxExecError 61 min 58 mod 58 ncpCM 58 ncpF 58 ncpV Upow 58 ncpVUsin 58 normal 58 pdfBVN 288 pdfTVN 288 pdfUVN 288 pi 58 286 poly 58 power 58 pwpFunc 280 randBinomial 58 randLinear 58 rand Triangle 58 rel_eq 60 rel_ge 60 rel_gt 60 rel le 60 rel_lt 60 rel_ne 60 round 58 rPower 58 304 INDEX setMode 286 execerr 178 sigmoid 58 execmode 178 sign 58 expand 178 signPower 58 ferr 178 sin 58 filecase 178 sine 286 forcework 178 sinh 58 forlim 178 sleep 61 g205 178 slexp 58 gdx 178 sllog10 58 gdxcompress 178 slrec 58 gdxconvert 178
66. call parameter 197 RMIQCP model type 16 80 rmpec GAMS call parameter 197 RMPEC model type 16 80 round function 58 rPower function 58 rules constructing tables 48 formating tables 48 save GAMS call parameter 197 savepoint GAMS call parameter 197 GAMS option 248 scalar 172 equation 75 example 46 statement 45 syntax 45 scale option 164 scaling models 164 of a variable 165 of an equation 165 of derivate 166 scenario analysis 87 serdir GAMS call parameter 197 scrext GAMS call parameter 197 scriptexit GAMS call parameter 197 scriptfrst GAMS call parameter 198 scriptnext GAMS call parameter 198 scrnam GAMS call parameter 198 Secure Work Files 257 seed GAMS call parameter 198 GAMS option 249 semi continuous variables Definition 163 Example 163 semi integer variables definition 163 example 163 semicolon 31 set 172 associated text 36 declaration for multiple sets 37 definition 35 dollar control option 236 dynamic 119 elements 36 multi dimensional 39 multi dimensional many to many 40 multi dimensional one to one mapping 39 names 35 sequences as set elements 37 simple 35 singleton 42 syntax 35 set operations complement 123 312 INDEX difference 124 actions triggered by 86 intersection 123 requirements 86 union 123 several in a program 87 setArgs several models 87 dollar control option 237 setComps dollar control option
67. can modify your cshrc file by adding the line set path path opt gams gams24 3_linux_x64_64_sfx Those of you using the Bourne sh or Korn ksh shells and their variants can modify their profile or bashrc file by adding the line PATH PATH opt gams gams24 3_linux_x64_64_sfx If neither profile nor bashrc exist yet profile needs to be created You should log out and log in again after you have made any changes to your path You may prefer to use an alias for the names of the programs instead of modifying the path as described above C shell users can use the following commands on the command line or in their cshrc file alias gams opt gams gams24 3_linux_x64_64_sfx gams alias gamslib opt gams gams24 3_linux_x64_64_sfx gamslib The correct Bourne or Korn shell syntax either command line or profile is alias gams opt gams gams24 3_linux_x64_64_sfx gams alias gamslib opt gams gams24 3_linux_x64_64_sfx gamslib Again you should log out and log in in order to put the alias settings in cshrc or profile into effect Casual users can always type the absolute path names of the GAMS programs e g opt gams gams24 3_linux_x64_64_sfx gams trnsport 294 Installation and System Notes Mac OS X K 5 Installation Like the other UNIX versions GAMS for Macintosh is a Mac OS X Terminal application and must be installed and executed using the command line interface It does not have a graphical user interface like th
68. control structures A value of 0 does not cause an execution profile to be generated A value of 1 reports execution times for each statement and the number of set elements over which the particular statement is executed A value of 2 reports specific times for statements inside control structures like loops etc Running TRNSPORT with profile 1 provides the following additional information in the listing file 1 ExecInit 0 000 0 000 SECS 3 Mb aias 44 Assignment c 0 000 0 000 SECS 4 Mb 6 asss 65 Solve Init transport 0 000 0 000 SECS 4 Mb TSE 57 Equation cost 0 000 0 000 SECS 4 Mb 1 59 Equation supply 0 000 0 000 SECS 4 Mb 2 RR 61 Equation demand 0 000 0 000 SECS 4 Mb 3 e 65 Solve Fini transport 0 000 0 000 SECS 4 Mb 19 65 GAMS Fini 0 015 0 015 SECS 4 Mb apan 1 ExecInit 0 000 0 000 SECS 2 Mb Jams 65 Solve Read transport 0 000 0 000 SECS 2 Mb SAAR 67 Display 0 000 0 000 SECS 3 Mb 67 GAMS Fini 0 000 0 000 SECS 3 Mb The first column provides the line number in the input file of the statement being executed The second column provides the type of statement being executed ExecInit denotes the beginning of the execution phase of the GAMS input file GAMS Fini denotes the end of this phase Note that GAMS finishes processing of an input file as soon as a solve statement is processed and passes control to the solver being called After the solver is done GAMS restarts This causes two ExecInit GAMS Fini pairs to be generated for TR
69. different blocks of equations solution values from the first are used as data in the next These decomposition methods are useful for certain classes of problems because the sub problems being solved are smaller and therefore more tractable One of the most common examples of such a method is the Generalized Bender s Decomposition method An example of a problem that is solved in this way is an input output system with endogenous prices described in Henaff 1980 The model consists of two groups of equations The first group uses a given final demand vector to determine the output level in each sector The second group uses some exogenous process and input output data to compute sectoral price levels Then the resulting prices are used to compute a new vector of final demands and the two block of equations are solved again This iterative procedure is repeated until satisfactory convergence is obtained Henaff has used GAMS statements to perform this kind of calculation The statements that solve the system for the first time and the next iteration are shown below model usaio mb output model dualmodel dual totp solve usaio using lp maximizing total solve dualmodel using lp maximizing totprice pbar ta sum ipd 1 i ta 4 d i t db i g t pd 1 i t pbar t solve usaio using lp maximizing total solve dualmodel using lp maximizing totprice Mb is a set of material balance input output equations and output
70. domain symbol definitions then they are permuted right to left lt or left to right lt A later example in this section will clarify this The following example demonstrates the two ways to do projection and aggregation on sets Sets i i1 i3 j j1rj2 k k1x k4 ijkGi j k i j k ijia i j ijib i j Scalars Count_1a Count_1b Count_2a Count_2b Method 1 by using assignment and the sum operator ijla i j sum k ijk i j k Count_1a sum ijla i j 1 Count_2a sum ijk i j k 1 Method 2 Option statement performs a projection Option ijib lt ijk Method 2 Option statement performs an aggregation counts elements Option Count_ib lt ijib Option Count_2b lt ijk Display ijia ijib ijk Count_ia Count_1b Count_2a Count_2b ts The OPTION statement for projection and aggregation operations can also be applied on parameters 42 Set Definitions However in the special case where a domain has identical domain symbol definitions e g set i1 i i i a permutation of the domain is ambiguous The projection can be performed by permuting the indices from right to left lt or left to right lt The below example clarifies the difference Set i i1 i3 i1 i i i Set members i1 i2 13 i3 i3 i1 i2a i i i2a i ii sum ii iii ii i 1 i2b i i Option i2b lt i1 right to left i3a i i i3a i ii sum ii i ii iii 1 i3b i i Option i3b lt i1 left to right
71. ee 9 SET i one two three 9 SET j four five zero aaa 9 PARAMETER x Messed up Data one 1 000 four 10 000 five 10 000 six 6 000 The domain violations are marked like normal compilation errors but are only treated as warnings and one can execute the code phantom id Used to designate id as a phantom set element Syntactically a phantom element is handled like any other set element Semantically however it is handled like it does not exist This is sometimes used to specify a data template that initializes the phantom records to default values Consider the following example phantom null set i null j a b null display i j The resulting section of the listing file is shown below 4 SET I EMPTY 4 SET J a b Note that null does not appear in the listing file t Assignment statements on the phantom label are ignored Consider the following extension to the previous example Parameter p j a 1 null 23 display p The resulting section of the listing file is shown below 6 PARAMETER P a 1 000 prefixPath Augments the search path in the Windows path environment variable The use of prefixpath value results in the text in value being appended to the beginning of the search path Consider the following example 236 Dollar Control Options display sysenv PATH prefixpath C somewhereelse anotherpath display sysenv PATH If sysenv PATHY contains C some pat
72. equivalent to if y gt 1 5 then x 2 else x 0 Therefore an if then else type of construct is implied but the else operation is predefined and never made explicit Notice that the statement in the illustrative example above can be re written with an explicit if then else and equivalent meaning as x 2 y gt 1 5 O y le 1 5 This use of this feature is more apparent for instances when an else condition needs to be made explicit Consider the next example adapted from FERTD The set i is the set of plants and are calculating mur i the cost of transporting imported raw materials In some cases a barge trip must be followed by a road trip because the plant is not alongside the river and we must combine the separate costs The assignment is mur i 1 0 0030 ied i barge ied i barge 0 5 0144 ied i road ied i road This means that if the entry in the distance table is not zero then the cost of shipping using that link which has a fixed and a variable components is added to the total cost If there is no distance entry there is no contribution to the cost presumably because that mode is not used 11 4 3 Filtering Controlling Indices in Indexed Operations The controlling indices can in certain cases be filtered through the conditional set without the use of the dollar operator Consider the example described in that section The total cost of shipment is obtained through the follo
73. errors an additional set of asterisks will be placed at the location of the error in the output file Since put errors are non fatal and are not overemphasized in the output file their presence is sometimes overlooked Without reviewing the program listing these put errors might go undetected especially in large output files Consequently GAMS has included the following file suffix to help one detect errors errors Allows one to display the number of put errors occurring in a file To illustrate its use the following statement could be inserted at any point of a program to detect the number of errors which have occurred up to its location The choice of output file could be the same file a different file or the console as appropriate putpage error put errors out errors 0 0 In this example it is assumed that the files out put and error put have previously been defined with a file statement With this statement the number of put errors that occur in the file out put are displayed in the file error put Using putpage would allow the immediate display to the screen of a PC system at the location of this statement if the console had been the output device 15 17 Simple Spreadsheet Database Application This last section provides a simple example of the preparation of output for spreadsheets databases or other software packages which allow importation of delimited files As mentioned in Section 15 3 output items c
74. expensive or difficult models you should read the chapter on workfiles to find out how to interrupt and continue program execution The next few sub sections discuss various instances where several solve statements may be needed in the same file 9 4 1 Several Models If there are different models then the solves may be sequential as below Each of the models in PROLOG consists of a different set of equations but the data are identical so the three solves appear in sequence with no intervening assignments solve nortonl using nlp maximizing Z solve nortonn using nlp maximizing Z solve nortone using nlp maximizing Z When there is more than one solve statement in your program GAMS uses as much information as possible form the previous solution to provide a starting point in the search for the next solution 9 4 2 Sensitivity or Scenario Analysis Multiple solve statements can be used not only to solve different models but also to conduct sensitivity tests or to perform case or scenario analysis of models by changing data or bounds and then solving the same model again While some commercial LP systems allow access to sensitivity analysis through GAMS it is possible to be far more general and not restrict the analysis to either solver or model type This facility is even more useful for studying many scenarios since no commercial solver will provide this information An example of sensitivity testing is in the simple oil refining mo
75. extended range arithmetic shown in the table above give non zero values for mapval For example mapval a takes a value of 6 if a is inf All regular numbers result in a mapval of 0 The following table shows a selection of results for exponentiation and division for a variety of input parameters 66 Data Manipulations with Parameters Value Operations a b a b power a b a b 2 2 4 4 1 2 2 undf 4 1 2 2 1 4 28 undf 952 na 2 5 na na na 3 0 1 1 undf inf 2 inf inf inf 2 inf undf undf 0 Table 6 3 Exponentiation and Division t One should avoid creating or using numbers with absolute values larger than 1 0E20 If a number is too large it may be treated by GAMS as undefined UNDF and all values derived from it in a model may be unusable Always use INF or INF explicitly for arbitrarily large numbers When an attempted arithmetic operation is illegal or has undefined results because of the value of arguments division by zero is the normal example an error is reported and the result is set to undefined UNDF From there on UNDF is treated as a proper data value and does not trigger additional error messages t GAMS will not solve a model if an error has been detected but will terminate with an error condition It is thus always necessary to anticipate conditions that will cause errors such as divide by zero This is most easily done with the dollar control and will be discussed in the next section 6 4 Summa
76. for inclusion because they have been used in other modeling systems Examples are network problems and production planning models These models permit the user to compare how problems are set up and solved in different modeling systems Most of the models have been contributed by GAMS users The submission of new models is encouraged If you would like to see your model in a future release of the library please send the model and associated documents and reports to GAMS Development Corporation The most convenient way Windows only to access the model library is from within the GAMS IDE by going through File Model Library Open GAMS Model Library A window will pop up and give you access to all models Another way to access the library is through the gamslib command This command copies a model from the library directory into the current directory If you enter gamslib without any parameters the command syntax will be displayed as shown below gt gamslib modelname target or gt gamslib modelnum target where modelname is the modelname modelnum is the model sequence number and target is the target file name If the target file name is not provided the default is modelname gms For example the TRNSPORT model could be copied in any of the following ways 176 The GAMS Model Library gt gamslib trnsport target file trnsport gms gt gamslib 1 trnsport gms gt gamslib trnsport myname myname gt gamslib 1 myname myname The
77. for syntax errors This option is useful when a large model is being put together from smaller pieces Values O standard compilation 1 check out compilation Consider the following example a i b i b i 5 c j By default running a file containing just the two statements shown above results in the following listing file 1 a i b i 5 kk 140 120 140 2 bi c j OK 140 120 149 120 Unknown identifier entered as set 140 Unknown symbol 149 Uncontrolled set entered as constant xo 6 ERROR S 0 WARNING S None of the sets i or j have been defined or initialized and the identifiers a b and c have not been defined Further an assignment cannot be made without the right hand side of the assignment being known In both assignments in the example above there is no data available for the right hand side Running the model with the setting mp 1 results in the following listing file 1 a i b i 5 2 bi c j kkk 149 Error Messages 149 Uncontrolled set entered as constant xx x 1 ERROR S 0 WARNING S Note that the statements in the example have now been processed independently of its context They are now checked only for consistency GAMS now assumes that sets i and j as well as the identifiers a b and c are defined and if necessary initialized elsewhere The only error that is reported is the inconsistency of indices in the second statement nlp nlp tezt default NLP solver nodlim nodlim 0
78. full and annotated list of the models of the GAMS Model Library is available at http www gams com modlib modlib htm C The GAMS Call The entire GAMS system appears to the user as a single call that reads the input files and produces output files Several options are available at this level to customize the GAMS run and define the output desired Although details will vary with the type of computer and operating system used the general operating principles are the same on all machines C 1 The Generic no frills GAMS Call The simplest way to start GAMS is to enter the command gt gams myfile from the system prompt and GAMS will compile and execute the GAMS statements in the file myfile If a file with this name cannot be found GAMS will look for a file with the extended name myfile gms The output will be written by default on the file myfile 1st For example the following statement compiles and executes the example problem TRNSPORT from the GAMS model library gt gams trnsport The output goes by default to the file trnsport 1st C 1 1 Specifying Options through the Command Line GAMS allows for certain options to be passed through the command line The syntax of the simple GAMS call described in Section C 2 is extended to look as follows gt gams myfile keyi valuei key2 value2 where key1 is the name of the option that is being set on the command line and valuel is the value to which the option is set Dependin
79. g0 with time stamp of 11 30 11 08 40 41 You may have to edit this file and the input file There are 5 labels Set WorkFileLabelOrder dummy set to establish the proper order seattle san diego new york chicago topeka Model transport Variable z total transportation costs in thousands of dollars Set i canning plants seattle san diego Set j markets new york chicago topeka Parameter c i j transport cost in thousands of dollars per case seattle new york 0 225 seattle chicago 0 153 seattle topeka 0 162 san diego new york 0 225 san diego chicago 0 162 san diego topeka 0 126 C 3 Detailed Description of Command Line Parameters 183 Positive Variable x i j shipment quantities in cases Parameter a i capacity of plant i in cases seattle 350 san diego 600 Parameter b j demand at market j in cases new york 325 chicago 300 topeka 275 Equation demand j satisfy demand at market j Equation supply i observe supply limit at plant i Equation cost define objective function EDITS FOR INPUT FILE x x x END OF DUMP Note that all the data entering the model in the solve statement has been regenerated The parameter d has not been regenerated since it does not appear in the model but the parameter c is Changing the value of the parameter dumpopt will result in alternate names being used for the identifiers in the regenerated file dumpparms dp 0 GAMS parameter logging The du
80. gamma x DNLP gamma function y x f 1 e tdt see MathWorld 0 gammaReg x a NLP regularized gamma function see MathWorld log x NLP returns the natural logarithm logarithm base e see Math World logBeta x y NLP log beta function log B x y logGamma x NLP log gamma function as discussed in MathWorld 6 3 Expressions 59 log10 x log2 x mapVal x max x1 x2 x3 min x1 x2 x3 mod x y ncpCM x y Z ncpF x y Z ncpVUpow r s MU ncpVUsin r s MU normal MEAN STDDEV pi poly x A0 A1 A2 A3 power x Y randBinomial N P randLinear LOW SLOPE HIGH randTriangle LOW MID HIGH round x DECPL NLP NLP none DNLP DNLP DNLP NLP NLP NLP NLP none any NLP NLP none none none DNLP returns the common logarithm logarithm base 10 see Math World returns the binary logarithm logarithm base 2 see MathWorld Function that returns an integer value associated with a nu merical result that can contain special values Possible values are 0 for all regular numbers 4 for UNDF which means undefined 5 for NA which means not available 6 for INF which means plus infinity 7 for INF which means minus infinity 8 for EPS which means very close to zero but different from zero returns the maximum of a set of expressions or terms the number of arguments is not limited returns the minimum of a set of expressions or terms
81. generation which includes the solution that follows The following three sub sections discuss these types of errors 10 6 1 Compilation Errors Compilation errors were discussed in some detail in Chapter 2 There is some overlap between the material in those sections and this one Several hundred different types of errors can be detected during compilation and can often be traced back to just one specific symbol in the GAMS input Most of the errors will be caused by simple mistakes forgetting to declare an identifier putting indices in the wrong order leaving out a necessary semicolon or misspelling a label For errors that are not caused by mistakes the explanatory error message text will help you diagnose the problem and correct it ts When a compilation error is discovered a symbol and error number are printed below the offending symbol usually to the right on a separate line that begins with the four asterisks If more than one error is encountered on a line possibly because the first error caused a series of other spurious errors the signs may be suppressed and error number squeezed GAMS will not list more than 10 errors on any one line t At the end of the echo print of the program a list of all error numbers encountered together with a description of the probable cause of each error will be printed The error messages are self explanatory and will not be listed here It is worth noting that it is easy to produce a mode
82. i j x i j beta solve newtrans using nlp minimizing z parameter basex i j base values of x basex i j x 1 i j Finally we transform the result by using a third model variable delta i j percentage change from base values equation defdelta i j definition of delta model rep defdelta defdelta i j basex i j delta i j e 100 x 1 i j basex i j basex i j solve rep using cns We will save the above GAMS code under the name p1 gms execute and make a save restart file with the name p1 g00 as follows gt gams pl s p1 Now we are ready to make some test runs similar to those we expect to be defined by the target user We will define three scenarios to be solved in a loop and name the file u1 gms set s one two three parameter sbeta s one 1 25 two 1 5 three 2 0 sf s one 85 two 75 three 50 G 6 Limitations and Future Requirements 261 parameter report summary report loop s beta sbeta s f sf s solve getc using cns solve newtrans using nlp minmizing Z solve rep using cns report i j s delta 1 i j report beta s beta report f s f report obj z s 2 10 display report When executing the above GAMS code together with the original transport model from the GAMS model library we will get the following results gt gams ul r p1 a 109 PARAMETER report summary report one two three seattle new york 4 050 6 96
83. in a document with the window being used for specific reporting These writing areas are always sequentially located on the page in the order shown on the following diagram It is important to note that the title and header blocks are essentially the same as the window and use exactly the same syntax rules However the window is required in each page of your document while the title and headers are optional Also note that once the window is written to any further modifications of the title or header blocks will be shown on subsequent pages and not the current page Writing to the window is what ultimately forces a page to be written 144 The Put Writing Facility Title Block Header Block Window In the illustrative example described in Section 15 3 all the data was written to the window A title block might have been included if more elaboration were needed to provide the model name along with the page number In addition a header block might have been used to display a disclaimer or an instruction which we wanted consistently repeated on every page Once this information is placed in the title or header blocks it is displayed on each page thereafter unless modified This could be especially useful for a long document covering many pages 15 6 1 Accessing Various Page Sections Each of these areas of a page are accessed by using different variations of the keyword put These variations are puttl write to title bl
84. in seconds of wall clock time handle Every solve gets unique handle number that may be used by handlecollect handlestatus or handledelete See Appendix I iterUsd Number of iterations used line Line number of last solve of the corresponding model linkUsed Integer number that indicates the value of solveLink used for the last solve modelStat Model status Range from 1 to 19 For details check page 100 nodUsd The number of nodes used by the MIP solver number Model instance serial number The first model solved gets number 1 the second number 2 etc The user can also set a value and the next model solved will get value 1 as number numDepnd Number of dependencies in a CNS model numDVar Number of discrete variables numEqu Number of equations numInfes Number of infeasibilities numNLIns Number of nonlinear instructions numNLNZ Number of nonlinear nonzeros numNOpt Number of nonoptimalities numNZ Number of nonzero entries in the model coefficient matrix 9 3 The Solve Statement 85 numRedef Number of MCP redefinitions numVar Number of variables numVarProj Number of bound projections during model generation objEst The estimate of the best possible solution for a mixed integer model objVal The objective function value procUsed Integer number that indicates the used model type Possible values are 1 LP MIP
85. is a total output equation Dual is a group of price equations and totp is an equation that sums all the sectoral prices The domestic prices pd used in the calculation of the average price pbar are divided by four because there are four sectors in this example Also the 1 is appended to pd to indicate that this is the level of the variable in the solution of the model namely in dualmodel Thus the iterative procedure uses solution values from one iteration to obtain parameter values for the next one In particular both pbar and pd are used to compute the demand d for the i th product in time period t d i t Also the base year demand db and the growth factor g are used in that calculation Then when the new final demand vector d is calculated the two blocks of equations are solved again 1Henaff Patrick 1980 An Input Output Model of the French Economy Master s Thesis Department of Economics University of Maryland 9 5 Making New Solvers Available with GAMS 89 9 5 Making New Solvers Available with GAMS This short section is to encourage those of you who have a favorite solver not available through GAMS Linking a solver program with GAMS is a straightforward task and we can provide documents that describe what is necessary and provide the source code that has been used for existing links The benefits of a link with GAMS to the developer of a solver are several They include gt Immediate access to a wide variety of test prob
86. is an extremely useful debugging aid It shows the variables that appear in each constraint and what the individual coefficients and right hand side value evaluate to after the data manipulations have been done Most of the listing is self explanatory The name text and type of constraints are shown The four dashes are useful for mechanical searching t All the terms that depend on variables are collected on the left and all the constant terms are combined into one number on the right any necessary sign changes being made Four places of decimals are shown if necessary but trailing zeroes following the decimal point are suppressed E format is used to prevent small numbers being displayed as zero t The nonlinear equations are treated differently If the coefficient of a variable in the equation listing is enclosed in parentheses then the corresponding constraint is nonlinear and the value of the coefficient depends on the activity levels of one or more of the variables The listing is not algebraic but shows the partial derivative of each variable evaluated at their current level values Note that in the equation listing from our example the equation dvar is nonlinear A simpler example will help to clarify the point Consider the following equation and associated level values eqi 2 sqr x power y 3 5 x 1 5 y e 2 x l 2 y l 3 then the equation listing will appear as EQ1 221 X 216 1667 Y E 2 LHS 225 5
87. la b eS ii i Dynamic Set b Singleton Set si i Dynamic Singleton Set b Les iic yes si c yes Display ii si Here is the output from the display statement in the listing file sae 8 SET ii Dynamic Set 8 SET si Dynamic Singleton Set This behavior can be changed with strictSingleton and option strictSingleton 12 3 Using Dollar Controls with Dynamic Sets The rest of this chapter requires an understanding of the dollar condition All the dollar control machinery is available for use with dynamic sets In fact the full power of dynamic sets can be exploited using these dollar controls Note that the dynamic set has values of yes and no only and can therefore be treated as a logical statement The only operations that can be performed on dynamic sets inside the dollar operator are therefore not and or or xor as well as the set operations described in Section 12 4 page 123 122 Dynamic Sets The main uses of dynamic sets inside dollar conditions are in assignments indexed operations and in equations Each of these will be discussed in detail in the following subsections Examples will be used to illustrate its use in each of the three cases 12 3 1 Assignments Dynamic sets can be used inside dollar conditions within assignments defining other dynamic sets or parameters As an illustration of its use in defining other dynamic sets the two statements in the example from Section 12 2 4 can be
88. left hand side is called an assignment and 128 Sets as Sequences Ordered Sets involves the definition of a domain of the assignment The concepts behind reference and assignment are equally valid for the linear and circular forms of the lag and lead operator However the importance of the distinction between reference and assignment is not pronounced for circular lag and lead operators because non existent elements are not used in this case t A reference to a non existent element causes the default value zero in this case to be used whereas an attempt to assign to a non existent element results in no assignment being made The next two sub sections provide examples illustrating the use of the linear form of the lag and lead operators for reference and assignment Section 13 5 3 will illustrate the use of the circular form of the lag and lead operator 13 5 1 Linear Lag and Lead Operators Reference Consider the following example where two parameters a and b are used to illustrate the linear lag and lead operators for reference set t time sequence y 1987 y 1991 parameter a t b t a t 1986 ord t b t 1 b t a t 1 option decimals 0 display a b The option statement suppresses the decimal places from the display The results are shown below Sass 6 PARAMETER A Y 1987 1987 Y 1988 1988 Y 1989 1989 Y 1990 1990 Y 1991 1991 eon 6 PARAMETER B Y 1988 1987 Y 1989 1988 Y 1990 1989 Y 1991 1990
89. limited set of facilities to change all the names and other documentation related to a specific model run before submitted for solution to a public cloud facility The results will then be transformed back inside the secure environment Imagine a company that needs to solve hundreds or even thousands of difficult optimization problems once day taking up to one hour to solve just one problem but only have a time window of little more than one hour There are two new save option SaveObjuscate so and XSaveObfuscate xso that create an obfuscated work file XSaveDbfuscate creates a compressed obfuscated work file One can combine the options with the regular Save s and XSave xs options The obfuscated work file is basically the original named work file but with a string pool that has obfuscated names for symbols and labels In order to keep the string pool structure for easier restoration of proper names we obfuscate by keeping the original length of the symbol label and create a sequence of strings e g for symbols of length 3 we create A00 A01 A02 Z_ Similar for labels but here we always use the single quote character and can create many weird looking labels For the other strings symbol text and label text we just change all characters in these strings to they do not need to be unique as symbols and labels The only other strings we obfuscate are the listing file titles and subtitles All other strings are strings that have some m
90. logarithmic and trigonometric functions The complete list of available functions is given in table 6 1 There are cautions to be taken when functions appear in equations these are dealt with in Section 8 4 page 76 In table 6 1 the Endogenous Classification second column specifies in which models the function can legally appear with endogenous non constant arguments In order of least to most restrictive the choices are any DNLP NLP or none see Section 9 2 2 for details The following conventions are used for the function arguments Lower case indicates that an endogenous variable is allowed Upper case indicates that a constant argument is required The arguments in square brackets can be omitted and default values will be used Those default values are specified in the function description provided in the last column 58 Data Manipulations with Parameters Function Endogenous Description Classifica tion Mathematical functions abs x DNLP returns the absolute value of an expression or term x arccos x NLP returns the inverse cosine of the argument x where x is a real number between 1 and 1 and the output is in radians see MathWorld arcsin x NLP returns the inverse sine of the argument x where x is a real number between 1 and 1 and the output is in radians see MathWorld arctan x NLP returns the inverse tangent of the argument x where x is a real number and the output is in radians see Math
91. model called file1 gms Sets i canning plants seattle san diego j markets new york chicago topeka Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 Table d i j distance in 1000 miles new york chicago topeka seattle 2 5 1 7 1 8 252 The Save and Restart Feature san diego 2 5 1 8 1 4 Scalar f freight in dollars case per 1000 miles 90 Parameter c i j transport cost in 1000 case c i j f d i j 1000 Variables x i j shipment quantities in cases z total transportation costs in 1000 Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j Model transport all Consider the following file say file2 gms Solve transport using lp minimizing z Display x 1 x m Note that TRNSPORT results from appending file2 gms at the end of file1 gms F 2 1 Saving The Work File The information in file1 gms can be stored by using the following call to GAMS gams filei s trans One work file called trans g00 is created in the working directory The Work file preserves all information including declarations values option settings and compil
92. must be identical 3 the first 10 labels point to the same addresses in the string pool All these checks can be done very quickly without reading too much of the named work file The first two checks imply that we can t do a continued compilation with code that introduces new symbols or labels off the obfuscated work file or even new strings display this is a new string We can t write useful code that can be executed off the obfuscated work file since we don t know the obfuscated symbols and labels So practically we can just execute the obfuscated work file off an empty GAMS program as shown above 264 Secure Work Files H Compressed and Encrypted Input Files H 1 Introduction When models are distributed to users other than the original developers issues of privacy security data integrity and ownership arise Besides using secure work files one can compress and encrypt GAMS input files The compression and decompression of files is available to any GAMS user The encryption follows the work file security model and requires special licensing Three new Dollar Control Options have been introduced Encrypt lt source gt lt target gt Encrypts into a GAMS system file Compress lt source gt lt target gt Compresses into a GAMS system file Decompress lt source gt lt target gt Decompresses a GAMS system file Encryption is only available if a system is licensed for secure work files and usually requires a target li
93. occur in an indexed assignment a subset or even a label can be used instead if you need to make the assignment over a subset instead of the whole domain Consider the following example a sro col 10 2 44 33 r sro where sro has already been established to be a proper subset of row 6 2 5 Issues with Controlling Indices t The number of controlling indices on the left of the sign should be at least as many as the number of indices on the right There should be no index on the right hand side of the assignment that is not present on the left unless it is operated on by an indexed operator Consider the following statement a row col 2 22 c col 6 3 Expressions 55 GAMS will flag this statement as an error since col is an index on the right hand side of the equation but not on the left There would be no error here if col would be a singleton set Since there is not more than one element in a singleton set it is not required that this index gets controlled by an controlling index on the left or an indexed operator t Each set is counted only once to determine the number of controlling indices If the same set appears more than once within the controlling domain the second and higher occurrences of the set should be aliases of the original set in order for the number of controlling indices to be equal to the number of indices Consider the following statement as an illustration b row row 7 7 r
94. of equations 77 manipulations with parameters 53 type 29 data types 169 decimals GAMS option 247 decimals global option 136 declaration 169 of a model 79 parameter 46 scalar 45 separation between and definition of 28 statements 28 table 47 decompress 265 dollar control option 209 default 169 defined a reference type 94 definition 170 of a model 79 of data 29 of equation 74 of scalars 46 of symbols 29 statements 28 definition statements 170 dformat GAMS call parameter 181 difference set operation 123 124 direction 170 of optimization 86 100 discontinuous 170 derivate 76 functions 80 discrete 170 variables 68 80 display controls local 136 example 133 generating data in list format 137 global controls 136 introduction 133 label order 134 syntax 133 distributions beta 281 283 binomial 282 284 cauchy 281 283 chiSquare 281 283 exponential 281 283 f 281 283 gamma 281 283 geometric 282 INDEX 301 gumbel 281 283 hyperGeo 282 284 invGaussian 281 laplace 281 283 logarithmic 282 284 logistic 281 283 logNormal 281 283 negBinomial 282 284 normal 281 283 pareto 281 283 poisson 282 284 rayleigh 281 student T 281 283 triangular 281 283 uniform 281 283 uniformInt 282 weibull 281 283 div function 58 divO function 58 dnlp GAMS call parameter 181 GAMS option 247 DNLP mode
95. of mean return on portfolio 44 dvar definition of variance 45 46 fsum sum i x i e 1 0 47 dmean sum i mean i x i e target 48 dvar sum i x i sum j v i j x j e variance 49 50 Model portfolio fsum dmean dvar 51 52 Solve portfolio using nlp minimizing variance That is the end of the echo of the input file If errors had been detected the explanatory messages would be found in this section of the listing file All discussion of error messages have been grouped in the section 10 6 page 105 10 3 2 The Symbol Reference Map The maps are extremely useful if one is looking into a model written by someone else or if trying to make some changes in one s own model after spending time away from it The first map is the Symbol Cross Reference which lists the identifiers symbols from the model in alphabetical order identifies them as to type shows the line numbers where the symbols appear and classifies each appearance The symbol reference map can be turned on by entering a line containing onsymxref at the beginning of the program The map that resulted from ALAN is shown Symbol Listing SYMBOL TYPE REFERENCES DMEAN EQU DECLARED 43 DEFINED 47 IMPL ASN 52 REF 50 DVAR EQU DECLARED 44 DEFINED 48 IMPL ASN 52 REF 50 FSUM EQU DECLARED 42 DEFINED 46 IMPL ASN 52 94 GAMS Output REF 50 HIGHRISK PARAM DECLARED 15 ASSIGNED 34 REF 35 I SET DECLARED 11 DEFINED 11 REF 11 17 24 33 2 34 37
96. of other places If one wished to replace some of them as well one could use macro f2 r i sum j r i j macro equ2 z d q equation equ2_ amp zk amp d equ2_ amp z amp d z q e 0 equ2 1 i 2 x i equ2 2 k 2 r k which would expand to become equation equ2_1 i equ2_1 i 1 sum j x i j equation equ2_2 k equ2_2 k 2 sum j r k j 0 0 ou on where the amp z and amp d are replaced One can also include expressions with spaces commas and unbalanced parentheses using amp amp which includes an expression removing the outer set of quotes macro d q display amp amp q macro ss q amp amp q d hereit is i k al au zz 25 z ss sum j at j z ss prod j at j Note that the d expressions contain quotes spaces and commas and the ss expression has unbalanced parentheses within the quoted parts In turn these expand to become display hereit is i k display zz z sum j a1 j z prod j ai j Nested macro use can result in an expansion of infinite length For example macro a b a display a will expand into display b b b b b b b b b b b b b b b b b Another feature of macros is the implicit use of the L suffix in report writing and other data manipulation statements This allows using the same algebra in model definitions and assignment statements The following code illustrates this feature macro sumit i term sum i term cost z e
97. on off Warning offWarning Switch for data domain checking In some cases it may be useful to accept domain errors in data statements that are imported from other systems and report warnings instead of errors Data will be accepted and stored even though it is outside the domain t This switch effects three types of domain errors usually referred to as error numbers 116 170 and 171 t This can have serious side affects and one has to exercise great care when using this feature Consider the following slice of code set i one two three onwarning j i four five k zero parameter x i Messed up Data one 1 0 five 2 0 x six 6 x j 10 x two x seven j k yes offwarning Noto that tna s t j although specified as a subset of i contains elements not belonging to its domain Similarly the parameter x contains data elements outside its domain The skeleton listing file that results from running this code is as follows D 3 Detailed Description of Dollar Control Options 235 1 set i one two three 3 j i four five kkk 170 170 4 k zero 5 parameter x i Messed up Data one 1 0 five 2 0 AK 170 6 x six 6 x j 10 x two x seven OK 170 116 170 7 jk yes AK 171 9 display i j x Error Messages 116 Label is unknown 170 Domain violation for element 171 Domain violation for set sx 0 ERROR S 7 WARNING S Execution
98. onlisting This directive stops the echo print of the input file onlisting restores the default offsymxref offsymlist onsymxref onsymlist These four directives are used to control the production of symbol maps Maps are most often turned on or off at the beginning of the program and left as initially set but it is possible to produce maps of part of the program by using a on map directive followed later by an off map The symlist lists all the symbols in the model The symxref shows a complete cross reference list of symbols by number Both these maps are suppressed by default offuelxref offuellist onuelxref onuellist These four directives are used to control the production of Unique Element maps which show set membership labels Maps are most often turned on or off at the beginning of the program and left as initially set but it is possible to produce maps of part of the program by using a on map directive followed later by an off map The uellist lists all labels in both GAMS entry and alphabetical order The uelxref shows a complete cross reference list by number These label maps are suppressed by default offupper onupper This directive causes the echo print of the portion of the GAMS program following the directive to appear on the output file in the case that it has been entered in This is the default on newer GAMS systems It is necessary if case conventions have been used in the program for example to distinguish betwee
99. row This statement has only one controlling index row If one steps through the elements of row one at a time assignments will be made only to the diagonal entries in b This will assign exactly 10 values None of the off diagonal elements of b will be filled If an additional name is provided for row and used in the second index position then there will be two controlling indices and GAMS will make assignments over the full Cartesian product all 100 values Consider the following example alias row rowp b row rowp 7 7 r row r rowp 6 2 6 Extended Range Identifiers in Assignments The GAMS extended range identifiers can also be used in assignment statements as in a row col 10 inf a row col 1 inf Extended range arithmetic will be discussed later in this Section The values most often used are NA in incomplete tables and INF for variable bounds 6 2 7 Acronyms in Assignments Acronyms can also be used in assignment statements as in acronym monday tuesday wednesday thursday friday parameter dayofweek dayofweek wednesday t Acronyms contain no numeric value and are treated as character strings only 6 3 Expressions An expression is an arbitrarily complicated specification for a calculation with parentheses nested as needed for clarity and intent In this section the discussion of parameter assignments will continue by showing in more detail the expressions that can be used on the rig
100. s domingo georgetown belem Then a set can be created to associate each port with its country viz set ptoc p c port to country relationship 40 Set Definitions kingston jamaica s domingo haiti georgetown guyana belem brazil The dot between kingston and jamaica is used to create one such pair Blanks may be used freely around the dot for readability The set ptoc has four elements and each element consists of a port country pair The notation p c after the set name ptoc indicates that the first member of each pair must be a member of the set p of ports and that the second must be in the set c of countries This is a second example of domain checking GAMS will check the set elements to ensure that all members belong to the appropriate sets 4 5 2 Many to many Mapping A many to many mapping is needed in certain cases Consider the following set set i a b j c d e ij1 i j a c a d ij2 i j a c b c ij3 i j a c b c a d b d iji represents a one to many mapping where one element of i maps onto many elements of j ij2 represents a many to one mapping where many elements of i map onto one element of j ij3 is the most general case where many elements of i map on to many elements of j These sets can be written compactly as set i a b j c d e ij1 i j a c d ij2 i j a b c ij3 1 j a b c d The parenthesis provides a list of elements that can be expanded when creating pair
101. seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 Table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 Scalar f freight in dollars per case per thousand miles 90 Parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 Variables x i j shipment quantities in cases Zz total transportation costs in thousands of dollars Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j xGi j supply i sum j x i j 1 a i 2 2 Structure of a GAMS Model 7 demand j sum i x i j g b j Model transport all Solve transport using lp minimizing z Display x 1 x m If you submit a file containing the statements above as input to the GAMS program the transportation model will be formulated and solved Details vary on how to invoke GAMS on different of computers but the simplest Cno frills way to call GAMS is to enter the word GAMS followed by the input file s name You will see a number of terse lines describing the progress GAMS is making including the name of the file onto which the output is being written When GAMS has finished examine this file and if all has gone well the optimal shipments will be displayed at the botto
102. solved with GAMS The type of the model must be known before it is solved The model types are briefly discussed in this section GAMS checks that the model is in fact the type the user thinks it is and issues explanatory error messages if it discovers a mismatch for instance that a supposedly linear model contains nonlinear terms This is because some problems can be solved in more than one way and the user has to choose which way to go For instance if there are binary or integer variables in the model it can be solved either as a MIP or as a RMIP The problem types and their identifiers which are needed in the a solve statement are listed below LP Linear programming There are no nonlinear terms or discrete binary or integer variables in your model QcP Quadratic constraint programming There are linear and quadratic terms but no general nonlinear term or discrete binary or integer variables in your model NLP Nonlinear programming There are general nonlinear terms involving only smooth functions in the model but no discrete variables The functions were classified as to smoothness in the previous chapter DNLP Nonlinear programming with discontinuous derivatives This is the same as NLP except that non smooth functions can appear as well These are more difficult to solve than normal NLP problems The user is strongly recommended not to use this model type RMIP Relaxed mixed integer programming The model can contain discrete
103. solvers and the second being specific to a particular one The section of the solve summary that is common for all solvers is first discussed The corresponding section for the example model is shown below SOLVE SUMMARY MODEL PORTFOLIO OBJECTIVE VARIANCE TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 48 x x SOLVER STATUS 1 NORMAL COMPLETION xxx MODEL STATUS 2 LOCALLY OPTIMAL OBJECTIVE VALUE 2 8990 RESOURCE USAGE LIMIT 0 020 1000 000 ITERATION COUNT LIMIT 5 10000 EVALUATION ERRORS 0 0 The common part of the solve summary is shown above It can be found mechanically by searching for four asterisks The explanation for the information provided in this section follows MODEL PORTFOLIO This provides the name of the model being solved TYPE NLP 100 GAMS Output This provides the model type of the model being solved SOLVER MINOS5 This provides the name of the solver used to solve the model OBJECTIVE VARIANCE This provides the name of the objective variable being optimized DIRECTION MINIMIZE This provides the direction of optimization being performed xxx SOLVER STATUS 1 NORMAL COMPLETION xxx MODEL STATUS 2 LOCALLY OPTIMAL These provide the solver status and model status for the problem and are discussed in greater detail at the end of this subsection x OBJECTIVE VALUE 2 8990 This provides the value of the objective function at the termination of the solve If the Solver and Model h
104. sumit i j c i j x i j supply i sumit j x i j l a i demand j sumit i x i j g b j Model transport all Solve transport using lp minimizing z onDotL parameter tsupply i total demand for report tdemand j total demand for report tsupply i sumit j x i j tdemand j sumit i x i j which will expand to cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j Model transport all Solve transport using lp minimizing z parameter tsupply i total demand for report tdemand j total demand for report tsupply i sum j x L i j tdemand j sum i x L i j 224 Dollar Control Options The onDotL enables the implicit L suffix for variables This feature was introduced to make macros more useful and is not limited to be used in macro bodies The matching offDotL will disable this feature maxcol n 80000 Sets the right margin for the input file All valid data is before and including column n in the input file All text after column n is treated as comment and ignored Consider the following example maxcol 30 set i vienna rome set definition scalar a 2 3 scalar definition The text strings set definition and scalar definition are treated as comments and ignored since they begin on or after column 31 Any changes in the margins via maxcol or mincol will be reported in the listing file with the mes
105. symbol as it is currently eolcom gt eolcom gt error This option will issue a compilation error and will continue with the next line Consider the following example if not exist myfile error File myfile not found will continue anyway This checks if the file myfile exists and if not it will generate an error with the comment File not found will continue anyway and then compilation continues with the following line 212 Dollar Control Options escape Allows one to print out or display the text sequence for the syntax It is employed using the syntax escape symbol This renders all subsequent commands of the form symbol to not have parameter substitution done for them and on display or in a put to come out as just a One may reverse this action with escape Consider the following example set tt DOIT file it put it display first tth display second h amp tth amp put display one system date put display two Z amp system date amp escape amp display third tth display fourth Z amp tt7Z amp put display third system date put display fourth amp system dateZk escape display fifth tt display sixth Z amp ttZ amp put display fifth system date put display sixth amp system date amp The resulting listing file contains sas 6 first DOIT 7 second amp tt e gt 12 third DOIT a 13 f
106. that indicates the distribution of GAMS you are installing For example if you are installing the 24 3 distribution in opt gams the installer will create the GAMS system directory opt gams gams24 3_linux_x64 64 sfx If the directory where you want to install GAMS is not below your home directory you may need to have root privileges on the machine Create the directory that should contain the GAMS system directory for instance opt gams Change to this directory cd opt gams Make sure pwd returns the name of this directory correctly Run the distribution file either from its current location or after transfering it to the directory that should contain the GAMS system directory By executing the distribution file the GAMS distribution should be extracted For example if you downloaded the distribution file into your home directory you might execute the following commands mkdir opt gams cd opt gams linux_x64_64_sfx exe K 4 Access to GAMS 293 Optionally create the license file gamslice txt in the GAMS system directory The license file is nowadays sent via email with instructions If no license file is present GAMS will still function in the demonstration mode but can only solve small problems Student and demonstration systems do not include a license file A license file can easily be added later so if you cannot find a license file you can safely proceed without one Change to the GAMS system directory and ru
107. that version 5 gdx files do not support compression gdxconvert gdxconvert v7 conversion to older version of gdx file This option specifies in which format the gdx files will be written Values v5 version 5 gdx file does not support compression v6 version 6 gdx file v7 version 7 gdx file griddir gdir text Grid file directory This option sets the grid file directory gridscript gscript gmsgrid grid submission script This option provides the name of a script file to submit grid computing jobs If only the file name is given the file is assumed to be located in the system directory A fully qualified name can be given as well Advanced knowledge of how GAMS sets up and calls solvers is needed for successful use heaplimit hl 1e20 maximum heap size allowed in Mb This option allows to limit the amount of memory a GAMS job can use during compilation and execution If the needed data storage exceeds this limit the job will be terminate holdfixed holdfixed 0 treat fixed variables as constants This option can reduce the problem size by treating fixed variables as constants Values O fixed variables are not treated as constants 1 fixed variables are treated as constants 188 The GAMS Call ide ide 0 Integrated Development Environment flag This option instructs GAMS to write special instructions to the log file that are in turn read by the IDE Values 1 causes the writing to occur default when running under the IDE
108. the same set definitions as described before parameter bigM i j variable shipped i j binary variable bin i j equation logical i j logical i j ij i j shipped i j 1 bigM i j bin i j The equation logical relates the continuous variable shipped i j to the binary variable bin i j This can be simplified as follows logical ij shipped ij l bigM ij bin ij Note that if the right hand side of the equation contained any term that was indexed over i or j separately then the equation logical i j ij i j would have to be simplified as logical ij i j 12 Dynamic Sets 12 1 Introduction All the sets that have been discussed so far had their membership declared as the set itself was declared and the membership was never changed In this chapter we will discuss changing the membership of sets A set whose membership can change is called a dynamic set to contrast it with a static set whose membership will never change The distinction is important and will be discussed in detail in this chapter This is a topic that has been avoided until now because of a potential confusion for new users Advanced Users will however find it useful 12 2 Assigning Membership to Dynamic Sets Sets can be assigned in a similar way to other data types One difference is that arithmetic operations cannot be performed on sets in the same way that they can on value typed identifiers parameters or variables and equations s
109. these results and transform and display them with GAMS statements For example in the transportation problem suppose we wish to know the percentage of each market s demand that is filled by each plant After the solve statement we would enter parameter pctx i j perc of market j s demand filled by plant i petx i j 100 0 x 1 i j b j display pctx Appending these commands to the original transportation problem input results in the following output pctx percent of market j s demand filled by plant I new york chicago topeka seattle 15 385 100 000 san diego 84 615 100 000 For an example involving marginal we briefly consider the ratio constraints that commonly appear in blending and refining problems These linear programming models are concerned with determining the optimal amount of each of several available raw materials to put into each of several desired finished products Let y i j be the variable for the number of tons of raw material put into finished product j Suppose the ratio constraint is that no product can consist of more than 25 percent of one ingredient that is y i j j 1 25 for all i j To keep the model linear the constraint is written as ratio i j y i j 25 q j l 0 0 rather than explicitly as a ratio The problem here is that ratio m i j the marginal value associated with the linear form of the constraint has no intrinsic meaning At optimality it tells us by at most h
110. three An error is triggered because four has not been used so far and the log file contains xxx 1 double dash variables not referenced four 44 setEnv Defines an operating system environment variable The syntax is setEnv varname value where varname is a user chosen environment variable name and value can contain text or a number Environment variables are destroyed with dropenv varname Consider the following example ondollar set env this is very silly log henv setenv verysilly env log sysenv verysilly if NOT env sysenv verysilly error setenv did not work dropenv verysilly if setenv verysilly error should not be true The following output is echoed to the log file Starting compilation this is very silly this is very silly setGlobal Establishes or redefines contents of a control variable that is accessible in the code where the command appears and all code included therein The syntax is setglobal varname expression where varname is any user chosen variable name and expression is optional and can contain text or a number These variables are destroyed using dropglobal varname In contrast to evalGlobal the setGlobal command does not evaluate the expression at compile time For differences to set and setLocal check the example in the description of set Note that GAMS allows one to define scoped local and global variables with the same name but treats them as different under some cases an
111. time and not when the GAMS program executes Not all data types can be cleared only set parameter equation and variable types can be reset Consider the following example set i 1 20 scalar a 2 clear i a display i a The clear option resets i and a to their default values The result of the display statement in the listing file shows that i is now an empty set and a takes a value of 0 3 SET I EMPTY 3 PARAMETER A 0 000 t The two pass processing of a GAMS file can lead to seemingly unexpected results Both the dollar control options and the data initialization is done in the first pass and assignments in the second irrespective of their relative locations This is an issue particularly with clear since data can be both initialized and assigned Consider the following example scalar a 12 a 5 clear a display a The scalar data initialization statement is processed during compilation and the assignment statement a 5 during execution In the order that it is processed the example above is read by GAMS as compilation step scalar a 12 clear a execution step a 5 display a The example results in a taking a value of 5 The display statement in the resulting listing file is as follows 4 PARAMETER A 5 000 clearError s clearError and clearErrors clear GAMS awareness of compiler errors Consider the following example D 3 Detailed Description of Dollar Control Options 209
112. val s 1 The use of reference and assignment have been reversed with no difference in effect 13 6 Lags and Leads in Equations The principles established in the previous section follow quite naturally into equation definitions A lag or lead operation in the body of an equation to the right of the symbol is a reference and if the associated label is not defined the term vanishes A lag or lead to the left of the is a modification to the domain of definition of the equation The linear form may cause one or more individual equations to be suppressed t All lag and lead operands must be exogenous The next two sub sections provide examples illustrating the use of the linear form of the lag and lead operators in equations for reference and to modify the domain of its definition Section 13 5 3 will illustrate the use of the circular form of the lag and lead operator in equations 130 Sets as Sequences Ordered Sets 13 6 1 Linear Lag and Lead Operators Domain Control Consider the following example adapted from RAMSEY sets t time periods 1990 2000 tfirst t first period tlast t last period tfirst t yes ord t eq 1 tlast t yes ord t eq card t display tfirst tlast variables k t capital stock trillion rupees i t investment trillion rupees per year equations kk t capital balance trillion rupees tc t terminal condition provides for post term growth kk t 1 k t 1 t
113. variables but the discrete requirements are relaxed meaning that the integer and binary variables can assume any values between their bounds MIP Mixed integer programming Like RMIP but the discrete requirements are enforced the discrete variables must assume integer values between their bounds RMIQCP Relaxed mixed integer quadratic constraint programming The model can contain both discrete variables and quadratic terms The discrete requirements are relaxed This class of problem is the same as QCP in terms of difficulty of solution RMINLP Relaxed mixed integer nonlinear programming The model can contain both discrete variables and general nonlinear terms The discrete requirements are relaxed This class of problem is the same as NLP in terms of difficulty of solution MIQCP Mixed integer quadratic constraint programming Characteristics are the same as for RMIQCP but the discrete requirements are enforced MINLP Mixed integer nonlinear programming Characteristics are the same as for RMINLP but the discrete requirements are enforced RMPEC Relaxed Mathematical Programs with Equilibrium Constraints MPEC Mathematical Programs with Equilibrium Constraints MCP Mixed Complementarity Problem CNS Constrained Nonlinear System EMP Extended Mathematical Program Each of these model types will be discussed in detail in later chapters 9 2 The Model Statement 81 9 2 3 Model Attributes Model attributes can be accessed throug
114. was not intended something is probably misspecified in the logic or the data LOCALLY INFEASIBLE This message means that no feasible point could be found for the problem from the given starting point It does not necessarily mean that no feasible point exists INTERMEDIATE INFEASIBLE This means that the current solution is not feasible but that the solver stopped either because of a limit e g iteration or resource or because of some sort of difficulty Check the solver status for more information FEASIBLE SOLUTION A feasible solution has been found to a problem without discrete variables INTEGER SOLUTION A feasible solution has been found to a problem with discrete variables There is more detail following about whether this solution satisfies the termination criteria set by options optcr and optca INTERMEDIATE NON INTEGER This is an incomplete solution to a problem with discrete variables A feasible solution has not yet been found INTEGER INFEASIBLE It has been proven that there is no feasible solution to a problem with discrete variables LIC PROBLEM NO SOLUTION The solver cannot find the appropriate license key needed to use a specific subsolver ERROR UNKNOWN After a solver error the model status is unknown ERROR NO SOLUTION An error occurred and no solution has been returned No solution will be returned to GAMS because of errors in the solution process NO SOLUTION RETURNED A solution is not expected for th
115. will be used The default setting is described in Section 14 4 bratio 0 25 Certain solution procedures can restart from an advanced basis that is constructed automatically This option is used to specify whether or not basis information probably from an earlier solve is used The use of this basis is rejected if the number of basic variables is smaller than bratio times the size of the basis Setting bratio to 1 will cause all existing basis information to be discarded which is sometimes needed with nonlinear problems A bratio of 0 accepts any basis and a bratio of 1 always rejects the basis Setting bratio to 0 forces GAMS to construct a basis using whatever information is available If bratio has been set to 0 and there was no previous solve an all slack sometimes called all logical basis will be provided This option is not useful for MIP solvers Range 0 1 cns default The default cns solver is set during installation The user can change this default by setting this option to the required solver The list of cns solvers available with your system can be obtained by reading the gamscmp txt file that is present in the GAMS system directory A value of default will change the cns solver back to the default one as specified in gamscmp txt decimals 3 Number of decimals printed for symbols not having a specific print format attached Range 0 8 dnlp default This option controls the solver used to solve dnlp m
116. will explain the use of variables in display statements 7 4 1 Assigning Values to Variable Attributes Assignment statements operate on one variable attribute at a time and require the suffix to specify which attribute is being used Any index list comes after the suffix The following example illustrates the use of assignment statements to set upper bounds for variables x up c i j 1000 phi lo inf p fx pellets ahmsa mexico df 200 c l t 4xcinit t Note that in the first statement the index set covering the domain of x appears after the suffix The first assignment puts an upper bound on all variables associated with the identifier x The statement on the second line bounds one particular entry The statement on the last line sets the level values of the variables in c to four times the values in the parameter cinit Remember that the order is important in assignments and notice that the two pairs of statements below produce very different results In the first case the lower bound for c 1985 will be 0 01 but in the second the lower bound is 1 c x 1985 1 c lo t 0 01 c lo t 0 01 c fx 19857 1 Everything works as described in the previous chapter including the various mechanisms described there of indexed operations dollar operations subset assignments and so on 7 4 2 Variable Attributes in Assignments Using variable attributes on the right hand sid
117. will get a good idea of what is allowed from the examples in this tutorial but precise rules of the road are given in the next Chapter 3 When you are a beginning GAMS user you should terminate every statement with a semicolon as in our examples The GAMS compiler does not distinguish between upper and lowercase letters so you are free to use either 4 Documentation is crucial to the usefulness of mathematical models Tt is more useful and most likely to be accurate if it is embedded within the model itself rather than written up separately There are at least two ways to insert documentation within a GAMS model First any line that starts with an asterisk in column 1 is disregarded as a comment line by the GAMS compiler Second perhaps more important documentary text can be inserted within specific GAMS statements All the lowercase words in the transportation model are examples of the second form of documentation 8 A GAMS Tutorial by Richard E Rosenthal Inputs Outputs e Sets e Echo Print Declaratio eles e Reference Maps Assignment of members Equation Listings e Data Parameters Tables Scalars Status Reports Declaration Assignment of values e Results e Variables Declaration Assignment of type e Assignment of bounds and or initial values optional e Equations Declaration Definition e Model and Solve statements e Display statement optional Table 2 2 The basic components of a GAMS model
118. with output items the page is written to file including the output items contained in the putpage statement The putpage statement is in fact another variation of the put statement In the following statement the quoted text is placed in the current page which is then written to the file out put putpage out This text is placed in window and the page ends Two additional file suffixes that can help the user in determining when to page a file are last page 1p Indicates the number of pages that are already in the document Note that setting this to 0 does not erase the pages that have previously been written to the file window size ws Shows the number of rows which can be placed in the window considering the number of lines that are in the title and header blocks of the current page and the existing page size The ws file suffix value is calculated by GAMS and is not changeable by the user This suffix is useful for manual pagination when used in conjunction with the 11 file suffix 15 15 Exception Handling In this section the topic of exception handling is dealt with As with other GAMS statements dollar control exception handling can be used with put statements to control whether particular output items are displayed In the following example the put statement is only displayed if the dollar condition is true If it is not the put statement is ignored put flag gt 10 some output items 15 16 Source of Error
119. with a not operator followed either of two types of conditional expressions a file operation or a string comparison The result of the conditional test is used to determine whether to read the remainder of the line which can be any valid GAMS input line The exist file operator can be used to check for the existence of the given file name specification The string compare consists of two strings quoted or unquoted for which the comparison result is true only if the strings match exactly Null empty strings can be indicated by an empty quote t The case of the strings provided either explicitly or more likely through a parameter substitution is preserved and therefore will effect the string comparison t Quoted strings with leading and trailing blanks are not trimmed and the blanks are considered part of the string ts If the string to be compared is a possibly empty parameter the parameter operator must be quoted New_input_line is the remainder of the line containing the if option and could be any valid GAMS input line 216 Dollar Control Options t The first non blank character on the line following the conditional expression is considered to be the first column position of the GAMS input line Therefore if the first character encountered is a comment character the rest of the line is treated as a comment line Likewise if the first character encountered is the dollar control character the line is treated as a dollar
120. x must be in radians see MathWorld tanh x NLP returns the hyperbolic tangent of x where x must be in radians see MathWorld trunc x DNLP truncation removes decimals from x uniform LOW HIGH none generates a random number between LOW and HIGH with uniform distribution see MathWorld uniformInt LOW HIGH none generates an integer random number between LOW and HIGH with uniform distribution see MathWorld vcPower x Y NLP returns zY for x gt 0 Logical functions bool_and x y DNLP boolean and returns 0 if x 0 V y 0 else returns 1 another possible command is x and y bool_eqv x y DNLP boolean equivalence returns 0 if exactly one argument is 0 else returns 1 another possible command is x eqv y bool_imp x y DNLP boolean implication returns 1 if z 0 V y 0 else returns 0 another possible command is x imp y bool_not x DNLP boolean not returns 1 if x 0 else returns 0 another possible command is not x bool_or x y DNLP boolean or returns 0 if x y 0 else returns 1 another possible command is x or y 6 3 Expressions 61 bool_xor x y DNLP ifThen cond iftrue else DNLP rel_eq x y DNLP rel ge x y DNLP rel_gt x y DNLP rel_le x y DNLP rel_1t x y DNLP rel_ne x y DNLP boolean xor returns 1 if exactly one argument is 0 else returns 0 another possible command is x xor y first argument contains a condition e g x gt y If the condi tion is true t
121. you succeed in building an input file devoid of compilation errors GAMS is able to generate a model The question remains and only you can answer it does GAMS generate the model you intended The equation listing is probably the best device for studying this extremely important question A product of the solve command the equation listing shows the specific instance of the model that is created when the current values of the sets and parameters are plugged into the general algebraic form of the model For example the generic demand constraint given in the input file for the transportation model is demand j sum i x i j g b j while the equation listing of specific constraints is A demand g satisfy demand at market j demand new york x seattle new york x san diego new york g 325 demand chicago x seattle chicago x san diego chicago g 300 demand topeka x seattle topeka x san diego topeka g 275 The default output is a maximum of three specific equations for each generic equation To change the default insert an input statement prior to the solve statement option limrow r 2 11 GAMS Output 23 where r is the desired number The default output also contains a section called the column listing analogous to the equation listing which shows the coefficients of three specific variables for each generic variable This listing would be particularly useful for verifying a GAMS model t
122. 00 10 000 10 000 1 933 EQU DVAR A a 1 000 FSUM fractions must add to 1 0 DMEAN definition of mean return on portfolio DVAR definition of variance VAR X fraction of portfolio invested in asset i LOWER LEVEL UPPER MARGINAL hardware a 0 303 INF software 0 087 INF EPS show biz 0 505 INF t bills 0 106 INF EPS LOWER LEVEL UPPER MARGINAL VAR VARIANCE INF 2 899 INF VARIANCE variance of portfolio The order of the equations and variables are the same as in the symbol listing described before and will be described later 104 GAMS Output The four columns associated with each entry have the following meaning LOWER lower bound 10 LEVEL level value 1 UPPER upper bound up MARGINAL marginal m For variables the values in the LOWER and UPPER columns refer to the lower and upper bounds For equations they are obtained from the constant right hand side value and from the relational type of the equation These relationships were described in Chapter 8 t The LEVEL and MARGINAL values have been determined by the solver and the values shown are used to update the GAMS values In the list they are shown with fixed precision but the values are returned to GAMS with full machine accuracy The single dots on the list represent zero EPS is the GAMS extended value that means very close to but different from zero It is common to see a marginal value given as EPS since GAMS uses the convention that ma
123. 2 2 3 Dynamic Sets with Multiple Indices o e o 120 12 2 4 Assignments over the Domain of Dynamic Sets o e 120 12 2 5 Equations Defined over the Domain of Dynamic Sets o 121 12 2 6 Assigning Membership to Singleton Sets o e e 121 12 3 Using Dollar Controls with Dynamic bets e lt 2 lt lt o sarral e 121 LoL Asoo colo do ee ea RA ee a A 122 Igoe Inder Operations occ eaa a a ae Bae Ge ee eed 122 Too MOUAG lt lt lt doc ae Phe ee BO be eds bad E bee 122 12 3 4 Filtering through Dynamic Sets oco a eae ee a 123 Bal Bet Opera aa A ea A ae a ae A Obed 123 12 4 1 Bet Union oa a ae eh ee eb a oe Re PEE a Se De ee G 123 TAZ Oot TOD ECO oat as SR Re BO ee ae ea PE ee a c 123 124 3 Bet Complement i 666544 hte a eee ebb ee tbbda aaa whee eee 123 1244 Set Diblerente lt ao c saci sd ee sa AAA A Re 124 lao GUMMA o Pi oet a ee a Ee ee eae a ee PS i a ede ee 124 13 Sets as Sequences Ordered Sets 125 I ra o e ck pe Ba ood PRR Oe eee Ee RK Re ASRS EEE RRR ES 125 152 Ordered and Unordered Sets oo face nr ee a a ee E ee ER AI E a 125 dose DA Ba Lal kk Ae is ee ea ate oe Gk Se Re ek hoch ck ee a ead 126 Tel The Ore Opirata oor ee bb he cada 126 doe The Card Deerier salia ceca eee ee oe A eh a A ee BS SO ee a A 127 134 Lag amd Lead Operators 6 cor horp A Pe eG Re Ee Ee ee es 127 135 Legs and Leads in Assignments ocas coe a sa Se eh
124. 227 on offEps dollar control option 228 on offExpand dollar control option 228 on offGlobal dollar control option 228 on offInclude dollar control option 228 on offInline dollar control option 229 on offListing dollar control option 229 on offLocal dollar control option 229 on offLog dollar control option 230 on offMacro dollar control option 230 on offMargin dollar control option 230 on offMulti dollar control option 230 on offNestCom dollar control option 231 on offOrder dollar control option 231 on offPut dollar control option 231 on offRecurse dollar control option 232 on offStrictSingleton dollar control option 232 on offSymList dollar control option 232 on offSymX Ref dollar control option 232 on offText dollar control option 233 on offUEIList dollar control option 233 on offUE XRef dollar control option 233 on offUNDF dollar control option 234 on offVerbatim dollar control option 234 on offWarning dollar control option 234 on115 GAMS call parameter 193 optca GAMS call parameter 193 GAMS option 248 optcr GAMS call parameter 193 GAMS option 248 optdir GAMS call parameter 193 optfile GAMS call parameter 193 optimal 172 option 172 introduction 245 310 INDEX syntax 245 or relational operator 121 ORANI example from GAMSLIB 38 ordered set 172 card operator 127 circular lag and lead operator 129 introduction 12
125. 237 setDDList dollar control option 238 setEnv dollar control option 238 setGlobal dollar control option 238 setLocal dollar control option 239 setMode function 286 setNames dollar control option 239 SHALE example from GAMSLIB 36 shift dollar control option 239 show dollar control option 240 sigmoid function 58 sign function 58 76 signed number 45 46 48 signPower function 58 simple assignment 53 simplex method 172 sin function 58 76 sine function 286 single dollar control option 240 sinh function 58 slack 172 slack variable 172 slash delimiter 32 140 sleep function 61 slexp function 58 sllog10 function 58 slrec function 58 smax operator 56 57 smin operator 56 57 smooth 172 functions 76 solprint GAMS call parameter 198 GAMS option 249 solslack GAMS option 249 solution listing 103 solve errors 107 errors messages 106 statement 79 solve statement syntax 85 solve summary 99 evaluation errors 100 iteration count 100 objective summary 100 resource usage 100 solver status 100 solvelink GAMS call parameter 198 GAMS option 249 solveopt GAMS option 249 solver 172 solver status 100 evaluation error limit 102 iteration interrupt 102 normal completion 102 other errors 102 resource interrupt 102 terminated by solver 102 unknown error 102 solvercntr GAMS call parameter 198 solverdict GAMS call parameter 198 solverinst
126. 3 Actions Triggered by the Solve Statement The solve statement triggers a sequence of steps that are as follows 1 The model is translated into the representation required by the solution system to be used 2 Debugging and comprehension aids are produced and written to the output file EQUATION LISTING etc 3 GAMS verifies that there are no inconsistent bounds or unacceptable values for example NA or UNDF in the problem 4 Any errors detected at this stage cause termination with as much explanation as possible using the GAMS names for the identifiers causing the trouble 5 GAMS passes control to the solution subsystem and waits while the problem is solved 6 GAMS reports on the status of the solution process and loads solution values back into the GAMS database This causes new values to be assigned to the 1 and m fields for all individual equations and variables in the model A row by row and column by column listing of the solution is provided by default Any apparent difficulty with the solution process will cause explanatory messages to be displayed Errors caused by forbidden nonlinear operations are reported at this stage The outputs from these steps including any possible error messages are discussed in detail in the next chapter 9 4 Programs with Several Solve Statements 87 9 4 Programs with Several Solve Statements Several solve statements can be processed in the same program If you have to solve sequences of
127. 3 Data Types and Definitions There are five basic GAMS data types and each symbol or identifier must be declared to belong to one of the following groups acronyms models sets equations parameters variables Scalars and tables are not separate data types but are a shorthand way to declare a symbol to be a parameter and to use a particular format for initializing the numeric data Definitions have common characteristics for example parameter a i j input output matrix data type keyword identifier domain list text The domain list and the text are always optional characteristics Other examples are set time time periods model turkey turkish fertilizer model variables X y Z In the last example a number of identifiers separated by commas are declared in one statement 3 4 Language Items Before proceeding with more language details a few basic symbols need to be defined and the rules for recognizing and writing them in GAMS established These basic symbols are often called lexical elements and form the building blocks of the language They are characters delimiters labels reserved words and tokens comments text numbers identifiers indents 30 GAMS Programs Each of these items are discussed in detail in the following sub sections t As noted previously we can use any mix of lower and upper case GAMS makes no distinction between upper and lower case 3 4 1 Characters A few characters are not allowed in a GAMS
128. 46 2 47 2 48 CONTROL 33 34 46 47 48 J SET DECLARED 11 REF 24 2 48 CONTROL 48 LOWYIELD PARAM DECLARED 14 ASSIGNED 33 REF 35 MEAN PARAM DECLARED 17 DEFINED 19 REF 33 47 PORTFOLIO MODEL DECLARED 50 DEFINED 50 IMPL ASN 52 REF 52 TARGET PARAM DECLARED 13 DEFINED 13 REF 47 V PARAM DECLARED 24 DEFINED 24 REF 34 48 VARIANCE VAR DECLARED 38 IMPL ASN 52 REF 48 52 X VAR DECLARED 37 IMPL ASN 52 REF 40 46 47 2 48 For each symbol the name and type of the symbol are first provided For example the last symbol listed is X which is defined to be of type VAR The complete list of data types are given in table 10 1 Entry in symbol reference table GAMS Data Type EQU equation MODEL model PARAM parameter SET set VAR variable Table 10 1 List of GAMS data types Then comes a list of references to the symbol grouped by reference type and identified by the line number in the output file The actual reference can then be found by referring to the echo print of the program which has line numbers on it In the case of the symbol X in the example above the list of references as shown in the symbol reference map are as follows DECLARED 37 IMPL ASN 52 REF 40 46 47 2 48 This means that X is declared on line 37 implicitly assigned through a solve statement on line 52 and referenced on lines 40 46 and 47 The entry 2 48 means that there are two references to X on line 48 of the input file The complete list of reference types is given be
129. 5 lags and leads in assignments 127 lags and leads in equations 129 linear lag and lead operator 128 ord operator 126 output 172 GAMS call parameter 194 output file 172 pagecontr GAMS call parameter 194 pagesize GAMS call parameter 194 pagewidth GAMS call parameter 194 parameter 172 examples 46 higher dimensions 47 statement 46 syntax 46 pareto distribution 281 283 parmfile GAMS call parameter 194 pdfBVN function 288 pdfTVN function 288 pdfUVN function 288 phantom dollar control option 235 pi function 58 286 plicense GAMS call parameter 194 poisson distribution 282 284 poly function 58 power function 56 58 precision fixed 104 prefixPath dollar control option 235 priorities for branching example 164 introduction 164 problem type 80 172 procdir GAMS call parameter 194 prod operator 56 94 PRODSCH example from GAMSLIB 73 profile GAMS call parameter 195 GAMS option 248 profilefile GAMS call parameter 196 profiletol GAMS call parameter 196 GAMS option 248 program 172 PROLOG example from GAMSLIB 79 87 protect dollar control option 236 purge dollar control option 236 put additional numeric control 149 appending to a file 142 assigning files 141 closing a file 142 cursor control 150 database database application 153 defining files 141 errors 152 example 140 149 exception handling 152 global item formatting 147 introduction
130. 66 The resulting listing file contains atrial 4 Anumber equals 11 NEO 5 Bnumber equals 22 ERE 6 Cnumber equals 33 Sane 9 Anumber equals 11 in test2 gms ae 12 Bnumber does NOT equal 22 in test2 gms Soe 13 Cnumber equals 33 in test2 gms 20 Dnumber equals 44 So 23 Enumber does NOT equal 55 ARA 25 Fnumber does NOT equal 66 Note that GAMS allows one to define scoped local and global variables with the same name and has to prioritize under some cases Consider the following slice of code setglobal notunique aa setlocal notunique bb set notunique cc if notunique aa display it is aa if notunique bb display it is bb if notunique cc display it is cc The resulting listing file contains 5 it is bb setArgs Sets up substitutable parameters as GAMS control variable names Consider the following example scalar a 2 b 4 c 5 batinclude test3 a b c where test3 gms is scalar x x hl 2 73 display x setargs aa bb cc x haa bb hcch display x x 1 2 3 display x The setArgs command that must appear in the Batincluded file allows this Batinclude file to use aah in place of 1 bb in place of 2 and cc in place of 43 Note that the use of 41 2 etc is still allowed The resulting listing file contains 5 PARAMETER x 22 000 A 8 PARAMETER x 18 000 10 PARAMETER x 22 000 setComps Establishes or redefines control va
131. 7 8 083 seattle chicago 18 797 27 202 31 550 seattle topeka 233 958 348 468 404 187 san diego new york 3 605 6 201 7 194 san diego chicago 28 138 40 719 47 228 san diego topeka 15 512 23 104 26 799 beta 1 250 1 500 2 000 of 85 000 75 000 50 000 obj Z 526 912 1652 963 13988 774 Note that all symbols are still completely exposed We need to add access controls to the model pl gms before we can ship it to the target client The information to be protected is the original distance matrix and derived information We start out by hiding everything and then give access to selected parts of the model We collect the access control information in the file s1 gms shown below and save the secure work file under the name s1 g00 Since we are still testing we use our own license as target user This will allows us to test the system the same way the target user will use it hide all expose getc newtrans rep expose i j z delta expose f beta a b gt gams si r pi s si plicense license To test the new secure file we run again the problem ul gms When doing so you will observe that equation variable and solution listings related to the hidden variables are not shown any more Any attempt to reference a hidden variable will case a compilation error gt gams ul r s1 Before we can ship a secure work file we need a copy of the target user license file We then will restart again from p1 gms zip the resulting secure files and we are rea
132. 710 103 3 755 104 5 306 105 2 382 106 2 174 107 6 537 108 4 975 109 8 260 i10 3 067 i11 6 216 112 4 349 286 Extrinsic Functions J 6 Build Your Own Trigonometric Library Example This library serves as an example of how to code and build an extrinsic function library The library is included in the GAMS distribution in binary form and also as source code written in C Delphi and FORTRAN respectively that comes along with the GAMS Test Library models trilib01 trilib02 and trilib03 Table J 7 lists the extrinsic functions that are implemented by the libraries Function Endogenous Description Classifica tion setMode MODE none sets mode globally could still be overwritten by MODE at Co Sine call possible values are 0 radians and 1 degree cosine x MODE NLP returns the cosine of the argument x default setting MODE 0 sine x MODE NLP returns the sine of the argument x default setting MODE 0 pi any value of 7 3 141593 Table J 7 Trigonometric functions The C implementation of this extrinsic function library can be found in the files tricclib c and tricclibql c Together with the API specification file extrfunc h these files document the callbacks that need to implemented by a GAMS extrinsic function library Note that the file tricclibql c which implements the querylibrary callback has been generated by the Python helper script q1 py The purpose of the querylibrary callback is to provide informa
133. 95 handling in equations 117 execerr GAMS call parameter 184 execError function 61 execmode GAMS call parameter 185 execSeed function 58 execution 170 errors 107 execution statements 170 exit dollar control option 214 exogenous 170 exp function 58 expand GAMS call parameter 185 explanatory text 68 79 170 exponent 56 170 exponential distribution 281 283 expose dollar control option 214 extended value 104 extended arithmetic 170 Extrinsic Functions CPP Library 288 Fitpack Library 279 GAMS Parameter File 287 Introduction 279 LINDO Sampling Library 283 Piecewise Polynomial Library 280 Stochastic Library 281 Trigonometric Library 286 f distribution 281 283 fact function 58 feasible 170 solution 100 feasible solution 171 ferr GAMS call parameter 185 FERTD example from GAMSLIB 114 FERTS example from GAMSLIB 118 file GAMS statement 139 defining 141 summary 104 filecase GAMS call parameter 186 fitFunc function 279 fitParam function 279 floor function 58 for example 159 statement 158 syntax 159 INDEX 303 forcework GAMS call parameter 186 forlim GAMS call parameter 186 frac function 58 fsave GAMS call parameter 186 funcLibIn dollar control option 214 functions abs 58 arccos 58 arcsin 58 arctan 58 arctan2 58 Beta 58 betaReg 58 binomial 58 bool_and 60 bool_eqv 60 bool_imp 60 bool_not x 60
134. Alias i ii iii Two ways to assign i1 13 13 12 i2a i ii sum il iii ii i 1 Option i2b lt ii Two ways to assign i1 i2 13 13 i3a i ii sum il i ii iii 1 Option i3b lt i1 Option 11 0 0 1 i2a 0 0 1 12b 0 0 1 i3a 0 0 1 13b 0 0 1 Display i1 i2a i2b i3a i3b Hence the left to right lt permutation might be more intuitive 4 6 Singleton Sets A singleton set in GAMS is a special set that has at most one element zero elements are allowed as well Like other sets singleton sets can have up to 20 dimensions Set i As by amp fi Singleton Set j d k i b 1 i j c d A data statement for a singleton set with more than one element will create a will create a compilation error 1 Singleton Set s si s3 OK 844 2 display s Error Messages 844 Singleton with more than one entry see onStrictSingleton This behavior can be changed with offStrictSingleton ts Singleton sets can be especially useful in assignment statements since they don t need to be controlled by an controlling index nor an indexed operator More information about this can be found in chapter 6 4 7 Summary In GAMS a simple set consists of a set name and the elements of the set Both the name and the elements may have associated text that explains the name or the elements in more detail More complex sets have elements that are pairs or even n tuples These sets with pairs and n tuples are ideal for establishin
135. As an illustration consider the example discussed in the previous section One can add page numbers to the title of the report file by modifying the putt1 statement to read puttl class2 GAMS Put Example 65 page system page This causes the word page followed by the page number to appear on the title of every page starting at column 65 15 9 Output Items Output items for the put statement are of the following forms text Any quoted text set element label or text any identifier symbol text or contents of the system suffixes numeric Values associated with parameters variables equations or any of the model suffixes set values Represent existence of set elements and carry the values yes or no only The methods for identifying and using each of these different types of output items are described in the following sub sections 146 The Put Writing Facility 15 9 1 Text Items Output items which are quoted text are any combination of characters or numbers set apart by a pair of single or double quotes However the length of quoted text as well as any output item has a limit No portion of the output item can be placed outside of the page margin When the page width is exceeded several asterisks are placed at the end of the line and a put error is recorded in the program listing In addition to quoted text the output of other text items is possible through the use of system and identifier suffixes The identifi
136. Computing 278 The GAMS Grid Computing Facility J Extrinsic Functions J 1 Introduction Functions play an important role in the GAMS language especially for non linear models Similarly to other programming languages GAMS provides a number of built in intrinsic functions However GAMS is used in an extremely diverse set of application areas and this creates frequent requests for the addition of new and often sophisticated and specialized functions There is a trade off between satisfying these requests and avoiding com plexity not needed by most users The GAMS Function Library Facility 6 3 3 provides the means for managing that trade off In this Appendix the extrinsic function libraries that are included in the GAMS distribution are described In addition we provide some pointers for users wishing to build their own extrinsic function library In the tables that follow the Endogenous Classification second column specifies in which models the function can legally appear with endogenous non constant arguments In order of least to most restrictive the choices are any NLP DNLP or none The following conventions are used for the function arguments Lower case indicates that an endogenous variable is allowed Upper case indicates that a constant argument is required The arguments in square brackets can be omitted and default values will be used J 2 Fitpack Library FITPACK by Paul Dierckx is a FORTRAN based library for one
137. Current Cursor Column These suffixes have numeric values corresponding to coordinates in the window of the page Because of this they can be used in conjunction with cursor control characters to manipulate the position of the cursor in the output file CC current cursor column in window hdcc header current column tlcc title current column t The convention for updating the values stored for the cc suffix is that it are updated at the conclusion of a put statement Consequently the cc value remains constant throughout the writing of items for the next put statement even if multiple items are displayed The following example illustrates the updating of the cursor control suffixes and the use of cursor control charac ters The example is trivial but instructive scalar lmarg left margin 6 file out put out put lmargt2 out cc out cc 0 0 7 put out cc x out cc y out cc z 7 put out cc out cc 0 0 The following is the resulting file out put out cc 1 x lt z out cc 23 Initially the scalar lmarg is set to a specific value to use as an alignment tab Symbols which hold common alignment values such as margins or tabs are often useful for large structured documents The first put statement uses the current column cursor control character to relocate the cursor In this example the cursor is moved to column 8where out cc and its value is displayed 15 13 Cursor Control 151
138. D_DEV DNLP inverse cumulative distribution function for Normal distri bution Table J 5 Normal distribution functions J 5 LINDO Sampling Library The LINDO Sampling Library provides samples of random numbers for certain distributions It is made available by the following directive FuncLibIn lt InternalLibName gt lsadclib The function sampleLS lt DistributionName gt creates a sample of the specified distribution according to the dis tribution parameters and returns a HANDLE that references the sample as illustrated in the example down below The Parameter SAMSIZE must be specified and describes the size of the sample while VARRED is optional and provides the possibility to define a variance reduction method 0 none 1 Latin Hyper Square 2 Antithetic If omitted Latin Hyper Square Sampling is used Function Description getSampleValues HANDLE Retrieve sampling induceCorrelation CORTYPE Induce correlation that has to be set with setCorrelation before CORTYPE describes the correlation type and must be one of 0 PEARSON 1 KENDALL or 2 SPEARMAN setCorrelation SAMPLE1 SAMPLE2 COR Define correlation between two samplings setSeed SEED Define the seed for random number generator setRNG RNG Define the random number generator to use possible values are 1 FREE 0 SYSTEM 1 LINDO1 2 LINDO2 3 LIN1 4 MULT1 5 MULT2 and 6 MERSENNE Continous distributions beta SHAPE_1 SHAPE_2 SAMSI
139. ER B 30 000 The third call leads to b sqr 6 6 which results in b taking a value of 30 w A batinclude call without any arguments is equivalent to a include call Passes a followed string command to the current operating system command processor and interrupts compilation until the command has been completed If the command string is empty or omitted a new interactive command processor will be loaded Consider the following slice of code call dir This command makes a directory listing on a PC The command string can be passed to the system and executed directly without using a command processor by prefixing the command with an sign Compilation errors are issued if the command or the command processor cannot be loaded and executed properly call gams trnsport call gams trnsport The first call runs TRNSPORT in a new command shell The DOS command shell does not send any return codes from the run back to GAMS Therefore any errors in the run are not reported back The second call however sends the command directly to the system The return codes from the system are intercepted correctly and available to the GAMS system through the errorlevel DOS batch function te Some commands like copy on a PC and cd in Unix are shell commands and cannot be spawned off to the system Using these in a system call will create a compilation error Consider the following slice of code call copy myfile txt myco
140. GAMS A User s Guide Tutorial by Richard E Rosenthal June 2015 GAMS Development Corporation Washington DC USA Table of Contents 1 Introduction 1 1 1 2 1 3 MIRES o a mu Gow ew A A BA a e aa Ser ark Bela as Pase Fontur o GANG o a a a Se 2 ae a E d a es LAT emerald Progpley eai a ioue a a A ee A A aak an lie Documentation 3 s ua botea eee e o id A HB S a a a EE A Ioe Toma Sondas cra ia a e a a id a Ea A S L24 User Ir ciuda ee a a Ma A a AA es E a E a Gee a Lee Model Libraiy ssaa ci sc AA ae GS Aa ERR ar ai a RLS ew EE Organization Of the Book ea Gh bade eh Ee Ee ee EE ERR ER Rae es 2 A GAMS Tutorial by Richard E Rosenthal 2 1 2 2 2 3 2 4 2 5 2 6 ET 2 8 2 9 2 10 2 12 Tarodd uctign aaa AE AE ARA A EE eS Structure of a GAMS Model ccoc co ee ee E ad be eee eee ONG ce eek A A ae ek SSS Owe be Bee ek Ee e oa ee et ee ge ee A es ee et 241 Data Entry by Lists lt soe coce heed A me DEGREE EET A DEAE Ee ES 242 Data Entry De Table oars be ee ea ee ee ae ea ee ae A Ee eee ee Ges 24 3 Data Entry by Direct Assignment oca we ee ew ee Worle ea hg s E BA Gees BEE ye SS ER AR BO OHS ee ORS o e i ee ek Gee a aces w a ea wee oe ee ee ee A ee ae a 26 Eguation Declaration ok ee OS Se RR KEE EAR MAD ee eee 2 6 2 GAMS Summation and Product Notation ie 0 0 0002 000 e 263 Eguation DERIO cis ee ae eee ee le PP ee eS Pojechine PaO m a p pad dred hk E eee Oo we AR ok ee Ene and Model an
141. GAMS call parameter 198 solvermatr GAMS call parameter 198 solversolu GAMS call parameter 198 solverstat GAMS call parameter 199 special languages features 161 special ordered sets introduction 161 type 1 example 162 type 1 definition 161 type 2 definition 162 sqexp function 58 sqlog10 function 58 sqr function 58 sqrec function 58 sqrt function 58 stars dollar control option 241 statements 172 static set 120 172 stepsum GAMS call parameter 199 stitle dollar control option 241 INDEX 313 stop dollar control option 241 strictSingleton GAMS option 249 strictsingleton GAMS call parameter 199 stringchk GAMS call parameter 199 studentT distribution 281 283 subsets 54 subsys GAMS call parameter 199 suffix field width 148 file 147 numerical display control 149 page control 152 put file 142 system 145 variable 69 77 sum operator 56 superbasic 104 172 variable 104 suppress GAMS call parameter 199 symbol 172 GAMS call parameter 200 symbol reference map assigned 94 control 94 declared 94 defined 94 equ 94 impl asn 94 model 94 param 94 ref 94 set 94 var 94 sys11 GAMS call parameter 200 sysdir GAMS call parameter 200 sysincdir GAMS call parameter 200 sysInclude dollar control option 241 sysout 103 GAMS call parameter 200 GAMS option 249 tabin GAMS call parameter 200 table 172 a statement
142. Gregorian minute of hour from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian month from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian second of minute from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian year from a serial day number date time where Jan 1 1900 is day 1 returns a serial day number starting with Jan 1 1900 as day 1 returns the current time as a serial day number starting with Jan 1 1900 as day 1 returns the time of the start of the GAMS job as a serial day number starting with Jan 1 1900 as day 1 returns fraction of a day that corresponds to hour minute and second GAMS utility and performance functions errorLevel none error code of the most recently used command 62 Data Manipulations with Parameters execError gamsRelease gamsVersion handleCollect HANDLE handleDelete HANDLE handleStatus HANDLE handleSubmit HANDLE heapFree heapLimit heapSize jobHandle jobKill PID none none none none none none none none none none none none number of execution errors may either be read or assigned to returns the version number of the current GAMS release for example 23 8 returns the current gams version for example 238 tests if the solve of the problem identified by the calling argu ment HANDLE is done and if so loads the solution into GAMS In
143. IDE CC GMS The file name echo will be completed with C PROGRAM FILES GAMSIDE echoN Sends a text message to an external file like echo but writes no end of line marker so the line is repeatedly appended to by subsequent commands Consider the following example echoN Text to be sent gt aaa echoN More text gt gt aaa echoN And more and more and more gt gt aaa echo This was entered with echo gt gt aaa echo This too gt gt aaa The created file aaa contains Text to be sentMore textAnd more and more and moreThis was entered with echo This too The redirection symbols gt and gt gt have the usual meaning of starting at the beginning or appending to an existing file Note that the text and the file name can be quoted or unquoted By default the file name will go in the working directory D 3 Detailed Description of Dollar Control Options 211 eject Advances the output to the next page Consider the following example eject Set i j Parameter data i j eject This will force the statements between the two eject calls to be reported on a separated page in the listing file else else always appears together with an ifThen E I statement It is followed by an instruction which is executed if the matching if statement is not true elself elself always appears together with an ifThen E I statement It is followed by another condition and instruction elselfE e
144. LICENSE sets the privacy license to the current license file This is convenient when experimenting with access controls When a secure work file is written the first time the first and second lines of the current license file and the privacy license file are inserted into the work file This information cannot be changed any more and the original source and the intended target users are locked into the work file A secure work file can be used just like any other work file and new work files can be derived from secure files However their use is restricted to the target user specified with the PLICENSE parameter The target user can if licensed add access controls to an existing secure file by using the PLICENSE LICENSE parameter but cannot change the original information about source and target users Secure work files can be tested on any GAMS system by specifying a non default license file with the LI CENSE target parameter G 4 Access Control Commands There are four Access Control Commands ACC that are processed during the compilation phase These com mands can be inserted anywhere and are processed in chronological order and have the following syntax acc ident1 ident2 acc ALL 260 Secure Work Files Where ace is one of the four ACC s PURGE remove the objects and all data associated HIDE hide the objects but allow them to be used in model calculations PROTECT the objects cannot be modified but used in model c
145. NSPORT Assignment c denotes an assignment statement involving the identifier c Solve Init Solver Fini are book ends enclosing the generation of the model TRNSPORT Note that only equations are listed and not variables This happens because GAMS uses an equation based scheme to generate a model The third and fourth columns provide the individual time needed to execute the statement and the cumulative time taken by the GAMS system so far The last column gives the number of assignments generated in the specified line At the end of the log file a profile summary is created which contains up to ten of the slowest execution steps For example such a summary looks like this Profile Summary 184 records processed 0 062 3621 GAMS Fini 0 047 3621 Solve Read wsisn 0 046 3529 Equation divcnlsea 86 0 032 3621 Solve Fini wsisn 39489 0 016 3274 Assignment wnr 2502 0 016 3447 Equation cost 15 0 016 3475 Equation laborc 180 0 016 3519 Equation waterbaln 180 0 016 3546 Equation subirrc 84 0 015 3030 Assignment gwtsa 273 196 The GAMS Call Note that this summary does not belong to TRNSPORT but is more capable for illustration because the summary of TRNSPORT is empty profilefile pfile text write profile information to this file This option causes profiling information to be written to a file Note that profiling information is only created with profile 1 or profile 2 For example such a file looks like thi
146. O UNBOUNDED 0 ERRORS If our example had display output for reporting it would come here 10 5 8 File Summary The last piece of the output file is important it gives the names of the input and output disk files If work files save or restart have been used they will be named here as well FILE SUMMARY INPUT C PROGRAM FILES gamsIDE ALAN GMS OUTPUT C PROGRAM FILES gamsIDE ALAN LST 10 6 Error Reporting 105 10 6 Error Reporting All the comments and description about errors have been collected into this section for easy reference when disaster strikes Effective error detection and recovery are important parts of any modeling system GAMS is designed around the assumption that the error State is the normal state of modeling Experience shows that most compilations during the early stages of development will produce errors Not to Worry The computer is much better at checking details that the human mind and should be able to provide positive feedback and suggestions about how to correct errors or avoid ambiguities Developing a model is like writing a paper or an essay many drafts and rewrites are required until the arguments are presented in the most effective way for the reader and meet all the requirements of proper English GAMS acts like a personal assistant with knowledge of mathematical modeling and of the syntactic and semantic details of the language Errors are detected at various stages in the modeling proces
147. OR ee ee A ee a Ss 152 15 15 Exception Hage se 22 eae eee bee ew bene edhe edad A ad we 152 15 16 Source of Errors Associated with the Put Statement 0 020 000 000 ee 152 10101 Syntax Eo e e c ue ee a a ad ee Sa ee ee ee a ae ee aS 152 a ER 1 A AR A EE en GS ee es Oe ee A D 152 15 17 Simple Spreadsheet Database Application 2 0 153 LIT A Fee a ee Sa ee ROS ee A ee OE Gal gd Pa eA ee 153 16 Programming Flow Control Features 155 16 1 rs 0 2 sac ee ee Ea eee ee ee ee AG Re A 155 16 2 The Loop Sarment co ea ae ae ee Pa kG A ed eae A ee a A x 155 ESI The SE ias Pa SRM EME ASG ES RE ERE RAY OBO BOOK 155 Gas eee lt lt ua Se ee a Ee Ee Ree tae ee ae eS ee te Fe Se 156 163 The It Blseit Else Statement co ccor a ae ea a a G 156 LGA The Syits e cece i armed aa ARE EER AE ROR EK EERE EEE EA we a 156 Wie Examples e 6 bre e Eek RO bee we eee ee a a eae 157 164 The Whale Statement ok he ee a ROR See eae ee RE Rh ee ae eae Bd 158 G41 o II 158 IGA ExsSuples cansa rama ee aE a A A eed eA 158 16 5 The For Statement oc co 4 62 he eee a eee Pe Pee Ge ek ae ee ae Aes 158 Webel THe yA ccoo ira a a Yh a A ee bbe a De we we 159 lira Examples ois beh RARER RoE eee ee a ba KR Ae me OE 159 17 Special Language Features 161 IFA IO e eee A he hee ode he Rae Be PLS Bes 161 172 Special MIP Desfiles lt lt me ee a pia PSR ba eee eae Me ek ee AE a EG 161 17 2 1 Types or Discrete Variables ne he Re eee a 161 17 2 2 Special Order Sets
148. Pa a PR ee ke ee ee oe ae ee SS 55 6 3 1 Standard Arithmetic Operations o a cap sace a a aa e go ee ee 56 Gee Indexed Operations uc a sa Ole e og e a AAA 56 G3 PUNGHONS o be ee bebe a A eee E a 57 6 3 4 Extended Range Arithmetic and Error Handling 04 4 65 GA CUMAR ons iu gad a Rhee ehh eed EERE ee eS 66 7 Variables 67 el epee ca s ema draag ee a RE OR AR ee ROS Se RY 67 T2 Variable Declarations oe 0 04 6 0 ee be rea ee ee eR GA ee we es 67 week The Bye ke ee ee ee ke ee eee bE be Pe we Be bas 67 Tae Watiable Types 20 2 ee ee eee Le ek RO Bae Pe AA os 68 72 3 Styles for Variable Declaration 00 0200 cee ee 68 o Varl ble BAER oia OR Reh ke wed eke A ERE ee aa 69 Tal Bomndson Variables s oa cc ccc ee ew Be Lk RRR we eee eee A 69 Taa Wii Variables sore eee A A dae oS 69 tao Peetrviby Levels er Variables co ceo sra EE RRR RR Ee 70 7 4 Variables in Display and Assignment Statements ooa e a eee 70 7 4 1 Assigning Values to Variable Attributes e eee eee eee 70 7 42 Variable Attributes in Assignments e 70 7 4 3 Displaying Variable Attributes e 71 Wea a II AN 71 8 Equations 73 Bl Tatroduction e ce ara oi a A a E o ewe es 73 8 2 Equati n Declarations 00 4 000 64040 e a PED Eee Ee eee e a 73 Sak Tho SYMON o op oa a ae we ee ea eS We he ae ee A a BLS 73 S2 2 An Illustrative Example o o araca 40554 ee ee ee ee Re eee 73 Ba Equation DENSAS
149. Parameters Variables and so forth and that the control over potential naming conflicts extends to the names of the individual functions The lt InternalFuncName gt is the one that you will use in the rest of your model code The lt InternalLibName gt is the one that you created with the FuncLibIn directive and lt FuncName gt is the name given the function when the library was created Once functions have been declared with the Function statement they may be used exactly like intrinsic functions in the remainder of your model code Example Here is an example that adds some concrete detail eolcom FuncLibln trilib testlib_ml system dirsep tridclib Make the library available trilib is the internal name being created now tridclib is the external name With no path GAMS will look for tridclib in the GAMS system directory Declare each of the functions that will be used myCos mySin and MyPi are names being declared now for use in this model Cosine Sine and Pi are the function names from the library Note the use of the internal library name XX Function myCos trilib Cosine mySin trilib Sine myPi trilib Pi scalar i grad rad intrinsic for i 1 to 360 intrinsic cos i 180 pi grad mycos i 1 abort round abs intrinsic grad 4 cos i intrinsic grad rad mycos i 180 pi abort round abs intrinsic rad 4 cos i intrinsic rad variable x equation e e
150. Parameters affecting output in listing file appendout output listing file append option case sets output case dformat sets date format limcol default column listing limrow default row listing output sets output file name C 3 Detailed Description of Command Line Parameters 179 pagecontr page control pagesize sets page size pagewidth sets page width profile global execution profiling option profiletol profile time tolerance solprint solution report print option stepsum controls step summary in listing file suppress compilation listing option sysout solver Status file reporting option tformat sets time format Parameters affecting other files appendexpand append to expand file appendlog log file append option dumpparms controls parameter logging expand expand file name ferr sets compilation error message file name filecase casing of new file names put gdx ref etc gdx GAMS data exchange file name gdxcompress compression of generated gdx file gdxconvert conversion to older version of gdx file logfile sets log file name logline controls amount of line tracing to log file logoption log file option profilefile write profile information to this file restart sets restart file name save sets save file name savepoint save solver point in GDX file xsave compressed save file name Table C 1 GAMS command line parameters C 3 Detailed Description of Command Line Parameters This section describes each of the command line parameters in d
151. S model library At a final note we have made no assumptions about what kind of solvers and what kind of computing environment we will operate The above example is completely platform and solver independent and it runs on your Windows laptop or on a massive grid network like the Condor system without any changes in the GAMS source code I 4 Advanced use of Grid Features In this section we will describe a few special application requirements and show how this can be handled with the current system Some of those applications may involve thousands of model instances with solution times of many hours each Some may fail and require resubmission More complex examples require communication and the use of GAMS facilities like the BCH Branch amp Cut amp Heuristic which submit other models from within a running solver 1 4 1 Very Long Job Durations Imagine a situation with thousands of model instances each taking between minutes and many hours to solve We will break the master program into a submitting program an inquire program and a final collection program We will again use the previous example to demonstrate the principle We will split the GAMS code of the modified QMEANVAR GAMS code into three components qsubmit qcheck and qreport The file qsubmit gms file will include everything up to and including the new submit loop To save the instances we will need a unique Grid Directory and to restart the problem we will have to create a save file
152. SPORT is used call gamslib trnsport compress trnsport gms t2 gms decompress t2 gms t3 gms The first command retrieves the transport file and the second command compresses it The third command decompresses the compressed file and t3 gms is exactly the same as the original file trnsport gms dollar This option changes the current symbol to a single character which follows immediately the dollar keyword When a include file is inserted all dollar control options are inherited and the current symbol may not be known The special substitution symbol can be used to get the correct symbol see batinclude Consider the following example dollar hidden now we can use as the symbol double The lines following the double statement will be echoed double spaced to the listing file Consider the following example set i 1 2 scalar a 1 double set j 10 15 scalar b 2 The resulting listing file looks as follows 210 Dollar Control Options 1 set i 1 2 2 scalar a 1 4 set j 10 15 5 scalar b 2 Note that lines before the double option are listed singly spaced while the lines after the option are listed with double space drop Destroys a variable that was defined with set The syntax is drop varname dropEnv Destroys an operating system envorinment variable The syntax is dropenv varname For detailed infoemation check setEnv dropGlobal Destroys a
153. TEMP FILE2 INC The first row always refers the parent file called by the GAMS call The first column gives the sequence number of the input files encountered The second column refers to the type of file being referenced The various types of files are O INPUT 1 INCLUDE 2 BATINCLUDE 3 LIBINCLUDE 4 SYSINCLUDE The third column provides the sequence number of the parent file for the file being referenced The fifth column gives the local line number in the parent file where the include appeared The sixth column gives the global expanded line number which contained the include statement The seventh column provides the total number of lines in the file after it is processed The eighth and last column provides the name of the file ferr ferr text compilation error message file Instructs GAMS to write error messages into a file Completing the name with the scratch directory and the scratch extension composes the file name The default is no compilation error messages This option can be used when GAMS is being integrated into other environments like Visual Basic The error messages that are reported in the listing file can be extracted through this option and their display can be controlled from the environment that is calling GAMS To illustrate the option consider the following slice of GAMS code used to explain the errmsg option Calling GAMS on this code with ferr myfile err will result in a file called myfile err being created in the
154. The functions which should be evaluated need to be defined and stored in a GDX file like it is done in the GAMS Test Library model pwp1ib01 Define two piecewise polynomial functions Table pwpdata 1st index function number 2nd index segment number 3rd index degree leftBound 0 1 2 Lol 1 2 4 2 7 0 3 1 2 4 5 6 4 3 0 5 2 1 0 0 6 3333 0 2 2 0 3333 1 0370 12 5554 9 3333 2 3 0 6667 9 7792 38 7791 29 Write pwp data to gdx file read by external library gdxout pwp gdx unload pwpdata gdxout On each row of the Table pwpdata we have FuncInd SegInd leftBound Coef0 Coef1 Coef2 FuncInd sets the function index SegInd defines the index of the segment or interval which is decribed here LeftBound gives the lower bound of the segment The upper bound is the lower bound on the next row or infinity if this is the last segment CoefX defines the Xth degree coefficient of the polynomial corresponding to this segment This library is made available by the following directive FuncLibIn lt InternalLibName gt pwpcclib Function Endogenous Description Classifica tion pwpFunc FUNIND x DNLP Piecewise Polynomials Table J 2 Piecewise polynomial functions J 4 Stochastic Library 281 J 4 Stochastic Library The stochastic library provides random deviates probability density functions cumulative density functions and inverse cumulative density functions for certain distributions This library is made a
155. The symbol listing in the listing file generated by running TRNSPORT with onsymlist is as follows Symbol Listing SETS I canning plants J markets PARAMETERS A capacity of plant i in cases B demand at market j in cases Cc transport cost in thousands of dollars per case D distance in thousands of miles F freight in dollars per case per thousand miles VARIABLES X shipment quantities in cases Z total transportation costs in thousands of dollars EQUATIONS COST define objective function DEMAND satisfy demand at market j SUPPLY observe supply limit at plant i MODELS TRANSPORT FILES FILE Current file name for FILE xxx use PREDEFINED DIAG SAMEAS This serves as a simple description of the symbols used in a model and can be used in reports and other documentation onjoff SymXRef offSymXRef This option controls the following gt Collection of cross references for identifiers like sets parameters and variables gt Cross reference report of all collected symbols in listing file D 3 Detailed Description of Dollar Control Options 233 gt Listing of all referenced symbols and their explanatory text by symbol type in listing file This is also reported by using onsymlist Consider the following slice of code onsymxref set i 1 6 k offsymxref set j i will not show 1 3 display i onsymxref k 1 yes The resulting listing file will contain the following unique element reference re
156. US 1 NORMAL COMPLETION x xx MODEL STATUS 1 OPTIMAL OBJECTIVE VALUE 153 6750 RESOURCE USAGE LIMIT 0 110 1000 000 ITERATION COUNT LIMIT 5 1000 The status reports are preceded by the same string as an error message so you should probably develop the habit of searching for all occurrences of this string whenever you look at an output file for the first time The desired solver status is 1 NORMAL COMPLETION but there are other possibilities documented in Section 10 5 page 97 which relate to various types of errors and mishaps There are eleven possible model status s including the usual linear programming termination states 1 OPTIMAL 3 UNBOUNDED 4 INFEASIBLE and others relating to nonlinear and integer programming In nonlinear pro gramming the status to look for is 2 LOCALLY OPTIMAL The most the software can guarantee for nonlinear programming is a local optimum The user is responsible for analyzing the convexity of the problem to determine whether local optimality is sufficient for global optimality 24 A GAMS Tutorial by Richard E Rosenthal In integer programming the status to look for is 8 INTEGER SOLUTION This means that a feasible integer solution has been found More detail follows as to whether the solution meets the relative and absolute optimality tolerances that the user specifies 2 11 7 Solution Reports If the solver status and model status are acceptable then you will be interested in examining the res
157. ZE VARRED Beta distribution specified by two shape parameters cauchy LOCATION SCALE SAMSIZE VARRED Cauchy distribution specified by location and scale pa rameter chisquare DF SAMSIZE VARRED Chi Squared distribution specified by degrees of free dom 284 Extrinsic Functions exponential RATE SAMSIZE VARRED f DF_1 DF_2 SAMSIZE VARRED gamma SHAPE SCALE SAMSIZE VARRED gumbel LOCATION SCALE SAMSIZE VARRED laplace LOCATION SCALE SAMSIZE VARRED logistic LOCATION SCALE SAMSIZE VARRED lognormal LOCATION SCALE SAMSIZE VARRED normal MEAN STD_DEV SAMSIZE VARRED pareto SCALE SHAPE SAMSIZE VARRED studentt DF SAMSIZE VARRED triangular LOW MID HIGH SAMSIZE VARRED uniform LOW HIGH SAMSIZE VARRED weibull SCALE SHAPE SAMSIZE VARRED Exponential distribution specified by rate of change F distribution specified by degrees of freedom Note that sampleLSgamma uses another version of the F distribution than dF from the stochastic library J 4 Gamma distribution specified by shape and scale pa rameter Note that the use of sampleLSgamma A B is equivalent to the use of dGamma B A from the stochastic library dd Gumbel distribution specified by location and scale pa rameter Laplace distribution specified by location and scale pa rameter Logistic distribution specified by location and scale pa rameter Log Normal
158. ady or could not be loaded 1 the model instance solution has been loaded HandleStatus handle returns the status of the solve identified by handle An execution error is triggered if GAMS cannot retrieve the status of the handle 0 the model instance is not known to the system 1 the model instance exists but no solution process is complete 2 the solution process has terminated and the solution is ready for retrieval 3 the solution process signaled completion but the solution cannot be retrieved HandleDelete handle returns the status of the deletion of the handle model instance In case of a nonzero return an execution error is triggered 0 the model instance has been removed 1 the argument is not a legal handle 2 the model instance is not known to the system 3 the deletion of the model instance encountered errors HandleSubmit handle resubmits a previously created instance for solution In case of a nonzero return an execution error is triggered 0 the model instance has been resubmitted for solution the argument is not a legal handle the model instance is not known to the system the completion signal could not be removed the resubmit procedure could not be found oF WN Fe the resubmit process could not be started In addition GAMS will issue execution errors which will give additional information that may help to identify the source of problems The property execerror can be used to get and set the number of execution errors 1
159. after you have made any changes to your path 3 You may prefer to use an alias for the names of the programs instead of modifying the path as described above C shell users can use the following commands on the command line or in their cshrc file alias gams Applications GAMS gams24 3_osx_x64_64_sfx gams alias gamslib Applications GAMS gams24 3_osx_x64_64_sfx gamslib The correct Bourne or Korn shell syntax either command line or profile is alias gams Applications GAMS gams24 3_osx_x64_64_sfx gams alias gamslib Applications GAMS gams24 3_osx_x64_64_sfx gamslib Again you should log out and log in in order to put the alias settings in cshrc or profile into effect 4 Casual users can always type the absolute path names of the GAMS programs e g Applications GAMS gams24 3_osx_x64_64_sfx gams trnsport K 7 Example The following shows the log of a session where a user downloads a GAMS 24 3 1 system and installs it under Applications GAMS gams24 3_osx_x64_64_sfx It is assumed that a GAMS license file has been stored as Users doe gamsinst txt doe mac Users doe curl L k 0 http d37drm4t2jghv5 cloudfront net distributions 24 3 1 macosx osx_x64_64_sfx exe Total Received Xferd Average Speed Time Time Time Current Dload Upload Total Spent Left Speed 100 148M 100 148M 0 O 4374k O 0 00 34 0 00 34 5906k 296 Installation and System Notes doe mac Users doe chmod 755 osx_x64_64_sfx exe doe mac User
160. alculations EXPOSE removes all restrictions The keyword ALL applies the ACC to all identifiers defined up to this point in the GAMS source code ACC s can be changed and redefined within the same GAMS program Identifiers inherited from a restart file cannot be changed however G 5 Advanced Use of Access Control We will again use the transport model to show how to hide input data and results from the target user The target user is only allowed to view percentage changes from an unknown base case In addition to the original model we will introduce a data initialization and a report model First we will define a new model to calculate input data The previous parameter c is now the variable newc and the model getc does the calculations include trnsport gms variable newc i j new tansport data equation defnewc i j definition of new transport data model getc compute new transport data defnewc defnewc i j newc i j e f d i j 1000 solve getc using cns Next we change the objective function of the original model to a more complicated nonlinear function Fur thermore we will compute a base case value to be used later in the reporting model Note the reference to newc 1 i j since nexc is a variable we have to specify that we only want the level value scalar beta scale coefficient 1 1 equation newcost definition of new objective function model newtrans newcost supply demand newcost z e sum i j newc 1
161. ame is the name of an equation that has been declared prior to the model statement As with all identifiers model_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long Explanatory text must not exceed 80 characters and must all be contained on the same line as the identifier or label it describes An example of a model definition in GAMS is shown below Model transport a transportation model all The model is called transport and the keyword all is a shorthand for all known declared equations Several models can be declared and defined in one model statement This is useful when experimenting with different ways of writing a model or if one has different models that draw on the same data Consider the following example adapted from PROLOG in which different groups of the equations are used in alternative versions of the problem Three versions are solved the linear nonlinear and expenditure versions The model statement to define all three is 80 Model and Solve Statements model nortonl linear version cb rc dfl bc obj nortonn nolinear version cb rc dfn bc obj nortone expenditure version cb rc dfe bc obj where cb rc etc are the names of the equations We will describe below how to obtain the solution to each of the three models 9 2 2 Classification of Models Various types of problems can be
162. ameters rPower x y NLP returns x for x gt 0 however if x 0 then other restrictions for y apply This function is equal to the arithmetic operation x y which is explained at 6 3 1 sigmoid x NLP Sigmoid calculation r see MathWorld sign x DNLP sign of x returns 1 if x gt 0 1 if x lt 0 and 0 if x 0 signPower x Y NLP signed power where Y must be greater than 0 returns xY if x gt 0and 1 a if lt 0 sin x NLP returns the sine of the argument x where x must be in radians see MathWorld sinh x NLP returns the hyperbolic sine of x where x must be in radians see Math World slexp x SP NLP smooth linear exponential function SP means smoothing pa rameter default setting SP 150 sllog10 x SP NLP smooth linear logarithm base 10 SP means smoothing pa rameter default setting SP 107150 slrec x SP NLP smooth linear reciprocal SP means smoothing parameter default setting SP 1071 sqexp x SP NLP smooth quadratic exponential funtion SP means smoothing parameter default setting SP 150 sqlogi0 x SP NLP smooth quadratic logarithm base 10 SP means smoothing parameter default setting SP 107150 sqr x NLP returns the square of an expression or term x sqrec x SP NLP smooth quadratic reciprocal SP means smoothing parame ter default setting SP 10710 sqrt x NLP returns the squareroot of x see MathWorld tan x NLP returns the tangent of the argument x where
163. an be prepared with comma delimiters and text items in quotes This is implemented by using pc suffix value 5 Delimited files are different than normal put files All output items are written with variable field widths and separated by delimiters Consequently all global and local format specifications for field widths and justification are ignored by GAMS Note that the number of decimals for numeric items can still be specified with the nd file suffix Each item is written immediately following the previous delimiter on the same line unless the cursor is reset t Avoid horizontal cursor relocations in a program which creates a delimited file Horizontally relocating the cursor in a delimited file is potentially damaging since a delimiter could be overwritten While the comma is the most common delimiting character for spreadsheets other delimiters like blank space and tab characters can also be used 15 17 1 An Example In the following example the capacity sub table of the MEXSS report program is prepared as a delimited file The following program segment demonstrates pc suffix value 5 The program segment could be placed at the end of the original MEXSS model file out put out out pc 5 put capacity metric tons loop i put i tl loop m put m te m loop i put k m i The first line of this program segment creates the file out put as the delimited file Notice that in the remainder of this program field wi
164. an identifier and follows the same naming convention as other identifiers like names of sets parameters or tables 5 5 2 Illustrative Example Consider the following example set machines m 1 m 5 acronyms monday tuesday wednesday thursday friday parameter shutdown machines m 1 tuesday 5 6 Summary 51 m 2 wednesday m 3 friday m 4 monday m 5 thursday 3 In the example above data entries are in the form of strings like monday and tuesday By declaring each of those character strings as acronyms this kind of data entry can be used by GAMS Sections 6 2 7 and 11 2 5 will explain the further use of acronyms once entered in this form 5 6 Summary In this chapter the declaration and initialization of parameters with the parameter scalar and the table statement have been discussed The next chapter will describe how this data can be changed with assignment statements 52 Data Entry Parameters Scalars amp Tables 6 Data Manipulations with Parameters 6 1 Introduction Data once initialized may require manipulation in order to bring it to the form required in the model The first part of this chapter will deal explicitly with parameter manipulation The rest of the chapter will be devoted to explaining the ramifications indexed assignment functions index operations 6 2 The Assignment Statement The assignment statement is the fundamental data manipulation statement in GAMS It may be used t
165. anch and bound search is mymodel prioropt 1 where mymodel is the name of the model specified in the model statement The default value is 0 in which case priorities will not be used Using the prior suffix sets the priorities of the individual variables Note that there is one prior value for each individual component of a multidimensional variable Priorities can be set to any real value The default value is 1 As a general rule of thumb the most important variables should be given the highest priority The following example illustrates its use w nono N z prior i small z prior i medium z prior i large In the above example z i large variables are branched on before z i small variables t The lower the value given to the prior suffix the higher the priority for branching t All members of any SOS1 or SOS2 set should be given the same priority value since it is the set itself which is branched upon rather than the individual members of the set 17 3 Model Scaling The Scale Option The rules for good scaling are exclusively based on algorithmic needs GAMS has been developed to increase the efficiency of modelers and one of the best ways seems to be to encourage modelers to write their models using a notation that is as natural as possible The units of measurement are one part of this natural notation and there is unfortunately a potential conflict between what the modeler
166. ange value being used as a matrix coefficient The example below shows the general format of these errors variable x equation eqi 1 2 3 4 eqi x 1 10 5 x lo 10 6 x up 5 7 model wrong eq1 8 solve wrong using lp maximizing x 9 x MATRIX ERROR LOWER BOUNDS gt UPPER BOUND X LO L UP 10 0 5 SOLVE from line 8 ABORTED EXECERROR 1 xxk USER ERROR S ENCOUNTERED Some solve statement require the evaluation of nonlinear functions and the computation of derivatives Since these calculations are not carried out by GAMS but by other subsystems not under its direct control errors associated with these calculations are reported in the solution report Unless reset with the domlim option the subsystems will interrupt the solution process if arithmetic exceptions are encountered They are then reported on the listing as shown in the following example variable x y equation one 1 2 3 4 one y e sqrt 10 x 5 x l 10 6 x lo 0 7 8 9 model divide all solve divide maximizing y using nlp SOLVE SUMMARY MODEL DIVIDE OBJECTIVE Y TYPE NLP DIRECTION MAXIMIZE SOLVER MINOS5 FROM LINE 9 108 GAMS Output xxx SOLVER STATUS 5 EVALUATION ERROR LIMIT xxx MODEL STATUS 7 FEASIBLE SOLUTION x OBJECTIVE VALUE 1 0000 RESOURCE USAGE LIMIT 0 141 1000 000 ITERATION COUNT LIMIT 0 10000 EVALUATION ERRORS 2 0 EXIT Termination requested by User in subroutine FUNOBJ afte
167. aracters are encountered Consider running the following slice of code oninline the default comment symbols are now active These comments can continue to additional lines till the closing comments are found ts inlinecom automatically sets foninline Consider running the following slice of code inlinecom lt lt gt gt lt lt the in line comment characters have been changed from the default gt gt t Nested in line comments are illegal unless onnestcom is set onjoff Listing onListing Controls the echoing of input lines to the listing file Note that suppressed input lines do not generate entries in the symbol and reference sections appearing at the end of the compilation listing Lines with errors will always be listed Consider running the following slice of code set i 0234 0237 j a b c table x i j very long table a b c 0234 1 2 3 offlisting 0235 4 5 6 0236 5 6 7 onlisting 0237 1 1 1 The resulting listing file looks as follows 1 set i 0234 0237 2 j a b c 3 table x i j very long table 4 a b c 5 0234 1 2 3 10 0237 1 1 1 Note that the lines in the source file between the offlisting and onlisting settings are not echoed to the listing file onjoff Local onLocal onLocal allows unlimited use of local on the same symbol in one control stack while 0ffLocal limits the use to one Consider the following example 230 Dollar Control Options set i 1 3 ali
168. ark the ambiguous entry 5 4 3 Continued Tables If a table has too many columns to fit nicely on a single line then the columns that don t fit can be continued on additional lines We use the same example to illustrate 5 4 Tables 49 table ka m i initial cap of productive units 100 tons per yr inchon ulsan atmos dist 3702 12910 steam cr 517 aromatics 181 hydrodeal 180 yosu atmos dist 9875 steam cr 1207 aromatics 148 SC The crucial item is the plus sign above the row labels and to the left of the column labels in the continued part of the table The row labels have been duplicated except that hydroreal has been left out not having associated data Tables can be continued as many times as necessary 5 4 4 Tables with more than Two Dimensions A table can have up to 20 dimensions Dots are again used to separate adjacent labels and can be used in the row or column position The label on the left of the row corresponds to the first set in the domain list and that on the right of each column header to the last Obviously there must be the same number of labels associated with each number in the table as there are sets in the domain list The actual layout chosen will depend on the size of the controlling sets and the amount of data and the ideal choice should be the one that provides the most intuitively satisfactory way of organizing and inspecting the data Most people can more easily look down a column of numb
169. ary sets i 1 3 j 1 2 gdxin transsol loadr i j gdxin display i j The resulting listing file contains gt 6 SET i canning plants seattle san diego 222 Dollar Control Options log SSF 6 SET j markets new york chicago topeka This option will send a message to the log file By default the log file is the console The default log file can be reset with the lo and 1f command line parameters t Leading blanks are ignored when the text is written out to the log file using the log option t All special symbols will be substituted out before the text passed through the log option is sent to the log file Consider the following example log log The following message will be written to the log file log with leading blanks ignored All special symbols will log be substituted out before this text is sent to the log file log This was line system incline of file system incnamef log The log file that results by running the lines above looks as follows Starting compilation CC GMS 0 138 Kb The following message will be written to the log file with leading blanks ignored All special symbols will be substituted out before this text is sent to the log file This was line 5 of file C PROGRAM FILES GAMSIDE CC GMS CC GMS 7 138 Kb Starting execution empty program Status Normal completion Note that system incline has been replaced by 5 which is the line n
170. as i j parameter xxx i j 1 1 1 2 2 2 3 3 3 1 3 13 3 1 31 display xxx parameter g i i g i local 1 i local xxx i i display g offlocal g i local 1 i local xxx i i 1 display g The use of offlocal causes a compilation error in the following line because local is used twice on the same symbol in one control stack onjoff Log onLog Turns on off line logging for information about the line number and memory consumption during compilation This is scoped like the on offListing applying only to included files and any subsequent included files but reverting to onlog in the parent files i e when filel includes file 2 and file 2 contains Sofflog then subsequent lines in file 2 will not be logged but lines in file 1 will be onjoff Macro onMacro Enables or disables the expansion of macros For example macro oneoverit y 1 y offmacro y oneoverit x1 display y causes an error because the macro oneoverit can not be expanded in line 3 onjoff Margin offMargin Controls the margin marking The margins are set with mincol and maxcol Consider running the following slice of code onmargin mincol 20 maxcol 45 Now we have set i plant US UK This defines I turned on the scalar x 3 145 A scalar example margin marking parameter a b Define some parameters offmargin Any statements between columns 1 and 19 and anything beyond column 45 are treated as comments onjoff Multi offMulti
171. ate file file2 gms Sets i seattle san diego j new york chicago topeka Parameters a i seattle 350 san diego 600 b j new york 325 chicago 300 topeka 275 Table d i j new york chicago topeka seattle 2 5 TT 1 8 san diego 2 5 1 8 1 4 Scalar f 90 c i j f d i j 1000 Solve transport using lp minimizing z Display x 1 x m This file contains the data for the model and the solve statement F 3 2 Incremental Program Development GAMS programs are often developed in stages A typically style is to put the sets first followed by tables and data manipulations then equations and finally the assignments used to generate reports As each piece of the model is built it should be run and checked for errors by inserting diagnostic display and abort statements As confidence mounts in the correctness of what has been done it is useful to save the completed parts in a work file Then by restarting it is possible to work only on the piece under active development thereby minimizing computer costs and the amount of output produced in each of the developmental runs This approach is especially useful when entering the statements needed for reporting The solution is much more expensive than the report but the report is likely to involve many details of content and layout that have to be tried several times before they are satisfactory The model can be solved and the result saved in a work file One can t
172. ate traditional if then else constructs 16 3 1 The Syntax The syntax for an if elseif else statement is 16 3 The If Elseif Else Statement 157 if condition statements felseif condition statements else statements where condition is a logical condition t One cannot make declarations or define equations inside an if statement 16 3 2 Examples Consider the following set of statements pCi f lt 0 1 p i f gt 0 and f lt 1 p i 2 p i f gt 1 p i 3 q j f lt 0 1 q j gt 0 and lt 1 q j 2 q j gt 1 q j 3 They can be expressed using the if elseif else statement as if f lt 0 p i 1 q j 1 elseif f gt 0 and f lt 1 pCi p i 2 a j q j 2 else p i p i 3 a j q j 3 Dis The body of the if statement can contain solve statements For instance consider the following bit of GAMS code if ml modelstat eq 4 model ml was infeasible relax bounds on x and solve again x up j 2 x up j solve ml using lp minimizing 1p else if ml modelstat ne 1 abort error solving model ml The following GAMS code is illegal since one cannot define equations inside an if statement if s gt O eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside an if statement if s gt 0 scalar y y 5 158 Pr
173. ately after the sum It is not likely to be useful to have two independent index operations controlled by the same index It is also possible to sum simultaneously over the domain of two or more sets in which case more parentheses are needed Also of course an arithmetic expression may be used instead of an identifier count sum i j a i j emp sum t 1 t m t The equivalent mathematical forms are count y 5 Aij and emp y LM i j t The smin and smax operations are used to find the largest and smallest values over the domain of the index set or sets The index for the smin and smax operators is specified in the same manner as in the index for the sum operator Consider the following example to find the largest capacity lrgunit smax i m capacity i m 6 3 3 Functions Functions play an important part in the GAMS language especially for non linear models Similar to other programming languages GAMS provides a number of built in intrinsic functions However GAMS is used in an extremely diverse set of application areas and this creates frequent requests for the addition of new and often sophisticated and specialized functions There is a trade off between satisfying these requests and avoiding complexity not needed by most users The GAMS Function Library Facility 6 3 3 provides the means for managing that trade off Intrinsic Functions GAMS provides commonly used standard functions such as exponentiation and
174. ation solslack 0 This option causes the equation output in the listing file to contain slack variable values instead of level values 0 Equation output in listing file contains level values between lower and upper bound values 1 Equation output in listing file contains slack values between lower and upper bound values solvelink 0 This option controls GAMS function when linking to solve 0 GAMS operates as always 1 the solver is called from a shell and GAMS remains open 2 the solver is called with a spawn if possible as determined by GAMS or a shell if the spawn is not possible and GAMS remains open 3 GAMS starts the solution and continues in a Grid computing environment 4 GAMS starts the solution and waits same submission process as 3 in a Grid computing environment 5 the problem is passed to the solver in core without use of temporary files solveopt merge This option tells GAMS how to manage the model solution when only part of the variables and equations are in the particular problem being solved replace All equations appearing in the model list will be completely replaced by the new model results Variables are only replaced if they appear in the final model merge The new model results are merged into the existing structures clear Similar to the replace option in addition variables appearing in the symbolic equations but squeezed out in the final model are removed strictSingleton 1 This option affects the beh
175. ation license only works with a specific work file which is locked to the license file licenseStatus any returns a non zero when a license error is incurred maxExecError none maximum number of execution errors may either be read or assigned to sleep SEC none execution pauses for SEC seconds timeClose none returns the model closing time timeComp none returns the compilation time in seconds timeElapsed none returns the elapsed time in seconds since the start of a GAMS run timeExec none returns the execution time in seconds timeStart none returns the model start time since last restart Table 6 1 GAMS functions Consider the following example of a function used as an expression in an assignment statement x j log y j which replaces the current value of x with the natural logarithm of y over the domain of the index set j Extrinsic Functions Using the GAMS Function Library Facility functions can be imported from an external library into a GAMS model Apart from the import syntax the imported functions can be used in the same way as intrinsic functions In particular they can be used in equation definitions Some function libraries are included with the standard GAMS software distribution see Appendix J but GAMS users can also create their own libraries using an open programming interface The GAMS Test Library instances trilib01 trilib02 trilib03 and cpplib00 are simple examples in the programming languages C Delphi
176. ations It is often necessary to use labels explicitly in equations This can be done as with parameters by using quotes around the label Consider the following example dz tz e y jan yC feb y mar y apr 76 Equations 8 4 Expressions in Equation Definitions The arithmetic operators and functions that were described in Section 6 3 page 55 can be used inside equations as well 8 4 1 Arithmetic Operators in Equation Definitions t All the mechanisms that may be used to evaluate expressions in assignments are also available in equations Consider the following example adapted from CHENERY showing parentheses and exponentiation dem i y i e ynot i pd p i thet i 8 4 2 Functions in Equation Definitions Function references in equation definitions can be classified into two types based on the type of the arguments Exogenous arguments The arguments s are known Parameters and variable attributes for example 1 and m attributes are used as arguments The expression is evaluated once when the model is being set up and all functions except the random distribution functions uniform and normal are allowed Endogenous arguments The arguments are variables and therefore unknown The function will be evaluated many times at intermediate points while the model is being solved t The occurrence of any function with endogenous arguments implies that the model is not linear ts It i
177. ations for the user interface The basic GAMS system is file oriented and no special editor or graphical input and output routines exist Rather than burden the user with having to learn yet another set of editing commands GAMS offers an open architecture in which each user can use his word processor or editor of choice This basic user interface facilitates the integration of GAMS with a variety of existing and future user environments 1 2 5 Model Library When architects begin to design a new building they develop the new structure by using ideas and techniques that have been tested in previous structures The same is true in other fields design elements from previous projects serve as sources of ideas for new developments From the early stages of the development of GAMS we have collected models to be used in a library of examples Many of these are standard textbook examples and can be used in classes on problem formulation or to illustrate points about GAMS Others are models that have been used in policy or sector analysis and are interesting for both the methods and the data they use All the substantive models in the library are described in the open literature A collection of models is now included with all GAMS systems along with a database to help users locate examples that cover countries sectors or topics of interest to them The syntax used to introduce features in the various chapters are presented using the Backus Naur form BNF
178. ave the right status this value is the optimum value for the problem RESOURCE USAGE LIMIT 0 109 1000 000 These two entries provide the amount of CPU time in seconds taken by the solver as well as the upper limit allowed for the solver The solver will stop as soon as the limit on time usage has been reached The default limit on time usage is 1000 seconds This limit can be changed by entering a line containing the statement option reslim xx in the program before the solve statement where xx is the required limit in wall clock seconds ITERATION COUNT LIMIT 5 1000 These two entries provide the number of iterations used by the solver as well as the upper limit allowed for the solver The solver will stop as soon as this limit is reached The default limit on iterations used is pratically infinity This limit can be changed by entering a line containing the statement option iterlim nn in the program before the solve statement where nn is the required limit on the iterations used EVALUATION ERRORS 0 0 These two entries provide the number of numerical errors encountered by the solver as well as the upper limit allowed for the solver These errors result due to numerical problems like division by 0 This is suppressed for LP RMIP and MIP models since evaluation errors are not applicable for these model types The default limit on evaluation errors used is 0 This limit can be changed by entering a line containing the statement opti
179. avior of a membership assignment to a singleton set 0 GAMS does not complain about an assignment with more than one element on the right hand side but takes the first one 1 GAMS creates an error for an assignment with more than one element on the right hand side sysout off This option controls the printing of the solver status file as part of the listing file The contents of the solver status file are useful if you are interested in the behavior of the solver If the solver crashes or encounters any difficulty the contents of the solver status file will be automatically sent to the listing file 250 The Option Statement on Prints the system output file of the solver off No subsystem output appears on output file unless a subsystem error has occurred threads 1 This option controls the number of threads or CPU cores to be used by a solver n number of cores to leave free for other tasks 0 use all available cores use n cores will be reduced to the available number of cores if n is too large F The Save and Restart Feature F 1 Introduction GAMS saves the information provided in the input files in intermediate mostly binary files These files are referred to as work files or scratch files Some of these files are used to exchange information between GAMS and the various solvers Just before a GAMS run is complete these files are usually deleted Input files can be processed in parts through the use of these intermediate
180. b display it4 endIf one The resulting listing file contains 2 it2 4 it3 because the first condition x y is obviously not true and the fourth condition b b is not tested because the second one a a was already true ifThenE ifThenE does the same as ifThen but evaluates numerical values of the control variables ifThenI ifThenI does the same as ifThen but is case insensitive include The include option inserts the contents of a specified text file at the location of the call The name of the file to be included which follows immediately the keyword include may be quoted or unquoted Include files can be nested The include file names are processed in the same way as the input file is handled The names are expanded using the working directory If the file cannot be found and no extension is given the standard GAMS input extension is tried However if an incomplete path is given the file name is completed using the include directory By default the library include directory is set to the working directory The default directory can be reset with the idir command line parameter The start of the include file is marked in the compiler listing This reference to the include file can be omitted by using the 0ffinclude option The following example illustrates the use of an include statement include myfile include myfile Both statements above are equivalent and the search order for the in
181. be the scratch directory This can be overwritten by using the GAMS parameter GridDir or short GDir For example gt gams myprogram GDir gridpath If gridpath is not a fully qualified name the name will be completed using the current directory If the grid path does not exist an error will be issued and the GAMS job will be terminated A related GAMS parameter is the DerDir SDir for short Recall the following default mechanism When a GAMS job starts a unique process directory is created in the current job submitting directory These directories are named 225a to 225z When a GAMS job terminates it will remove the process directory at the completion of a GAMS job Any file that has not been created by the GAMS core system will be flagged Using the program gamskeep instead of gams will call another exit script which the default script will do nothing and the process directory will not be removed If we do not specify a scratch directory the scratch directory will be the same as the process directory If we do not specify a grid directory the grid directory will be the same as the scratch directory If there is a danger that some of the model instances may fail or we want to break the GAMS program into several pieces to run as separate jobs we need to be careful not to remove the model instance we have not completely processed In such cases we have to use the GridDir option in order to be able to access previously created model
182. before the data This is a particularly useful order when the model may be solved repeatedly with different data sets There is a separation between declaration and definition For example sets and parameters may be declared first with the statements set c crops parameter yield crop yield and then defined later with a statement set c wheat clover beans parameter yield wheat 1 5 clover 6 5 beans 1 0 73 3 3 Data Types and Definitions 29 Style 1 Style 2 Data Set declarations and definitions Parameter declarations and definitions Variable declarations Equation declaration Equation definition Model definition Model Set declarations Parameter declarations Assignments Variable declarations Displays Equation declaration Model Equation definition Model definition Data Set definitions Parameter definitions Solution Assignments Solve Displays Displays Solution Solve Displays Table 3 1 Organization of GAMS programs The first statement declares that the identifier c is a set and the second defines the elements in the set tx Sets and parameters used in the equations must be declared before the equations are specified they can be defined however after the equation specifications but before a specific equation is used in a solve statement This gives GAMS programs substantial organizational flexibility 3
183. c If not specified it will be set to the curdir directory 202 The GAMS Call workfactor workfactor 1 0 work space multiplier This option tells the solver how much workspace to allocate for problem solution relative to the GAMS estimate workspace workspace number workspace in Mb This option tells the solver how much workspace in Megabytes to allocate for problem solution If not given by the user the solver can choose the size and usually it is the memory available on the machine xsave xs text extended save file name In older GAMS systems versions older than 21 7 the name of a save file written in ASCII format so it is platform independent and can be moved to machines with different operating systems otherwise like save In GAMS systems from release 22 3 and newer it causes writing of compressed save files zerores zerores 0 0 set results of certain operations to zero This option specifies the threshold value for internal rounding to zero in certain operations zeroresrep zeroresrep 0 report underflow as a warning This option causes GAMS to issue warnings whenever a rounding occurs because of zerores Values O no warning when a rounding occurs because of zerores 1 issue warnings whenever a rounding occurs because of zerores D Dollar Control Options D 1 Introduction The Dollar Control Options are used to indicated compiler directives and options Dollar control options are not part of the GAMS language and
184. c tlast g k tlast k t i t i tlast e 1 The declaration of t is included as are a couple of dynamic sets that are used to handle the first and last periods terminal conditions in a clean way The interesting equation is kk the capital balance The set t contains members 1990 to 2000 and so there will be a capital stock constraint for 1991 to 2000 Spelling out the constraint for 1991 k 1991 e k 1990 i 1990 The lead operator on the domain of definition has restricted the number of constraints generated so that there are no references to non existent variables the generated problem will have 10 kk constraints defining the relationship between the 11 k capital values The other interesting point in the RAMSEY excerpt is that the constraint tc is explicitly defined only for the final period because of the assignment to the set tlast Notice the use of dynamic sets to control the domain of the two equations The set tfirst is also used in other parts of the model to set initial conditions particularly the capital stock in the first period k 1990 13 6 2 Linear Lag and Lead Operators Reference In the example discussed in Section 13 6 1 equation kk can be rewritten with equivalent effect as kk t mot tfirst t k t 1 e k t it The dollar condition will cause one of the individual equations to be suppressed However note that using lags and leads in the equation domain will always ca
185. call parameter 187 gridscript GAMS call parameter 187 gsecond function 61 gt relational operator 30 GTM example from GAMSLIB 116 117 gumbel distribution 281 283 gyear function 61 handleCollect function 61 handleDelete function 61 handleStatus function 61 306 INDEX handleSubmit function 61 heapFree function 61 heaplimit GAMS call parameter 187 heapLimit function 61 heapSize function 61 hidden dollar control option 215 hiddenCall dollar control option 215 hide dollar control option 215 holdfixed GAMS call parameter 187 hyperGeo distribution 282 284 ide GAMS call parameter 188 identifiers 171 if dollar control option 215 if elseif else a statement 156 example 157 syntax 156 if dollar control option 216 iff dollar control option 217 ifThen dollar control option 217 ifThen function 60 ifThenE dollar control option 218 ifThenI dollar control option 218 impl asn reference type 94 include dollar control option 218 index position s 171 indices controlling 56 INDUS example from GAMSLIB 50 inequality constraint 171 inf an extended range value 107 as a variable bound 77 134 extended range value 32 65 variable bound 68 infeasible 98 100 104 171 infes solution marker 104 initial values 28 70 initialization 94 171 of data 45 of parameters 46 inlinecom dollar control option 219 input GAMS call parameter 188
186. can be used to specify various attributes of variables A GAMS parameter has one number associated with each unique label combination A variable on the other hand has seven They represent lo The lower bound for the variable Set by the user either explicitly or through default values up The upper bound for the variable Set by the user either explicitly or through default values fx The fixed value for the variable 1 The activity level for the variable This is also equivalent to the current value of the variable Receives new values when a model is solved m The marginal value also called dual value for the variable Receives new values when a model is solved scale This is the scaling factor on the variable This is normally an issue with nonlinear programming problems and is discussed in detail in Section 17 3 prior This is the branching priority value of a variable This parameter is used in mixed integer programming models only and is discussed in detail later The user distinguishes between these suffix numbers when necessary by appending a suffix to the variable name 7 3 1 Bounds on Variables All default bounds set at declaration time can be changed using assignment statements ts For binary and integer variable types the consequences of the type declaration cannot be completely undone Bounds on variables are the responsibility of the user After variables have been declared default bounds have already been as
187. cd as the first parameter bbbb as the second parameter and cccc dddd as the third parameter Consider the following slice of code parameter a b c a 1l b 0O0 c 2 batinclude inc2 inc b a display b batinclude inc2 inc b c display b batinclude inc2 inc b a b display b where inc2 inc contains the following line D 3 Detailed Description of Dollar Control Options 207 call 1 sqr 2 2 the listing file that results is as follows 1 parameter a b c 2 a 1 b 0 3Cc 2 BATINCLUDE D GAMS INC2 INC 4 b sqr a a 5 display b BATINCLUDE D GAMS INC2 INC 7 b sqr c c 8 display b BATINCLUDE D GAMS INC2 INC 10 b sqr at5 at5 11 display b Note that the three calls to batinclude with the various arguments lead to GAMS interpreting the contents of batch include file in turn as b sqr a a b sqr c c b sqr a 5 a 5 Note that third call is not interpreted as sqr a 5 a 5 but instead as sqr a 5 a 5 The results of the display statement are shown at the end of the listing file EN 5 PARAMETER B 0 000 Sass 8 PARAMETER B 2 000 Sam 11 PARAMETER B 40 000 The third call leads to b sqr 6 1 5 which results in b taking a value of 40 If the statement in the batch include file was modified to read as follows 1 sqr 2 42 the results of the display statement in the listing file would read EN 5 PARAMETER B 0 000 Soe 8 PARAMETER B 2 000 ass 11 PARAMET
188. ce the elements that form the set have been defined the set cannot be redefined through the data statment For example the following set of statements are all invalid set i seattle san diego set i seattle san diego portland Similar rules apply to Scalar Parameter and Table declarations One can only use assignment statments to change values of scalars parameters and tables once they have been specified by the data statement For example parameter a i seattle 20 san diego 50 a seattle a san diego 10 100 One can however separate the definition of the data type from the actual data entry For example the following succession of statements is valid Set i Set i seattle san diego This is true with the other data types as well This last feature is very useful in completely separating the model definition from the data and leads to the development of a good runtime GAMS model ts It is the responsibility of the modeler to ensure that the contents of the input file matches that of the work file although the compiler will issue errors if it detects any inconsistencies such as references to symbols not previously declared t A Work file can be used only by GAMS tasks requesting a restarted run t A Work file can be saved following a restarted run thus producing another work file that reflects the state of the job following completion of the statements in the continuation file F 3 Way
189. cense file which will contain the user or target encryption key Once a file has been encrypted it cannot be decrypted any more The use of a PLICENSE parameter will specify the target or privacy license to be used as a user key for encrypting Decompression and encrypting is done on the fly into memory when reading the GAMS system files GAMS will recognize if a file is just plain text or compressed and or encrypted and will validate and process the files accordingly Finally all compressed and encrypted files are of course platform independent as any other GAMS input file H 2 A First Example The model TRNSPORT from the GAMS model library will be used to illustrate the creation of a compressed input file First we will copy the model from the GAMS model and create a compressed version Spaces are recognized as separators between the source and target file names which means you have to use quotes single or double if the filenames contain spaces gt gamslib trnsport gt echo compress trnsport gms t1 gms gt t2 gms gt gams t2 Compress Source C support 28Dec trnsport gms Compress Target C support 28Dec t1 gms gms Compress Time Omsec Now we can treat the compressed input files like any other GAMS input file and the listing files will be identical because the decompressed input is echoed just like any normal input line 266 Compressed and Encrypted Input Files gt gams transport gt gams ti We can deco
190. clude file is as follows 1 myfile in current working directory 2 myfile gms in current working directory 3 myfile and myfile gms in that order in directories specified by idir parameter ts The current settings of the dollar control options are passed on to the lower level include files However the dollar control options set in the lower level include file are passed on to the parent file only if the onglobal option is set Compiler errors in include files have additional information about the name of the include file and the local line number At the end of the compiler listing an include file summary shows the context and type of include files The line number where an include file has been called is given For example in the Include File Summary below we see that SEQ GLOBAL TYPE PARENT LOCAL FILENAME 1 1 INPUT 0 0 C TEST TEST1 GMS 2 1 INCLUDE i 1 C TEST FILE1 INC 3 6 INCLUDE 1 4 C TEST FILE2 INC The first column named SEQ gives the sequence number of the input files encountered The first row always refers the parent file called by the GAMS call The second column named GLOBAL gives the global expanded line number which contained the include statement The third column named TYPE refers to the type of file being referenced The various types of files are INPUT INCLUDE BATINCLUDE LIBINCLUDE and SYSINCLUDE The fourth column named PARENT provides the sequence number of the parent file for the file being reference
191. control line An alternative to placing new_input_line on the same line as the conditional is to leave the remainder of the line blank and place new_input_line on the line immediately following the if line If the conditional is found to be false either the remainder of the line if any is skipped or the next line is not read Consider the following example if exist myfile dat include myfile dat The statement above includes the file myfile dat if the file exists Note that the character at the beginning of the include option is the first non blank character after the conditional expression if exist myfile dat and is therefore treated as the first column position The above statement can also be written as if exist myfile dat include myfile dat Consider the following additional examples if not 1a a goto labelname if not exist 41 display file 1 not found The first statement illustrates the use of the if option inside a batch include file where parameters are passed through the batinclude call from the parent file The if condition checks if the parameter is empty and if not processes the goto option Note that the string comparison attempted fla a can also be done using 1 The second statement illustrates using standard GAMS statements if the conditional is valid If the file name passed as a parameter through the batinclude call does not exist the GAMS display statement is processed t In line
192. costs in thousands of dollars positive variable x equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j model transport all All comments have been removed from TRNSPORT for brevity Running this model and saving the work files through the save parameter leads to the generation of eight work files The second file say trans2 gms generated from TRNSPORT looks as follows solve transport using lp minimizing z display x 1 x m One can then run trans2 gms restarting from the saved work files generated from running trans1 gms The result obtained is equivalent to running TRNSPORT t In order to use the dumpopt parameter effectively it is required that the first line in the restart file is the solve statement To illustrate the use of the dumpopt option run the second model using the following command gams trans2 r trans dumpopt 1 where trans is the name of the saved files generated through the save parameter from transi gms A new file trans2 dmp is created as a result of this call and looks as follows This file was written with DUMPOPT 1 at 11 30 11 08 43 06 INPUT DUMP RESTART C Fred GAMS options test trnsport2 gms C Fred GAMS options test trnsport2 dmp C Fred GAMS options test trans1
193. ct dollar control option 211 GAMS option 247 else dollar control option 211 elself dollar control option 211 elselfE dollar control option 211 elselfI dollar control option 211 emp GAMS call parameter 183 EMP model type 16 80 encrypt 265 dollar control option 211 end of line 31 48 endlf dollar control option 211 endogenous 170 arguments 76 302 INDEX entropy function 58 eolcom dollar control option 211 eolonly GAMS call parameter 183 eps a reserved word 30 definition 65 used with variables 104 eq a relational operator 109 equation 170 indexed 75 listing 97 scalar 75 equation declaration 73 example 73 74 syntax 73 equation definition arithmetic operators 76 functions 76 preventing undefined operations 76 syntax 74 errmsg GAMS call parameter 183 errnam GAMS call parameter 184 error dollar control option 211 GAMS call parameter 184 handling 65 no solution 100 other 102 reporting 105 reporting compilation 105 reporting compilation time errors 106 reporting execution errors 107 reporting solve errors 107 setup failure 102 unknown 100 errorf function 58 errorLevel function 61 errorlog GAMS call parameter 184 escape dollar control option 212 etlim GAMS call parameter 184 eval dollar control option 212 evalGlobal dollar control option 213 evalLocal dollar control option 213 evaluation error limit 102 exception handling
194. ctories will cause errors t Note that if the sdir parameter is set the default system include directory is not searched Consider the following illustration gams myfile sdir mydir GAMS searches for any referenced sysinclude file in the directory mydir sysout sysout 0 expand solution output This option controls the printing of the solver status file as part of the listing file The contents of the solver status file are useful if you are interested in the behavior of the solver If the solver crashes or encounters any difficulty the contents of the solver status file will be automatically sent to the listing file Values O suppress additional solver generated output 1 include additional solver generated output tabin tabin 8 tab spacing This option sets the tab spacing By default tabs are not allowed in GAMS However the most common setting is 8 which results in the positions of the tabs corresponding to columns 1 9 17 and the intermediate columns being replaced by blanks C 3 Detailed Description of Command Line Parameters 201 Values O tabs are not allowed 1 tabs are replaced by blanks n tabs are 1 n 1 2n 1 tformat tf 0 time format This option controls the time format in the listing file The three date formats correspond to the various con ventions used around the world For example the time 7 45 PM will be written as 19 45 00 with the default tf value of 0 and as 19 45 00 with tf 1 Values O hh mm
195. d The fifth column named LOCAL gives the local line number in the parent file D 3 Detailed Description of Dollar Control Options 219 where the include appeared In the example listed above the include files file1 inc and file2 inc were included on lines 1 and 4 of the parent file test1 gms inlinecom This option redefines the in line comment symbols which are a pair of one or two character sequence By default the system is initialized to and but is not active The oninline option is used to activate the in line comments The inlinecom option sets the oninline automatically Consider the following example inlinecom set this is an inline comment i 1 2 The character pair serves as the indicator for in line comments t GAMS requires that one not reset the inlinecom option to an existing symbol The following code is illegal since inlinecom is being reset to the same symbol as it is currently inlinecom inlinecom t The onnestcom enables the use of nested comments kill Removes all data for an identifier and resets the identifier only the type and dimension are retained Note that this is carried out during compile time and not when the GAMS program executes Not all data types can be killed only set parameter equation and variable types can be reset Consider the following example set i 1 20 scalar a 2 kill ia Note that this is different from clear in t
196. d Solve Statements s oc ke a EEE a A Display Statements s lt ae Ree ee we a ee Ae ew Pw er A The Io ly A DE DAS ce a Ae ee RRS REG De ee Eee Ee 2 10 1 Assignment of Variable Bounds and or Initial Values o o 2 10 2 Transformation and Display of Optimal Values gt s sea oa ses sead neau a dua CPS COMPE E a Se a he a a E AAA a A a 2AL Ee PINS ees sa ga A AAA a a Ek A e aA Ede oe 211 2 Error Messages rato A a a ea a a A SUL AORTA pi sas noda ea ea da BS ak RIA a eee a a 2 114 Equation Listings oe 22024 ee oa a a oa E a aean A at a BUS Model Staol ra ise A A a a G o la da a e a 2110 Statua Repais e peca wa a ee Bee A aoa a ha E a ek ee ZAS Ola REPOTI re du A a kA a E AA A A ie ea es he ee ee oe ee we ae EO wh ree Ge es 3 GAMS Programs 3 1 a2 Tatro iGO 6 oes a Bek ee ho ee Gee Be es A ee a eee Be Go The Structure of GAMS Programs 2 66 44 A RA Oe RE iriri SN ee ee S20 Format or CAMS DOUE oc ek ee A ee Be Re a ee eee ees 32 2 Classification of GAMS Statements o arada na ea EE EnG TABLE OF CONTENTS 3 2 0 Organization of GAMS Programs o 0 e sa ee 28 oan Data Types and Detinitiows lt lt dss sa a e A 29 oe Language tems 0 nek A A A A ARA 29 3l Characters AAA 30 SL Reserved Words eses sea adorons dadd duio e pi ali e ee eee ee a 30 sdo Idanha NN 30 GA Labels coso de ekinera e ka a aea a a E ee ee a eA a E 31 DO MI a A E a e Ww Oe Eos A aie a i E a 31 se NOMP o pu ceed
197. d be used to set to a low value while debugging the input file Values O no error limit n stop after n errors charset charset 1 extended character set Values O use limited GAMS characters set 1 accept any character in comments and text items foreign language characters cns cns text default CNS solver curdir curdir tezt set current directory This option sets the current directory It is useful when GAMS is called from an external system like Visual Basic If not specified it will be set to the directory the GAMS module is called from C 3 Detailed Description of Command Line Parameters 181 dformat df 0 date format This option controls the date format in the listing file The three date formats correspond to the various con ventions used around the world For example the date December 2 1996 will be written as 12 02 96 with the default df value of 0 as 02 12 96 with df 1 and as 96 12 02 with df 2 Values 0 mm dd yy 1 dd mm yy 2 yy mm dd dnlp dnlp tewt default DNLP solver domlim domlim 0 domain error limit This controls the maximum number of domain errors undefined operations like division by zero a nonlinear solver will perform while calculating function and derivative values before it terminates the run Nonlinear solvers have difficulty recovering after attempting an undefined operation dumpopt dumpopt 0 workfile dump option This option creates a GAMS file of input that will reproduce resul
198. d into one of two groups gt declaration and definition statements or gt execution statements A declaration statement describes the class of symbol Often initial values are provided in a declaration and then it may be called a definition The specification of symbolic relationships for an equation is a definition The declaration and definition statements are acronym parameter equation declaration set scalar equation definition alias table model variable Execution statements are instructions to carry out actions such as data transformation model solution and report generation The execution statements are option display solve assignment abort loop for while repeat execute Although there is great freedom about the order in which statements can be placed in a GAMS program certain orders are commonly used The two most common arrangements are discussed in the next sub section 3 2 3 Organization of GAMS Programs The two most common ways of organizing GAMS programs are shown in table 3 1 The first style places the data first followed by the model and then the solution statements In this style of organization the sets are placed first Then the data are specified with parameter scalar and table statements Next the model is defined with the variable equation declaration equation definition and model statement Finally the model is solved and the results are displayed A second style emphasizes the model by placing it
199. d of file on the include file However if you encounter a stop in an include file GAMS will stop reading all input sysInclude Equivalent to bat Include sysinclude file argl arg2 However if an incomplete path is given the file name is completed using the system include directory By default the system include directory is set to the GAMS system directory The default directory can be reset with the sdir command line parameter Consider the following example sysinclude abc x y This call first looks for the include file GAMS System Directory abc and if this file does not exist looks for GAMS System Directory abc gms The arguments x and y are passed on to the include file to interpret as explained for the batinclude option Consider the following example sysinclude c abc myinc inc x y This call first looks specifically for the include file c abc myfile inc terminate terminate terminates compilation and execution immediately title This option sets the title in the page header of the listing file to text which follows immediately the keyword title The next output line will appear on a new page in the listing file Consider the following example title Production Planning Model stitle Set Definitions unload This dollar command unloads specified items to a GDX file It is employed using the syntax unload iteml item2 but must be used in conjunction with the command gdxOut unload must be procee
200. d prioritizes them when using ife or if D 3 Detailed Description of Dollar Control Options 239 Consider the following example ple setglobal notunique aa setlocal notunique bb set notunique cc if notunique aa display it is aa if notunique bb display it is bb if notunique cc display it is cc The resulting listing file contains E 5 it is bb setLocal Establishes or redefines contents of a control variable that is accessible only in the code module where defined The syntax is setLocal varname expression where varname is any user chosen variable name and expression is optional and can contain text or a number These variables are destroyed using droplocal varname In contrast to evalLocal the setLocal command does not evaluate the expression at compile time For differences to set and setGlobal check the example in the description of set Note that GAMS allows one to define scoped local and global variables with the same name but treats them as different under some cases and prioritizes them when using ife or if Consider the following example ple setglobal notunique aa setlocal notunique bb set notunique cc if notunique aa display it is aa if notunique bb display it is bb if notunique cc display it is cc The resulting listing file contains zasa 5 it is bb setNames Establishes or redefines three control variables so they contain th
201. d too many iterations Use option iterlim to increase the iteration limit if everything seems normal 3 RESOURCE INTERRUPT This means that the solver was interrupted because it used too much time Use option reslim to increase the time limit if everything seems normal 4 TERMINATED BY SOLVER This means that the solver encountered difficulty and was unable to continue More detail will appear following the message 5 EVALUATION ERROR LIMIT Too many evaluations of nonlinear terms at undefined values You should use variable bounds to prevent forbidden operations such as division by zero The rows in which the errors occur are listed just before the solution 6 CAPABILITY PROBLEMS The solver does not have the capability required by the model for example some solvers do not support certain types of discrete variables or support a more limited set of functions than other solvers 7 LICENSING PROBLEMS The solver cannot find the appropriate license key needed to use a specific subsolver 8 USER INTERRUPT The user has sent a message to interrupt the solver via the interrupt button in the IDE or sending a Control C from a command line 9 ERROR SETUP FAILURE The solver encountered a fatal failure during problem set up time 10 ERROR SOLVER FAILURE The solver encountered a fatal error 11 ERROR INTERNAL SOLVER FAILURE The solver encountered an internal fatal error 12 SOLVE PROCESSING SKIPPED The entire solve step has been skipped This
202. d users will make errors GAMS attempts to catch the errors as soon as possible and to minimize their consequences 2 11 1 Echo Prints Whether or not errors prevent your optimization problem from being solved the first section of output from a GAMS run is an echo or copy of your input file For the sake of future reference GAMS puts line numbers on the left hand side of the echo For our transportation example which luckily contained no errors the echo print is as follows 3 Sets 4 i canning plants seattle san diego 5 j markets new york chicago topeka 6 7 Parameters 8 9 a i capacity of plant i in cases 10 seattle 350 11 san diego 600 12 13 b j demand at market j in cases 14 new york 325 15 chicago 300 16 topeka 275 17 18 Table d i j distance in thousands of miles 19 new york chicago topeka 20 seattle 2 5 La 1 8 2 11 GAMS Output 19 21 san diego 2 5 1 8 1 4 22 23 Scalar f freight in dollars per case per thousand miles 90 24 25 Parameter c i j transport cost in thousands of dollars per case 26 27 c i j f d i j 1000 28 29 Variables 30 x i j shipment quantities in cases 31 Zz total transportation costs in thousands of dollars 32 33 Positive Variable x 34 35 Equations 36 cost define objective function 37 supply i observe supply limit at plant i 38 demand j satisfy demand at market j 39 40 cost z e sum i j c i j x i j 41
203. ded and succeeded by a gdx0ut The proceeding gdxOut specifies the GDX file name and opens the file The succeeding gdx0ut closes the file More than one unload can appear in between Consider the following slice of code 242 Dollar Control Options Sets i canning plants seattle san diego j markets new york chicago topeka Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 Table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 gdxout tran unload i j unload b dem a sup unload d gdxout This will create a file tran gdx containing i j d and parameters a and b which are now declared as dem and sup use205 This option sets the GAMS syntax to that of Release 2 05 This is mainly used for backward compatibility New keywords have been introduced in the GAMS language since Release 2 05 Models developed earlier that use identifiers that have since become keywords will cause errors when run with the latest version of GAMS This option will allow one to run such models Consider the following example use205 set if 1 2 3 scalar x The word if is a keyword in GAMS introduced with the first version of Release 2 25 The setting of the use205 option allows if to be used as an identifier since it was not a keyword in Release 2 05 use225 This opti
204. definitions 8 3 1 The Syntax The syntax in GAMS for defining an equation is as follows eqn_name domain_list expression eqn_type expression Eqn _name is the name of the equation as in the equation declaration The two dots are always required between the equation name and start of the algebra The expressions in the equation definition can be of the forms discussed in the Chapters before but can involve variables as well Eqn_type refers to the symbol between the two expressions that form the equation and can be of the following types e Equality rhs must equal lhs g Greater than lhs must be greater than or equal to rhs 1 Less than lhs must be less than or equal to rhs n No relationships enforced between lhs and rhs This equation type is rarely used x External equation Only supported by selected solvers c Conic constraint Only supported by selected solvers ts As with the assignment statement equation definitions can be carried over as many lines of input as needed Blanks can be inserted to improve readability and expressions can be arbitrarily complicated t An equation once defined can not be altered or re defined If one needs to change the logic a new equation with a new name will have to be defined It is possible however to change the meaning of an equation by changing the data it uses or by using exception handling mechanisms dollar operations built into the definition 8 3 2 An Illust
205. del MARCO Because of pollution control one of the key parameters in oil refinery models is an upper bound on the sulfur content of the fuel oil produced by the refinery In this example the upper bound on the sulfur content of the fuel oil produced in the refinery In this example the upper bound on the sulfur content of fuel oil was set at 3 5 percent in the original data for the problem First the model is solved with this value Next a slightly lower value of 3 4 percent is used and the model is solved again Finally the considerably higher value of 5 percent is used and the model is solved for the last time After each solve key solution values the activity levels are associated with z the process levels by process p and by crude oil type cr are saved for later reporting This is necessary because a following solve replaces any existing values The complete sequence is parameter report process level report qs upper fuel oil sulfur 3 5 solve oil using lp maximizing phi report cr p base z 1 cr p report sulfur limit base qs upper fuel oil sulfur qs upper fuel oil sulfur 3 4 solve oil using lp maximizing phi report cr p one z l cr p report sulfur limit one qs upper fuel oil sulfur qs upper fuel oil sulfur 5 0 solve oil using lp maximizing phi
206. departments that sell items supplied by bic Note that the dynamic set is used to limit the domain of summation to those for which supply item bic is true 12 3 3 Equations Dynamic sets can be used inside dollar conditions in equations both as part of the equation algebra or while defining the domain of the equation The first case is similar to the case of assignments discussed in Section 12 3 1 The latter case is used to restrict the equation over the domain of a dynamic set The equation defined in the example from Section 12 2 5 can be rewritten with equivalent effect as follows 12 4 Set Operations 123 prodbal allr r allr activity allr price e revenue allr The domain of definition of equation prodbal is restricted to those elements that belong to the dynamic set r 12 3 4 Filtering through Dynamic Sets The filtering process explained in previous sections is valid when the conditional set is a dynamic one Consider the following two examples as described before inventory item subitemi item 25 prodbal allr r allr activity allr price e revenue allr These statements can be rewritten as inventory subitem1 25 prodbal r activity r price e revenue r 12 4 Set Operations This section describes how various symbolic set operations can be performed in GAMS using dynamic sets The Union Intersection Complement and Difference set operations are described individually in the following
207. development of algorithms and computer codes to solve large mathematical programming problems The number of applications of these tools in the 1970s was less then expected however because the solution procedures formed only a small part of the overall modeling effort A large part of the time required to develop a model involved data preparation and transformation and report preparation Each model required many hours of analyst and programming time to organize the data and write the programs that would transform the data into the form required by the mathematical programming optimizers Furthermore it was difficult to detect and eliminate errors because the programs that performed the data operations were only accessible to the specialist who wrote them and not to the analysts in charge of the project GAMS was developed to improve on this situation by gt Providing a high level language for the compact representation of large and complex models gt Allowing changes to be made in model specifications simply and safely gt Allowing unambiguous statements of algebraic relationships gt Permitting model descriptions that are independent of solution algorithms 1 2 Basic Features of GAMS 1 2 1 General Principles The design of GAMS has incorporated ideas drawn from relational database theory and mathematical program ming and has attempted to merge these ideas to suit the needs of strategic modelers Relational database theory provides a struct
208. ding is determined by the field width Default value is 1 0e 5 The maximum size of a displayed number must fit within 20 spaces using at most 10 significant digits The remaining 10 spaces are used for the sign exponential notation or padding with zeros 15 12 1 Illustrative Example The following illustrative example shows the results of different combinations of these numeric file suffixes The example uses five combinations of the numeric file suffixes nd nz nr and nw Four number values each of which is shifted by three decimal places from its predecessor are used with these suffix combinations The com binations are chosen to show various format results when these suffix values are used together in put statements set c suffix combinations combi comb4 value indices valuei value3 table suffix c numeric suffix combinations nd nz nr nw comb1 3 0 0 12 comb2 3 le 5 0 12 comb3 3 le 5 1 12 comb4 8 0 0 10 comb5 6 le 5 2 12 parameter value v test values valuel 123 4567 value2 0 1234567 value3 0 0001234567 file out put out out nj 2 out lw 10 out cc 11 loop v put v t1 21 loop c out nd suffix c nd out nz suffix c nz out nr suffix c nr out nw suffix c nw put c tl loop v put ord v 21 10 value v For readability the numeric values have purposely been made left justified using the nj suffix since the numeric field width is changed as the model goes through t
209. distribution specified by location and scale parameter Normal distribution specified by given mean and stan dard deviation Pareto distribution specified by shape and scale param eter Student s t distribution specified by degrees of freedom Triangular distribution specified by lower and upper limit and mid value Uniform distribution specified by the given bounds Weibull distribution specified by scale and shape param eter Note that the use of sampleLSweibull A B is equivalent to the use of dWeibull B A from the stochastic library deb Discrete distributions binomial N P SAMSIZE VARRED hypergeo TOTAL GOOD TRIALS SAMSIZE VARRED logarithmic P FACTOR SAMSIZE VARRED negbinomial SUCC P SAMSIZE VARRED Binomial distribution specified by number of trials N and success probability P in each trial Hypergeometric distribution specified by total number of elements number of good elements and number of trials Logarithmic distribution specified by P Factor Note that sampleLSlogarithmic uses another version of the logarithmic distribution than dLogarithmic from the stochastic library J 4 Negative Binomial distribution specified by the number of successes and the probability of success The gener ated random number describes the number of failures until we reached the defined number of successes Note that the use of sampleLSnegbinomial R P is equiv alent to the use of dNegBinomia
210. distribution with location parameter LOCATION and scale parameter SCALE see MathWorld Normal distribution with mean MEAN and standard deviation STD_DEV see MathWorld Pareto distribution with scaling parameter SCALE and shape parameter SHAPE see MathWorld Rayleigh distribution with parameter SIGMA see MathWorld Student s t distribution with degrees of freedom DF see MathWorld Triangular distribution between LOW and HIGH MID is the most probable number see MathWorld Uniform distribution between LOW and HIGH see MathWorld Weibull distribution with shape parameter SHAPE and scaling parameter SCALE see MathWorld 282 Extrinsic Functions Discrete distributions binomial N P geometric P hyperGeo TOTAL GOOD TRIALS logarithmic P FACTOR negBinomial FAILURES P poisson LAMBDA uniformInt LOW HIGH Binomial distribution with number of trials N and success probability P in each trial see MathWorld Geometric distribution with success probability P in each trial see Math World Hypergeometric distribution with total number of elements TOTAL num ber of good elements GOOD and number of trials TRIALS see MathWorld Logarithmic distribution with parameter P FACTOR also called log series distribution see MathWorld Negative Binomial distribution with the number of failures until the ex periment is stopped FAILURES and success probability P in each trial The generated random number d
211. dn autumn sold autumn avail spring e prodn winter sold winter Note that none of the equations are suppressed 13 7 Summary This chapter introduced the concept of ordering in sets All the features in GAMS that dealt with this issue including the ord and card functions as well as the linear and circular forms of the lag and lead operators were described in detail 132 Sets as Sequences Ordered Sets 14 The Display Statement 14 1 Introduction In this chapter we will provide more detail about display statements including the controls that a user has over the layout and appearance of the output These controls are a compromise to provide some flexibility The display statement will not provide a publication quality reporting function but is instead aimed for functionality that is easy to use and provides graceful defaults The execution of the display statement allows the data to be written into the listing file only 14 2 The Syntax In general the syntax in GAMS for the display statement is display ident ref quoted text 1 ident ref quoted text Ident ref means the name without domain lists or driving indices of a set or parameter or a sub field of an equation or variable The identifier references and the text can be mixed and matched in any order and the whole statement can be continued over several lines The output produced by a display consists of labels and data For sets the character string ye
212. dollar operator An operator used for exceptions handling in assignment statements and in equation definitions domain checking The check that ensures that only legal label combination are used on every assignment to or reference of an identifier domain definition The label combinations whose data will be updated in an assignment statement or that will generate an individual constraint in an equation definition domain restriction condition The alteration to the domain of definition caused when a dollar operator is used on the left of the in an assignment or of the in an equation definition driving set The set that determine the domain of definition or that control and index operation such as sum dynamic set A set is dynamic if it has been changed with an assignment statement Dynamic sets cannot be used with lag operations or in domain definitions endogenous Data values that change when a solve statement is processed In GAMS most often associated with variables equation The GAMS data type used to specify required relationships between activity levels of variables execution The second phase of GAMS processing when GAMS is actually carrying out data transformations or generating a model execution statements Instructions to carry out actions such as data transformations model solutions and report generation Some examples are the assignment and the option display loop and solve statements exogenous Data val
213. dths justifications and horizontal cursor relocations are completely avoided All text items are quoted The following is the resulting output file 154 The Put Writing Facility CAPACITY tons AHMSA FUNDIDORA SICARTSA HYLSA HYLSAP BLAST FURNACES 3 25 1 40 1 10 0 00 0 00 OPEN HEARTH FURNACES 1 50 0 85 0 00 0 00 0 00 BASIC OXYGEN CONVERTERS 2 07 1 50 1 30 0 00 0 00 DIRECT REDUCTION UNITS 0 00 0 00 0 00 0 98 1 00 ELECTRIC ARC FURNACES 0 00 0 00 0 00 1 13 0 56 Notice that each item is delimited with a comma and that textual output is quoted 16 Programming Flow Control Features 16 1 Introduction The previous chapters have focused on the ability of GAMS to describe models This chapter will describe the various programming features available in GAMS to help the advanced user The various programming flow control features discussed in this chapter are Loop Statement If Else Statement For Statement While Statement Each of these statements will be discussed in detail in the following sections 16 2 The Loop Statement The loop statement is provided for cases when parallel assignments are not sufficient This happens most often when there is no analytic relationship between for example the values to be assigned to a parameter It is of course also useful to have a looping statement for general programming for example the production of reports with the put statement 16 2 1 The Syntax The s
214. dy to distribute the model gt gams si r p1 plicense target txt s target gt zip target target g00 G 6 Limitations and Future Requirements One of the design goals for secure work files has been to minimize the impact on other components of the GAMS system Solvers used out of a secure environment should work as if called out of a normal environment This 262 Secure Work Files implies that in principle certain information could be recovered if one has knowledge of GAMS solvers internals and is willing to expand considerable programming effort In this section we will discuss current limitations and possible extension to the security features The following limitations exist gt Solvers are not security aware and it would be possible to write a special GAMS solver that extracts information about a specific model instance Primal and duals values as well as first partial derivatives could be extracted and displayed gt The names and explanatory text of all GAMS symbols are retained in the work file and could be accessed by a special GAMS solver gt The source and target license files locked to the secure work file cannot be changed If the target user upgrades the GAMS system and receives a new license file the secure work file cannot be read any more G 7 Obfuscated Work Files Massive parallel operations often require solving models on computational grids or clouds outside a secure com puting environment GAMS offers a
215. e and the debugging output from the solution algorithm generated with sysout option set to on 17 3 2 Variable Scaling The scale factor on a variable Vs is used to relate the variable as seen by the user V to the variable as seen by the algorithm Va as follows Va Vi Vs For example consider the following equation positive variables x1 x2 equation eq eq 200 x1 0 5 x2 1 5 x1 up 0 01 x2 up 10 x1 scale 0 01 x2 scale 10 By setting x1 scale to 0 01 and x2 scale to 10 the model seen by the solver is positive variables xprime1 xprime2 equation eq eq 2 xprimel 5 xprime2 1 5 xprimel up 1 xprime2 up 1 Note that the solver does not see the variables x1 or x2 but rather the scaled and better behaved variables xprimel and xprime2 t Upper and lower bounds on variables are automatically scaled in the same way as the variable itself ts Integer and binary variables cannot be scaled 17 3 3 Equation Scaling Similarly the scale factor on an equation Gs is used to relate the equation as seen by the user Gu to the equation as seen by the algorithm Ga as follows Ga Gu Gs For example consider the following equations positive variables y1 y2 equation eqi eq2 eqi 200 y1 100 y2 1 500 eq2 3xy1 4 y2 g 6 By setting eq1 scale to 100 the model seen by the solver is positive variables y1 y2 equation eqprimel eq2 eqprimel 2 y1 1xy2 1 5
216. e ll 2 amount of line tracing to log file This option is used to limit the number of line tracing sent out to the log file during the compilation phase of a GAMS run Values of 0 and 1 are special Setting 11 0 will cause the line tracing to be suppressed for all phases of the GAMS processing Values O all line tracing suppressed 1 limited line tracing 2 full line tracing The log file that results from running TRNSPORT with the option 11 0 is shown below Starting compilation Starting execution elapsed 0 00 00 003 Generating LP model transport 6 rows 7 columns 19 non zeroes Executing CPLEX elapsed 0 00 00 007 IBM ILOG CPLEX Jul 14 2011 23 7 1 WEX 26779 26792 WEI x86_64 MS Windows Cplex 12 3 0 0 C 3 Detailed Description of Command Line Parameters 191 Reading data Starting Cplex Tried aggregator 1 time LP Presolve eliminated 1 rows and 1 columns Reduced LP has 5 rows 6 columns and 12 nonzeros Presolve time 0 00 sec Iteration Dual Objective In Variable Out Variable 1 73 125000 x seattle new york demand new york slack 2 119 025000 x seattle chicago demand chicago slack 3 153 675000 x san diego topeka demand topeka slack 4 153 675000 x san diego new york supply seattle slack LP status 1 optimal Optimal solution found Objective 153 675000 Restarting execution Reading solution for model transport Executing after solve elapsed 0 00 00 096 Status
217. e your existing GAMS projects will be preserved Choose the default solvers Run the GAMS IDE by double clicking gamside exe from the GAMS directory To view or edit the default solvers choose File gt Options Solvers from the IDE You can accept the existing defaults if you wish but most users want to select new default solvers for each model type Run a few models to test the GAMS system The on line help for the IDE Help gt GAMS IDE Help Topics gt Guided Tour describes how to copy a model from the GAMS model library run it and view the solution To test your installation run the following models from the GAMS model library LP trnsport objective value 153 675 NLP chenery objective value 1058 9 292 Installation and System Notes MIP bid optimal solution 15210109 512 MINLP procsel optimal solution 1 9231 MCP scarfmcp no objective function MPSGE scarfmge no objective function K 2 Command Line Use of GAMS Users wishing to use GAMS from the command line aka the console mode may want to perform the following steps These steps are not necessary to run GAMS via the IDE 1 We recommend to add the GAMS directory to your environment path in order to avoid having to type in an absolute path name each time you run GAMS Run the installer in advanced mode and mark the check box Add GAMS directory to PATH environment variable 2 Run the program gamsinst gamsinst is a command line program used
218. e 2 3 Variable Type Allowed Range of Variable free default oo to 00 positive 0 to 00 negative oo to 0 binary 0 or 1 integer 0 1 100 default Table 2 3 Permissible variable types The variable that serves as the quantity to be optimized must be a scalar and must be of the free type In our transportation example z is kept free by default but x i j is constrained to non negativity by the following statement Positive variable x Note that the domain of x should not be repeated in the type assignment All entries in the domain automatically have the same variable type Section 2 10 describes how to assign lower bounds upper bounds and initial values to variables 2 6 Equations The power of algebraic modeling languages like GAMS is most apparent in the creation of the equations and inequalities that comprise the model under construction This is because whenever a group of equations or inequalities has the same algebraic structure all the members of the group are created simultaneously not individually 2 6 Equations 13 2 6 1 Equation Declaration Equations must be declared and defined in separate statements The format of the declaration is the same as for other GAMS entities First comes the keyword Equations in this case followed by the name domain and text of one or more groups of equations or inequalities being declared Our transportation model contains the following equation declaration
219. e GAMS Model Library contains a more elaborate example that can be easily modified to test the use of compressed files This example will also show how to use the PLICENSE LICENSE parameter to test the creation and use without having a target license file available title Compressed Input Files CEFILES SEQ 317 ontext This model demonstrates the use of compressed input files Remember if the file names contain spaces you need to use single or double quotes around the file names o0fftext get model ondollar call gamslib q trnsport g q P compress and run model compress trnsport gms t1 gms decompress t1 gms ti org call diff trnsport gms tl org gt system nullfilef if errorlevel 1 abort files trsnport and t1 are different check to see if we get the same result H 4 The ENCRYPT GAMSLIB Model 267 call gams trnsport gdx trnsport lo gams lo if errorlevel 1 abort model trnsport failed call gams t1 gdx t1 lo gams 1o if errorlevel 1 abort model t1 failed call gdxdiff trnsport t1 system redirlog if errorlevel 1 abort results for trnsport and ti are not equal also works with include files echo include ti gms gt t2 gms call gams t2 gdx t2 lo gams lof if errorlevel 1 abort model t2 failed call gdxdiff trnsport t2 system redirlog if errorlevel 1 abort results for trnsport and t2 are not equal terminate H 4 The ENCRYPT GAMSLIB Model The ENCRYPT mode
220. e Windows version To install GAMS please follow the steps below as closely as possible We advise you to read this entire document before beginning the installation procedure Additionally a video on how to install GAMS on Mac OS X is available at https www youtube com watch v OLtvjcOZkTM 1 Obtain the GAMS distribution file which is available from http www gams com download in one large self extracting zip archive with a _sfx exe file extension e g osx_x64 64 sfx exe Check that it has the execute permission set If you are not sure how to do this just type in the command chmod 755 osx_x64_64_sfx exe Choose a location where you want to create the GAMS system directory the GAMS system directory is the directory where the GAMS system files should reside At this location the GAMS installer will create a subdirectory with a name that indicates the distribution of GAMS you are installing For example if you are installing the 24 3 distribution in Applications GAMS the installer will create the GAMS system directory Applications GAMS gams24 3_osx_x64_64 sfx If the directory where you want to install GAMS is not below your home directory you may need to have root privileges on the machine Create the directory that should contain the GAMS system directory for instance Applications GAMS Change to this directory cd Applications GAMS Make sure pwd returns the name of this directory correctly Run the distribution f
221. e are none the default LP solver will be used To activate use model_name trylinear 1 Default value is 0 The procedure also checks to see if QCP and DNLP models can be reduced to an LP MIQCP and MINLP can be solved as an MIP RMIQCP and RMINLP can be solved as an RMIP workFactor This attribute tells the solver how much workspace to allocate for problem x solution relative to the GAMS estimate workSpace This attribute tells the solver how much workspace in Megabytes to allo x cate for problem solution Table 9 1 Model Attributes mainly used before solve Model Attributes mainly used after solve Attribute Description domUsd Number of domain violations etAlg This attribute returns the elapsed time it took to execute the solve algorithm The time does not include the time to generate the model reading and writing of files etc The time is expressed in seconds of wall clock time etSolve This attribute returns the elapsed time it took to execute a solve statement in total This time includes the model generation time time to read and write files time to create the solution report and the time taken by the actual solve The time is expressed in seconds of wall clock time etSolver This attribute returns the elapsed time taken by the solver only This does not include the GAMS model generation time and time taken to report and load the solution back into the GAMS database The time is expressed
222. e drive subdirectory filename and extension of a file named with full path The syntax is setnames FILE filepath filename fileextension where FILE is any filename filepath is the name of a control variable that will contain the name of the subdirectory where the file is located filename is the name of a control variable that will contain the root name of the file and fileextension is the name of a control variable that will contain the extension of the file Consider the following example setnames d gams xxx txt filepath filename fileextension setglobal name filepath filename fileextension log name FILE is seperated into its three components placing d gams into filepath xxx into filename and txt into fileextension The three items can be recombined back into the original filename by using filepath filename fileextension as shown in the example shift The shift option is similar to the DOS batch shift operator It shifts the order of all parameters passed once to the left This effectively drops the lowest numbered parameter in the list Consider the following example scalar a b c a 1 batinclude inc inc abc display a b c where the batch include file inc inc is as follows 12 1 1 shift 12 1 1 5 The resulting listing file contains 1 scalar a b c a l_ BATINCLUDE C PROGRAM FILES GAMSIDE INC INC 3 b atil 6 cH b 1 6 display a b c 240 In the first statement in the include
223. e end user will have full control of the data and will be able to manipulate the number of elements in the set and the values of the various scalars parameters and tables The end user will run the model with the following command gams file2 r trans 256 The Save and Restart Feature G Secure Work Files G 1 Introduction When models are distributed to users other than the original developers or embedded in applications to be deployed by other developers issues of privacy security data integrity and ownership arise We may have to hide protect or purge some parts of the model before it can be released The information to be protected can be of numeric or symbolic nature For example Privacy A Social Accounting Matrix supplied by a Statistical Office is required in a general equilibrium model to be used by the Ministry of Finance The data from the statistical office needs to be protected for obvious privacy reasons and the model experiments are used to evaluate policy options that are highly confidential Most of the model structure is public most of the data however is private and model results need to be transformed in such a way as to prohibit the discovery of the original data Security Components of a model contain proprietary information that describes mathematically a chemical reaction The associated algebra and some of the data are considered of strategic importance and need to be hidden completely The final model howev
224. e file inc inc contains the lines ondollar hidden text inside include file The resulting listing file is as follows INCLUDE D GAMS INC INC 2 ondollar 3 hidden text inside include file INCLUDE D GAMS INC INC 7 ondollar 8 hidden text inside include file 9 hidden after second call to include file Note that the effect of the ondollar dollar control option inside the include file does not affect the parent file until onglobal is turned on The hidden text is then echoed to the listing file on off Include onInclude Controls the listing of the expanded include file name in the listing file Consider running the following slice of code D 3 Detailed Description of Dollar Control Options 229 include inc inc offinclude include inc inc where the file inc inc contains the line ondollar hidden text inside include file The resulting listing file is as follows INCLUDE D GAMS INC INC 2 ondollar 3 hidden text inside include file 6 ondollar 7 hidden text inside include file Note that the include file name is echoed the first time the include file is used However the include file name is not echoed after offinclude is set fonjoff Inline offInline Switch to control the use of in line comments By default the in line comment symbols are set to the two character pairs and but the processing is disabled These comments can span lines till the end of comment ch
225. e line work space allocated 0 04 MB provides the amount of memory used by the solver for the prob lem If the amount of memory the solver estimates that it needs is not available GAMS will return a message saying that not enough memory was allocated GAMS will also return the maximum amount of memory available on the machine The user can direct the solver to use less memory by entering a line containing the statement mymodel workspace xx were mymodel is the name of the model being solved as specified by the model state ment and xx is the amount of memory in Megabytes Note that the solver will attempt to solve the problem with xx MB of memory however it is not guaranteed to succeed since the problem may require more memory More information can be obtained for a successful run by entering a line containing the statement option sysout on in the program above the solve statement 10 5 6 The Solution Listing The next section of the listing file is a row by row then column by column listing of the solutions returned to GAMS by the solver program Each individual equation and variable is listed with four pieces of information This section of the listing file can be turned off by entering a line containing the statement option solprint off in the program above the solve statement The solution listing section from our example is shown below LOWER LEVEL UPPER MARGINAL EQU FSUM 1 000 1 000 1 000 13 529 EQU DMEAN 10 0
226. e of assignment statements is important for a variety of reasons Two common uses are for generating reports and for generating initial values for some variables based on the values of other variables The following examples adapted from CHENERY illustrate the use of variable attributes on the right hand side of assignment statements scalar cva total value added at current prices rva real value added cli cost of living index sum i v 1 i x 1 1 sum i p 1 i ynot i sum i ynot i cva cli cva cli rva display cli cva rva 7 5 Summary 71 As with parameters a variable must have some non default data values associated with it before one can use it in a display statement or on the right hand side of an assignment statement After a solve statement to be discussed later has been processed or if non default values have been set with an assignment statement this condition is satisfied ts The fx suffix is really just a shorthand for 1o and up and can therefore only be used only on the left hand side of an assignment statement 7 4 3 Displaying Variable Attributes When variables are used in display statements you must specify which of the six value fields should be displayed Appending the appropriate suffix to the variable name does this As before no domain specification can appear As an example we show how to display the level of phi and the level and the marginal values of v from MEXSS displa
227. e same file If the target label is not found in the current file and error is issued hidden This line will be ignored and will not be echoed to the listing file This option is used to enter information only relevant to the person manipulating the file Consider the following example hidden You need to edit the following lines if you want to hidden hidden 1 Change form a to b hidden 2 Expand the set The lines above serve as comments to the person who wrote the file However these comments will not be visible in the listing file and are therefore hidden from view hiddenCall hide hiddencall does the same as ca11 but makes sure that the statement is neither shown on the log nor the listing file hides the named items so they cannot be displayed or computed but still allows them to be used in model calculations commands when the solve statement is executed The syntax is hide iteml item2 or hide all In the first case the listed items are hidden and in the second case all items are hidden These restrictions can be removed with expose or purge Note that special license file is needed for this feature to work The if dollar control option provides the greatest amount of control over conditional processing of the input file s The syntax is similar to the IF statement of the DOS Batch language if not exist filename string1 string2 new_input_line The syntax allows for negating the conditional
228. e than one name 4 4 Subsets and Domain Checking It is often necessary to define sets whose members must all be members of some larger set The syntax is set set_ident1 set_ident2 where set_ident1 is a subset of the larger set set_ident2 For instance we may wish to define the sectors in an economic model following the style in CHENERY 4 5 Multi dimensional Sets 39 set i all sectors light ind foodtagr heavy ind services t i traded sectors light ind foodtagr heavy ind nt non traded sectors services Some types of economic activity for example exporting and importing may be logically restricted to a subset of all sectors In order to model the trade balance for example we need to know which sectors are traded and one obvious way is to list them explicitly as in the definition of the set t above The specification t i means that each member of the set t must also be a member of the set i GAMS will enforce this relationship which is called domain checking Obviously the order of declaration is important the membership of i must be known before t is declared for checking to be done There will be much more on this topic in succeeding chapters For now it is important to note that domain checking will find any spelling errors that might be made in establishing the members of the set t These would cause errors in the model if they went undetected It is legal but unwise to define a subset without re
229. e with case sensitive com pare ifThen elself structure with expression evalua tion ifThen elself structure with case insensitive com pare GDX operations gdxIn gdx0ut load loadDC loadDCM Environment drop dropEnv dropGlobal dropLocal escape eval evalLocal evalGlobal prefixPath open GDX file for input open GDX file for output load symbols from GDX file domain filtered load symbols from GDX file domain checked Load symbols from GDX file domain checked merge variables drop a scoped environment variable drop an OS environment variable drop a global environment variable drop a local environment variable define the escape symbol evaluates and defines a scoped environment vari able evaluates and defines a local environment vari able evaluates and defines a global environment vari able prefix the path environment variable Macro definitions macro offDotL of fExpand offLocal offMacro preprocessing macro definition do not assume l for variables in assignments do not expand macros when processing macro arguments limit local nesting to one do not recognize macros for expansion Compression and encrypting of source files compress decompress encrypt expose create compressed GAMS system file decompress a GAMS system file create encrypted GAMS system file remove all access control restrictions of fStrictSingleton onGlobal onMulti onOrder onRecurse o
230. eR ee RE RR ee eg 247 F The Save and Restart Feature 251 Fl Tatroduction o cierra a A a ee EEG we ee ew a a 251 F2 The Save end Restart Feature c o cc ec ee a ea ia ee ee ea A a ees 251 F21 Saving The Work Wild ecos eg 55244445464 Pew dee bebe PO Hee hd 252 F22 Restarting fromthe Work File 2 6 5655 e 6 MG kaag eaea sta a eS 252 F3 Ways in which a Work File is Useful 2 00444544 4h 5 62 Jee ede ee ewe eee es 253 F31 Separation ol Model end Data lt s sss ea eek ee eee A 253 F 3 2 Incremental Program Development ee 254 F 3 3 Tacking Sequences of Difficult Solves 2 0 0 0 0 0200 ee eee eee 255 EA Multiple Scenarios lt p es 24 6 5 rra RR A AA Se A 255 F35 The GAMS Runtime License o o ee ee Ra 255 G Secure Work Files 257 L Eg AE 257 G2 A ere te eee ee ee ae ee ee ee we ES 258 fy ECHES Work Pilea e o p op i d aa aone a a a a AOD EE a e aoa Be ek eG a ee ee a 259 GA Access Control Commands lt lt es ee a s osoena a ER a aa 259 G 5 Advanced Use of Access Control o so s scs e co na e ee 260 G6 Limitations and Future Requirements lt lt a a e Se eee a ees 261 GY Obmecsted Work Pales ca care we ss a a eae Ree e h a ea ee Ek eee ds 262 H Compressed and Encrypted Input Files 265 HL ra os s oea ea E NN 265 H2 A First Example gt ccsa co moo goe na ioe a Aaa a A e Bea a ee 265 Ho The GEFILES tramslily Made 0 ioe doni nae a AR ds 266 HA The ENCRYPT GAMSLIB Model c c0o 0 cos
231. eS 141 eat STE DUES a Sho eae A Sed a e ewe Doh ee eS ee a ee a 141 TABLE OF CONTENTS 154 2 Assigning Files ocioso sia a a vd oe dowd 141 lota Close a Fe ossu doada aa eh a ee A We E 142 44 Appendios tos File cronos aaoi aa OR ee a a aa RR 142 Ios Fase POr ici o ie a A a ca A a w 142 ie Pape a AI AN 143 15 6 1 Accessing Various Page Sections o e 144 O A a Moar ee i ee ee den ae Pe A ee ae a 144 15 7 Pesitionming the Cursor ana Page ioe raae aa ee sena g aoa Go a ee hm go Be 144 15 5 System DU IES ocs a 6 ka hee ded bea whee heed da Be Pe be bth daw 145 A AAA 145 legt Tes Ione oia co a a ee A a a eG 146 159 2 Numere Hems e ee a eb a a daa de a 147 15 9 8 pet Value hems ac ee AA rara Ree Re A e A a 147 15 10 Global Rem Formatting co ee era ds eh Gee RS See EO He a 147 15 10 1 Field Justificsti n lt sc co he ER EEA a ee eae bh eee ae De ee 147 WG A0S Fed Vadis 2 nue ge eh RHA ada ee ee ARG Se DRE RE RO ad PES 148 16 11 Local Mera Formatting ooa y Eaa a bw eo ee ee A ae ee Re gE eei 148 15 12 Additional Numeric Display Control ais cresa a AA 149 15 12 1 Mhustrative Example o e c iora eee ee ee Ee ee eet eda ee 149 io kursor Control ee be Poe ee we a es eee a ee 150 1513 1 Cusrent Cursor Columii i caca ke a a ee a RA a a a 150 15 132 Current Cursor ROW 464 62 44 44 26 6b A eee DER be eee td awa 151 15 133 Last Line Control o 2 6 6204 a eh Ree BEA ek AK RE Re Pe ows 151 1514 Paping Lemral son ks ee A
232. eaning in the execution of GAMS e g Execute_Load MyFileName sym GDXNameSym MyFileName as well as GDXNameSym are part of the string pool and cannot be changed Other than the changes in the string pool the obfuscated work file has all the capabilities of normal work file The indented use of such an obfuscated work file is the following We compile only a GAMS model into a named and an obfuscated work file gt gamslib trnsport gt gams trnsport a c s Onamed so Oobfuscated Now we move the obfuscated work file to a non secure machine and execute there gt echo Empty gt empty gms gt gams empty r Oobfuscated s lobfuscated We bring the new still obfuscated work file lobfuscated g00 with the results back to the safe machine and do a continued compilation with reporting and export The continued compilation restarts from the obfuscated work file with all the results but gets a second work file r Onamed with proper names through a new option RestartNamed rn gt echo execute_unload supply supply m gt unload gms gt gams unload r 10bfuscated rn Onamed G 7 Obfuscated Work Files 263 We take everything from the obfuscated work file but only read the string pool and the listing file title and subtitle from the file specified via rn We do the following checks to ensure that the named and obfuscated work files are consistent 1 number of labels and symbols must be identical 2 the size of the string pool
233. ed to over ride the global controls The next two sub sections will deal with each of these display controls in turn 136 The Display Statement 14 5 1 Global Display Controls The simplest of these options is the one controlling the number of digits shown after the decimal point It affects numbers appearing in all display output following the option statement unless changed for a specific identifier as shown below The general form of the statement is option decimals value where value is an integer between 0 and 8 If you use 0 the decimal point is suppressed as well The width of the number field does not change just the number of decimals but this may cause numbers which would normally be displayed in fixed to appear in E format i e with the exponent represented explicitly Consider the following extension to the example discussed in the previous section option decimals 1 display x GAMS has rounded or converted numbers to E format where necessary and the output is as follows SENA 12 PARAMETER X a four dimensional structure INDEX 1 first i ii one b 5 6 two a 2 9 2 873000E 2 two b 10 3 three b 6 3 INDEX 1 second i ii one a INF 1 0 one b 17 3 two a INF two b 19 8 14 5 2 Local Display Control It is often more useful to control the number of decimals for specific identifiers separately Using a statement whose general form can do this option ident d value Ident represent the name of a pa
234. efault justification and a field width of variable size with no decimals loop i put dist i 0 0 put Right justified comment gt 50 Center justified truncated comment lt gt 20 left justified scalar with a six space field width and two decimals put f lt 6 2 15 12 Additional Numeric Display Control 149 15 12 Additional Numeric Display Control In addition to the numeric field width and the numeric justification as mentioned in the previous section the following file suffixes can also be globally specified for numeric display number of decimals displayed nd Sets the number of decimals displayed for numeric items A value of 0 results in only the integer portion of a number being displayed The maximum value is 10 The default value is 2 numeric round format nr Allows one to display a numeric value in scientific notation which would otherwise be displayed as zero because of being smaller than the number of decimals allowed by the nd suffix This situation occurs when a number is smaller than the nd specification but is larger than the zero tolerance level set by nz In many situations it is important to know that these small values exist The default is 1 0 displayed in F or E format 1 rounded to fit fields 2 displayed in scientific notation numeric zero tolerance nz Sets the tolerance level for which a number will be rounded to zero for display purposes When it is set equal to zero roun
235. efined in a similar syntax to that used for a set 5 3 2 An Illustrative Examples The fragment below is adapted from MEXSS We also show the set definitions because they make the example clearer Set i steel plants hylsa monterrey hylsap puebla j markets mexico df monterrey guadalaja parameter dd j distribution of demand mexico df 55 guadalaja 15 5 4 Tables 47 The domain checking specification for dd means that there will be a vector of data associated with it one number corresponding to every member of the set j listed The numbers are specified along with the declaration in a format very reminiscent of the way we specified sets in this simple case a label followed by a blank separator and then a value Any of the legal number entry formats are allowable for the value The default data value is zero Since monterrey has been left out of the data list then the value associated with dd monterrey the market share in monterrey would be zero We can also put several data elements on a line separated by commas parameter a i seattle 350 san diego 600 b i seattle 2000 san diego 4500 As with sets commas are optional at end of line 5 3 3 Parameter Data for Higher Dimensions A parameter can have up to 20 dimensions The list oriented data initialization through the parameter statement can be easily extended to data of higher dimensionality The label that appears on each line
236. efore if an option statement comes between two solve statements the new values are assigned between the solves and thus apply only to the second one t The values associated with an option can be changed as often as necessary with the new value replacing the older one each time An example of a list of option statements is shown below 246 The Option Statement option profit 0 3 2 option eject iterlim 100 solprint off solve mymodel using lp maximizing profit display profit 1 input vali 5 3 option iterlim 50 solve mymodel using lp maximizing profit The option statement in the second line affects the display format of the identifier profit More details on this option can be found under the heading lt identifier gt in the following section The option on the second line has no value associated with it and serves to advance the output in the listing file to the next page The third line contains two options iterlim and solprint The values associated with the two options on the fourth line are of different types iterlim has an integer value while solprint requires a character string as a value Note also that the end of line and the comma serve as legal separators between two options The option iterlim serves to limit the number of iterations taken by the solver while attempting to solve the lp model mymodel After mymodel is solved for the first time some of the input data is changed and the model is
237. elationship between rhs and 1 is satisfied only if the constraint is feasible at the solution point Type lo up l e rhs rhs rhs 1 inf rhs rhs g rhs inf rhs n inf inf any Table 8 2 Subfield definitions for equations The meaning of the marginal value m in terms of the objective value is discussed in detail in most texts on mathematical programming The crude but useful definition is that it is the amount by which the objective function would change if the equation level were moved one unit 78 Equations 9 Model and Solve Statements 9 1 Introduction This chapter brings together all the concepts discussed in previous chapters by explaining how to specify a model and solve it 9 2 The Model Statement The model statement is used to collect equations into groups and to label them so that they can be solved The simplest form of the model statement uses the keyword all the model consists of all equations declared before the model statement is entered For most simple applications this is all you need to know about the model statement 9 2 1 The Syntax In general the syntax in GAMS for a model declaration is model s model_name text all eqn_name eqn_name model_name text all eqn_name eqn_name Model_name is the internal name of the model also called an identifier in GAMS The accompanying text is used to describe the set or element immediately preceding it Eqn_n
238. elim Controls whether data in table statements are in comma delimited format Consider running the following slice of code SETS PLANT PLANT LOCATIONS NEWYORK CHICAGO LOSANGLS MARKET DEMANDS MIAMI HOUSTON PORTLAND table dist plant market ondelim MIAMI HOUSTON PORTLAND D 3 Detailed Description of Dollar Control Options 225 NEWYORK 1300 1800 1100 CHICAGO 2200 1300 700 LOSANGLS 3700 2400 2500 offdelim display dist The resulting listing file contains 12 PARAMETER dist MIAMI HOUSTON PORTLAND NEWYORK 1300 000 1800 000 1100 000 CHICAGO 2200 000 1300 000 700 000 LOSANGLS 3700 000 2400 000 2500 000 onjoff Digit onDigit Controls the precision check on numbers Computers work with different internal precision Sometimes a GAMS problem has to be moved from a machine with higher precision to one with lower precision Instead of changing numbers with too much precision the offdigit tells GAMS to use as much precision as possible and ignore the rest of the number If the stated precision of a number exceeds the machine precision an error will be reported For most machines the precision is 16 digits Consider running the following slice of code parameter y toolarge 12345678901234 5678 offdigit ignored 12345678901234 5678 The resulting listing file contains 1 parameter y toolarge 12345678901234 5678 AK 103 3 ignored 12345678901234 5678 Error Messages 103 Too many digits in nu
239. ense LICENSE lo gams lof if errorlevel 1 abort encryption failed eolcom if NOT errorfree abort pending errors decompress t1 gms t1 org this has to fail if errorfree abort decompress did not fail clearerror execute original and encrypted model call gams trnsport gdx trnsport lo gams lo if errorlevel 1 abort model trnsport failed Although this reads license DEMO this license file is the one specified with plicense from the si call call gams t1 license DEMO gdx t1 lo gams lo if errorlevel 1 abort model t1 failed call gdxdiff trnsport t1 system redirlog 268 Compressed and Encrypted Input Files if errorlevel 1 abort results for trnsport and ti are not equal use the encrypted file as an include file onecho gt t2 gms offlisting this is hidden option limrow 0 limcol 0 solprint off include t1 gms onlisting this will show o0ffecho call gams t2 license DEMO lo gams lo if errorlevel 1 abort model t2 failed protect against viewing now we will show how to protect parts of an input file from viewing and extracting original source via the gams DUMPOPT parameter We just need to encrypt again encrypt new model call rm f t3 gms echo encrypt t2 gms t3 gms gt s1 gms call gams si license DEMO plicense LICENSE lo gams 1o if errorlevel 1 abort encryption failed call gams t3 license DEMO gdx t3 dumpopt 19 lo gams lo if error
240. ent from zero objective row or function Solver system require the specification of a row on for nonlinear systems a function whose value will be maximized or minimized GAMS users in contrast must specify a scalar variable 172 Glossary objective value The current value of the objective row or of the objective variable objective variable The variable specified in the solve statement optimal A feasible solution in which the objective value is the best possible option The statement that allows users to change the default actions or values in many different parts of the system ordered set A set is ordered if its content has been initialized with a set definition statement and the entry order of the individual elements of the set has the same partial order as the chronological order of the labels A set name alone on the left hand side of an assignment statement destroys the ordered property Lag and Ord operations rely on the relative position of the individual elements and therefore require ordered sets Ordered sets are by definition constant output A general name for the information produced by a computer program output file A disk file containing output A GAMS task produces one such file that can be inspected parameter A constant or group of constants that may be a scalar a vector or a matrix of two or more dimensions Of the six data types in GAMS problem type A model class that is dependent on functional form and spec
241. ent to having reached the end of file Consider the following example scalara a 5 display a exit a at5 display a The lines following the exit will not be compiled Note that there is a difference to stop If you have only one input file stop and exit will do the same thing If you are in an include file exit acts like an end of file on the include file However if you encounter a stop in an include file GAMS will stop reading all input expose removes all privacy restrictions from the named item or items The syntax is expose iteml item2 or expose all In the first case the privacy restrictions are removed only for the listed items and in the second case they are removed for all items One can set these privacy restrictions with hide or protect Note that a special license file is needed for this feature to work and that the expose only takes effect in subsequent restart files funcLibIn Function libraries are made available to a model using the compiler directive FuncLibIn lt InternalLibName gt lt ExternalLibName gt Similar to sets parameters variables and equations functions must be declared before they can be used Function lt InternalFuncName gt lt InternalLibName gt lt FuncName gt gdxIn This dollar command is used in a sequence to load specified items from a GDX file It is employed using the syntax gdxIn filename where filename gives the name of the GDX file with or
242. entifier of the subset j is written first This is followed with the labels for the subset j and the associated element text found in its domain that is the set i Notice the driving set j is used for the element text specification of the set i Since there was no set element text associated with the i5 element of set i the set element label was displayed again By placing the following before the last line out tf 0 The missing element text is now no longer replaced with the label text The resulting file out put file would now look like subset of sites i3 San Francisco i4 Los Angeles i5 15 10 Global Item Formatting 147 15 9 2 Numeric Items The syntax used for the display of numeric items is generally easier to work with To output a parameter only the identifier along with its index set as appropriate has to be used To output a variable or equation value the identifier is combined with one of the variable and equation suffixes The variable and equation suffixes are 1 level or marginal value lo lower bound m marginal or dual value prior priority scale scaling up upper bound 15 9 3 Set Value Items Set value items are easy to work with To output the set value only the identifier along with its index set has to be used In the example from Section 15 9 1 consider altering the loop statement to read loop i put i tl j i gt i te j The resulting output file looks like follows subset of si
243. ep of the solution process and will be read when calling execute_loadhandle 4 Place all standard GAMS solver interface files into the above instance directory 276 The GAMS Grid Computing Facility 5 Execute the submission wrapper called gmsgrid cmd under Windows or gmsgrid run under Unix These submission scripts are usually located in the GAMS system directory but are found via the current path if not found in the GAMS system directory The grid submission script gmsgrid cmd or gmsgrid run is called with three arguments needed to make a standard GAMS solver call 1 The solver executable file name 2 The solver control file name 3 The solver scratch directory The submission script then does the final submission to the operating system This final script will perform the following steps call the solver call a utility that will create the final gdx file gmsgrid gdx set the completion signal finished If we want to use the function handlesubmit we also have to create the gmsrerun cmd or gmsrerun run script which could later be used to resubmit the job For example the default submission script for Windows is shown below echo off gams grid submission script argl solver executable 2 control file 3 scratch directory gmscr_nx exe processes the solution and produces gmsgrid gdx note 3 will be the short name because START cannot handle spaces and or We could use the original and use s3 which wi
244. er Either single or double quotes can be used but the closing quote has to match the opening one A label quoted with double quotes can contain a single quote and vice versa Most experienced users avoid quoted labels because they can be tedious to enter and confusing to read There are a couple of special circumstances If one wants to make a label stand out then one can for instance put asterisks in it and indent it A more subtle example is that GAMS keywords can be used as labels if they are quoted If one needs to use labels like no ne or sum then they will have to be quoted Examples of quoted labels are gt TOTAL MATCH gt 104 INCR 12 FOOT LINE 1 t Labels do not have a value The label 1986 does not have the numerical value 1986 and the label 01 is different from the label 1 The rules for constructing identifiers and labels are shown in table 3 4 Identifiers Unquoted Labels Quoted Labels Number of Characters 63 63 63 Must Begin With A letter A letter or a number Any character Permitted Special Characters None or Characters Any but the starting quote Table 3 4 Rules for constructing identifiers and labels 3 4 5 Text Identifiers and simple labels can also be associated with a line of descriptive text This text is more than a comment it is retained by GAMS and is displayed whenever results are written for the identifier Text can be quoted or unquoted Quoted text can contain any c
245. er dollar directives known to GAMS at the end of the run that created them ts The work file is not machine specific it is portable between platforms For example a work file generated on a PC running Windows can be re used on a Sun machine running Solaris F 2 2 Restarting from the Work File Consider the following call gams file2 r trans GAMS reads the work file named trans g00 and regenerates the information stored in file1 gms Then file2 gms is run and the result is as if the two files were concatenated A restarted run also requires a continuation input file The restart does not alter work files They can be used repeatedly to continue a particular run many times possibly with many different continuation input files The most common mistake that occurs in using the save and restart feature is running GAMS on the same file twice so all the data and equation definitions get repeated which causes compilation errors during restart The following calls will cause errors F 3 Ways in which a Work File is Useful 253 gams trnsport s trans gams trnsport r trans In general definitions of data constructs should not be repeated either in the same file or across files used in the Save and Restart operation GAMS works as if the two files are actually concatenated In order to avoid any syntax problems one needs to understand the GAMS syntax regarding data entry By default GAMS requires that each data item be entered only once On
246. er will be used at different locations around the world Integrity Data integrity safeguards are needed to assure the proper functioning of a model Certain data and symbolic information needs to be protected from accidental changes that would compromise the operation of the model To address these issues access control at a symbol level and secure restart files have been added to the GAMS system Access Control The access to GAMS symbols like sets variables parameters and equations can be changed once with the compile time commands purge hide protect and expose Purge will remove any information associated with this symbol Hide will make the symbol and all its information invisible Protect prevents changes to information Expose will revert the symbol to its original state Secure Restart Files The GAMS licensing mechanism can be used to save a secure model in a secure work file A secure work file behaves like any other work file but is locked to a specific users license file A privacy license the license file of the target users is required to create a secure work file The content of a secure work file is disguised and protected against unauthorized access via the GAMS license mechanism A special license is required to set the access controls and to create a corresponding secure work file Reporting features have been added to allow audits and traces during generation and use of secure work files Work files are used
247. er directory Please remember if you want to install two different versions of GAMS they must be in separate directories If you choose to use the advanced mode the installer will also ask you for a name of a start menu folder if GAMS should be installed for all users if the GAMS directory should be added to the PATH environment variable and if a desktop icon should be created Copy the GAMS license file You will be asked for the GAMS license file gamslice txt during the installation If you are not sure or you have no a license file choose No license demo only when asked for the GAMS license options You can always do this later If no valid license file is found GAMS will still function in the demonstration mode but will only solve small problems All demonstration and student systems do not include a license file If you have a license file you wish to copy to the GAMS directory at this time answer Copy license file You will now be given the opportunity to browse the file system and find the license file gamslice txt When you have found the correct file choose open to perform the copy Instead of copying a license file you could also copy the content of that file to the clipboard If you have done this select Copy license text from clipboard Create a project file If this is the first installation of GAMS on your system the installation program will create a default GAMS project in a subdirectory of your documents folder Otherwis
248. er suffixes are identifier symbol text ts Displays the text associated with any identifier set element labels t1 Displays the individual element labels of a set set element text te index Displays the text associated with an element of a set Notice that the te suffix requires a driving index This driving index controls the set which will be displayed and does not necessarily have to be the same as the controlled set Often a subset of indices of the controlled set is used text fill tf Used to control the display of missing text for set elements 0 suppresses the fill of missing explanatory text with element names leaving blanks E results in blank entries when an element is referenced which does not exist and does the default fill otherwise default always fills empty explanatory text with the element name always fills the te output with the element names not using the defined explanatory text puts out the te as when 3 in quotes with comma separators same as 4 with periods as separators aor WwW HY same as 4 with blanks as separators The following example illustrates these ideas file out put out set i master set of sites il Seattle i2 Portland i3 San Francisco i4 Los Angeles i5 j subset of sites i3 id put j ts loop j put j tl i te j The resulting file out put will look like subset of sites i3 San Francisco i4 Los Angeles i5 i5 In this example the symbol text for the id
249. ermont maine corr r s north vermont maine south florida texas parameter y r income s income of each state florida 4 5 vermont 4 2 texas 6 4 maine 4 1 The set corr provides a correspondence to show which states belong to which regions The parameter income is the income of each state Y r can be calculated with this assignment statement y r sum s corr r s income s For each region r the summation over s is only over those pairs of r s for which corr r s exists Concep tually set existence is analogous to the Boolean value True or the arithmetic value not zero The effect is that only the contributions for vermont and maine are included in the total for north and south includes only texas and florida Note that the summation above can also be written as sum s income s corr r s but this form is not as easy to read as controlling the index of summation 11 6 Conditional Equations 117 11 5 1 Filtering Controlling Indices in Indexed Operations The controlling indices can in certain cases be filtered through the conditional set without the use of the dollar operator Consider the example described in that section The total cost of shipment is obtained through the following equation variable shipped i j totcost equation costequ cost totcost e sum i j ij i j shipcost i j shipped i j where shipped is the amount of material shipped
250. ers than across a row but to put extra labels on the row leads to a greater density of information The following example adapted from MARCO illustrates the use of tables with more than two dimensions Sets ci commodities intermediate naphtha naphtha dist distillate gas oil gas oil cr commodities crude oils mid c mid continent w tex west texas q attributes of intermediate products density sulfur table attrib ci cr q blending attributes density sulfur naphtha mid c 272 283 naphtha w tex 272 1 48 dist mid c 292 526 dist wotex 297 2 83 gas oil mid c 295 98 gas oil w tex 303 5 05 s The table attrib could also be laid out as shown below table attrib ci cr q blending attributes w tex density mid c density w tex sulfur mid c sulfur naphtha 272 272 1 48 283 dist 297 297 2 83 526 gas oil 303 303 5 05 98 5 4 5 Condensing Tables All the mechanisms using asterisks and parenthesized lists that were introduced in the discussion of sets are available here as well The following example shows how repeated columns or rows can be condensed with asterisks and lists in parentheses follows The set membership is not shown but can easily be inferred 50 Data Entry Parameters Scalars amp Tables table upgrade strat size tech small techi small tech2 medium techi medium tech2 strategy 1 05 05 05 05 strategy 2 2 2 2 2 strategy 3 2 2 2 2 strategy 4 2 52
251. ersion to version Every attempt is made to be backward compatible and ensure that all new GAMS systems are able to read save files generated by older GAMS systems However at certain versions we are forced to concede default incompatibility regarding save files not source files in order to protect efficiency The forcework option is used to force newer GAMS systems into translating and reading save files generated by older systems Values O no translation 1 try translation forlim forlim 2 1 GAMS looping limit This option specifies the maximum number of allowable executions of Control Structures involving a For While or Repeat before GAMS signals an execution error and terminates the control structure fsave fsave 0 force workfile to be written This option allows to save a file even in the face of execution or other errors How it works depends on the save option Values O workfile only written to file specified by save if no errors occur 1 workfile always written to file specified by save or if save is not present to a file made up by GAMS The option value 1 is mainly used by solvers that can be interrupted from the terminal g205 g205 0 GAMS version 2 05 backward compatability This option sets the level of the GAMS syntax This is mainly used for backward compatibility New key words have been introduced in the GAMS language since Release 2 05 Models developed earlier that use identifiers that have since become keyw
252. erstand the difference between the symbols and e The symbol is used only in direct assignments and the e symbol is used only in equation definitions These two contexts are very different A direct assignment gives a desired value to a parameter before the solver is called An equation definition also describes a desired relationship but it cannot be satisfied until after the solver is called It follows that equation definitions must contain variables and direct assignments must not 2 7 Objective Function 15 gt Variables can appear on the left or right hand side of an equation or both The same variable can appear in an equation more than once The GAMS processor will automatically convert the equation to its equivalent standard form variables on the left no duplicate appearances before calling the solver gt An equation definition can appear anywhere in the GAMS input provided the equation and all variables and parameters to which it refers are previously declared Note that it is permissible for a parameter appearing in the equation to be assigned or reassigned a value after the definition This is useful when doing multiple model runs with one GAMS input The equations need not be defined in the same order in which they are declared 2 7 Objective Function This is just a reminder that GAMS has no explicit entity called the objective function To specify the function to be optimized you must create a
253. escribes the number of successes until we reached the defined number of failures see MathWorld Poisson distribution with mean LAMBDA see MathWorld Integer Uniform distribution between LOW and HIGH see MathWorld Table J 3 Random number generators For each distribution in table J 3 the library offers four functions Function Endogenous Description Classifica tion d lt DistributionName gt none generates a random number pdf lt DistributionName gt cdf lt DistributionName gt icdf lt DistributionName gt DNLP none for discrete distributions probability density function DNLP none for discrete distributions cumulative distribution function DNLP none for discrete distributions inverse cumulative distribution func tion Table J 4 Distribution functions The function d lt DistributionName gt needs the arguments described in table J 3 The other functions get an additional argument at the first position The point to evaluate This parameter can be an endogenous variable The following table shows all fours functions for the Normal distribution J 5 LINDO Sampling Library 283 Function Endogenous Description Classifica tion dNormal MEAN STD_DEV none generates a random number with Normal distribution pd Normal x MEAN STD DEV DNLP probability density function for Normal distribution cdfNormal x MEAN STD_DEV DNLP cumulative distribution function for Normal distribution icdfNormal x MEAN ST
254. etail These parameters are in alphabetical order for easy reference In each of the following options an abbreviation and the default value if available are bracketed action a ce Processing option GAMS currently processes the input file in multiple passes The three passes in order are Compilation During this pass the file is compiled and syntax errors are checked for Data initialization statements like scalar parameter and table statements are also processed during this stage Execution During this stage all assignment statements are executed Model Generation During this stage the variables and equations involved in the model being solved are generated Values c compile only execute only ce compile and execute r restart g glue code generation gt trace report The a e setting can only be used during restart on files that have previously been compiled since models first need to be compiled before they can be executed appendexpand ae 1 append to expand file This option controls the manner of file opening of the expand file Values O reset expand file 1 append to expand file appendlog al 0 log file append option This option is used in conjunction with the lo 2 setting where the log from the GAMS run is redirected to a file Setting this option to 1 will ensure that the log file is appended to and not rewritten 180 The GAMS Call Values O reset log file 1 append to log file appendout ao 0 output li
255. f a subset in an indexed expression has already been shown to provide some ability to handle exceptions 11 2 Logical Conditions Logical conditions are special expressions that evaluate to a value of True or False Numerical Expressions can also serve as logical conditions Additionally GAMS provides for numerical relationship and logical operators that can be used to generate logical conditions The next four sub sections discuss these various building blocks that can be used to develop complex logical conditions 11 2 1 Numerical Expressions as Logical Conditions ts Numerical expressions can also serve as logical conditions a result of zero is treated as a logical value of False and a non zero result is treated as a logical value of True The following numerical expression can be used to illustrate this point 2 a 4 This expression results in a logical value of False when a is 2 because the expression numerically evaluates to 0 For all other values of a the expression results in a non zero value and therefore is equivalent to a logical value of True 11 2 2 Numerical Relationship Operators Numerical relationship operators compare two numerical expressions For completeness all numerical relationship operators are listed below lt lt strictly less than 110 Conditional Expressions Assignments and Equations le lt less than or equal to eq equal to ne lt gt not equal to ge gt greater than or equal to
256. ference to the larger set as is done above for the set nt If services were misspelled no error would be marked but the model would give incorrect results So we urge you to use domain checking whenever possible It catches errors and allows you to write models that are conceptually cleaner because logical relationships are made explicit This completes the discussion of sets in which the elements are simple This is sufficient for most GAMS appli cations however there are a variety of problems for which it is useful to have sets that are defined in terms of two or more other sets 4 5 Multi dimensional Sets It is often necessary to provide mappings between elements of different sets For this purpose GAMS allows the use of multi dimensional sets t GAMS allows sets with up to 20 dimensions The next two sub sections explain how to express one to one and many to many mappings between sets 4 5 1 One to one Mapping Consider a set whose elements are pairs A b d a c c e In this set there are three elements and each element consists of a pair of letters This kind of set is useful in many types of modeling As an illustrative example consider the world aluminum model ALUM where it is necessary to associate with each bauxite supplying country a port that is near to the bauxite mines The set of countries is set c countries jamaica haiti guyana brazil and the set of ports is set P ports kingston
257. file 1 is the first argument in the batinclude call and is interpreted in this case as a 2 is the second argument in the batinclude call and is interpreted as b This leads to the overall assignment being interpreted as b a 1 The shift option shifts the arguments to the left So now 1 is interpreted as b and 2 is interpreted as c This leads to the second assignment being interpreted as c b 1 The result of the display statement in the input file is therefore gt 6 PARAMETER A PARAMETER B PARAMETER C show Shows current values of the control variables plus a list of the macros Consider the following example set it 1 setlocal yy setglobal gg what include includ show where indlud gms is set inincs setlocal inincsl setglobal inincsg show The resulting listing file contains Level SetVal 1 inincsl 1 inincs 0 yy O it 0 gg 1 inincsg Level SetVal 0 yy O it 0 gg 1 inincsg Note that only the item defined as setglobal in the included file carries over single The lines following a single option will be echoed single spaced on the compiler listing This option is the default and is only useful as a switch to turn off the double option Consider the following example set i 1 2 scalar a 1 double set j 10 15 scalar b 2 single set k 5 10 scalar c 3 1 000 2 000 3 000 Type Text LOCAL SCOPED LOCAL SCOPED 1 GLOBAL what GLOBAL Type Text
258. files This is an extremely powerful feature that can reduce the time needed when several runs of the same model are being made with different data It may be clearer if the process is described in a different way Imagine taking a large GAMS program and running it producing one output file Then think of splitting the program into two pieces The first piece is run and the resulting work file is saved along with the resulting listing file Then the second piece is run after reading in the data from the work file saved previously A new listing file is generated for the second piece The content of the output that results is the same though slightly rearranged as the case when the large file was run Splitting the files allows one to interrupt a GAMS task and restart it later without loss of information Furthermore changes could be made or errors corrected to the later parts F 2 The Save and Restart Feature Using the save and restart command line parameters provides a mechanism to break up the compilation of a large input file into many components and stages Some of the reasons for using these features and running a model in pieces are explained in Section F 3 The next two sub sections explain the save and restart mechanisms in GAMS The save and restart command line parameters described in Appendix C are used for this purpose TRNSPORT is used for the purposes of illustration Consider the following file containing code extracted from this
259. from i to j and totcost is the total cost of all shipment The equation above can be written as cost totcost e sum ij shipcost ij shipped ij However if the original equation is expressed as cost totcost e sum i j ij i j factor congestfac j distance i j shipped i j Index j appears separately from i in congestfac j The equation then needs to be simplified as cost totcost e sum ij i j factor congestfac j distance ij shipped ij Note that the presence of j separately in the indexed expression necessitated the use of ij i j rather than ij 11 6 Conditional Equations The dollar operator is also used for exception handling in equations The next two subsections discuss the two main uses of dollar operators within equations within the body of an equation and over the domain of definition 11 6 1 Dollar Operators within the Algebra A dollar operator within an equation is analogous to the dollar control on the right of assignments as discussed in Section 11 4 2 and if one thinks of on the right as meaning on the right of the then the analogy is even closer An if else operation is implied as it was with assignments It is used to exclude parts of the definition from some of the generated constraints Consider the following example adapted from CHENERY mb i x i g y i e i m i t i The term is added to the right hand side of the equation only for those elements of i
260. g example libinclude abc x y 220 Dollar Control Options This call first looks for the include file GAMS System Directory inclib abc and if this file does not exist GAMS looks for the file GAMS System Directory inclib abc gms The arguments x and y are passed on to the include file to interpret as explained for the batinclude option Consider the following example libinclude c abc myinc inc x y This call first looks specifically for the include file c abc myfile inc The arguments x and y are passed on to the include file to interpret as explained for the batinclude option lines n load This option starts a new page in the listing file if less than n lines are available on the current page Consider the following example hidden Never split the first few lines of the following table lines 5 table io i j Transaction matrix This will ensure that if there are less than five lines available on the current page in the listing file before the next statement in this case the table statement is echoed to it the contents of this statement are echoed to a new page This dollar command loads specified items from a GDX file It is employed using the syntax load item1 item2 but must be used in conjunction with the command gdxIn e load must be preceded and succeeded by a gdxIn The preceding gdxIn specifies the GDX file name and opens the file The succeeding gdxIn closes the file More than one load can appea
261. g on the option value1 could be a character string an integer number or a real number For example consider the following commands to run TRNSPORT from the GAMS model library gams trnsport o myrun lst lo 2 gams trnsport o myrun 1lst lo 2 gams trnsport o myrun lst lo 2 gams trnsport o myrun lst lo 2 All the four commands above are equivalent and each directs the output listing to the file myrun 1st o is the name of the option and it is set to myrun 1st In addition in each case the log of the run is redirected to the file trnsport log 178 The GAMS Call C 2 List of Command Line Parameters The options available through the command line are grouped into the following functional categories affecting the specific GAMS run input file processing other files system settings output in listing file Table C 1 briefly describes the various options in each of the categories Section C 3 contains a reference list of all options available through the command line with detailed description for each Parameters controlling the specific GAMS run action processing options bratio basis acceptance threshold cerr sets compile time error limit domlim domain error limit dumpopt workfile dump option eolonly singe keyword value pair option errmsg error message option error parameter error message etlim elapsed time limit in seconds execmode limits on call execute put and echo commands forcework force workfile translation forlim GAMS loo
262. g relationships between the elements in different sets GAMS also uses a domain checking capability to help catch labeling inconsistencies and typographical errors made during the definition of related sets The discussion here has been limited to sets whose members are all specified as the set is being declared For many models this is all you need to know about sets Later we will discuss more complicated concepts such as 4 7 Summary 43 sets whose membership changes in different parts of the model assignment to sets and other set operations such as unions complements and intersections 44 Set Definitions 9 Data Entry Parameters Scalars amp Tables 5 1 Introduction One of the basic design paradigms of the GAMS language has been to use data in its most basic form which may be scalar list oriented or tables of two or more dimensions Based on this criterion three data types are introduced in this chapter Scalar Single scalar data entry Parameter List oriented data Table Table oriented data Must involve two or more dimensions Each of these data types will be explained in detail in the following sections ts Initialization of data can only be done once for parameters thereafter data must be modified with assignment statements 5 2 Scalars The scalar statement is used to declare and optionally initialize a GAMS parameter of dimensionality zero That means there are no associated sets and that there i
263. g to a File The put writing facility has the ability to append to or overwrite an existing file The file suffix ap determines which operation occurs The default suffix value 0 overwrites the existing file while the value 1 causes appending to the file Let s consider our report txt file to be an existing file Using the following statement appends output items to it class2 ap 1 Any items put into report txt will from that point on be added to the end of the existing file contents If the file had not existed the file would be created 15 5 Page Format The pages within files can also be structured using file suffixes to specify many attributes such as the printing format page size page width margins and the case which text is displayed in The following file suffixes can be used for formatting print control pc Used to specify the format of the external file The options 4 5 6 and 8 create delimited files which are especially useful when preparing output for the direct importation into other computer programs such as spreadsheets 0 Standard paging based on the current page size Partial pages are padded with blank lines Note that the bm file suffix is only functional when used with this print control option 1 FORTRAN page format This option places the numeral one in the first column of the first row of each page in the standard FORTRAN convention 2 Continuous page default This option is similar to pc option zero with
264. ge header replacing the default tile which just announces GAMS The following directives are used to display more information in the output file and we be discussed The text within the ontext offtext pair is listed without line numbers whereas comments starting with asterisks have line numbers shown Line numbers always refer to the physical line number in your input file t Dollar control directives are only listed if a directive to list them is enabled or if they contain errors Here is the rest of the echo print 10 11 Set i securities hardware software show biz t bills alias i j 10 3 Compilation Output 93 12 13 Scalar target target mean annual return on portfolio 10 14 lowyield yield of lowest yielding security 15 highrisk variance of highest security risk 16 17 Parameters mean i mean annual returns on individual securities 4 18 19 hardware 8 20 software 9 21 show biz 12 22 t bills 7 23 24 Table v i j variance covariance array squared annual return 25 26 hardware software show biz t bills 27 28 hardware 4 3 1 0 29 software 3 6 1 0 30 show biz t 1 10 0 31 t bills 0 o 0 0 32 33 lowyield smin i mean i 34 highrisk smax i v i i 35 display lowyield highrisk 36 37 Variables x i fraction of portfolio invested in asset i 38 variance variance of portfolio 39 40 Positive Variable x 41 42 Equations fsum fractions must add to 1 0 43 dmean definition
265. ght C 1987 2001 GAMS Development Licensee Target User Name Target User Company Restarting from a Secure Restart File created by xk Source User Name eK Source Company Name Starting continued compilation T3 GMS 5 1 Mb Note that the originator owner of the secure work file is mentioned by name on the log file A similar message is contained in the listing file gt type t3 1st EXECUTION TIME 0 000 SECONDS 1 1 Mb WIN201 124 k Secure Save Restart File Source Source User Name Source Company Name xkxk Secure Save Restart File Target Target User Name Target User Company A more detailed inspection of the listing file will show that the hidden variables and equations do not appear in the usual equation variable listings and the solution print The hidden items can only be accessed via a public exposed model and a solve statement In the following two sections we will describe secure work files and the access control commands in more detail G 3 Secure Work Files Secure Work Files control access to symbolic and numeric information and can only be read by a specific GAMS user The initial creation or additions to access control requires a special GAMS license Saving Secure Work Files without new access controls does not require a special GAMS license The creation or addition of access control is signaled by the use of the GAMS parameter PLICENSE which gives the name of a privacy license file The shortcut PLICENSE
266. h model_name attribute Some of the attributes are mainly used before the solve statement to provide information to GAMS or the solver link Others are set by GAMS or the solver link and hence are mainly used after a solve statement Moreover some of the input attributes can also be set globally via an option statement or the command line e g option reslim 10 gamsmodel gms reslim 10 Note that a model specific option takes presedence over the global setting and that a setting via an option statement takes presedence over via the command line parameter The complete list of model attributes is shown below The third and fourth column indicate whether there is also a global option and or a command line parameter Model Attributes mainly used before solve Attribute Description option command line bRatio Basis acceptance test A bratio of O accepts any basis and a bratio of 1 x x always rejects the basis cheat Cheat value Requires a new integer solution to be a given amount better than the current best integer solution Default value is 0 cutOff Cutoff value Occasionally used attribute that causes MIP solvers to delete parts of the branch and bound tree with an objective worse than the numerical value of the cutoff attribute dictFile Force writing of a dictionary file if dictfile gt 0 domLim Maximum number of domain errors This attribute allows errors to occur x X up to a given number during solution
267. h somehwere in the beginning it will also contain C somewhereelse anotherpath after the second line and the resulting listing file contains 1 C some path somehwere 3 C somewhereelse anotherpath C some path somehwere protect Freezes all values of the named parameters not allowing modification but still allowing their use in model calculation commands when models are set up in a privacy setting The syntax is protect item1 item2 or protect all where one can list multiple items to protect them The word all causes protection of all items These privacy restrictions can be removed with expose or purge purge removes the items and all data associated in a privacy setting The syntax is purge item1 item2 or purge all In the first case only the listed items are removed in the second case all items are removed One can set the corresponding privacy restrictions with hide or protect Note that a special license file is needed for this feature to work and that the removal only takes effect in the restart files remark set Adds a comment to the listing file with parameter substitution and suppressed line number Consider the following example set it TEST remark write it to the listing file The resulting listing file contains write TEST to the listing file Establishes or redefines contents of a control variable that is accessible in the code where the command appears and all code inc
268. happens if execution errors were encountered and the GAMS parameter ExeErr has been set to a nonzero value or the property MaxExecError has a nonzero value 13 ERROR SYSTEM FAILURE This indicates a completely unknown or unexpected error condition 10 5 5 Solver Report The next section in the listing file is the part of the solve summary that is particular to the solver program that has been used This section normally begins with a message identifying the solver and its authors MINOS was used in the example here There will also be diagnostic messages in plain language if anything unusual was detected and specific performance details as well some of them probably technical The Solver Manual will help explain these In case of serious trouble the GAMS listing file will contain additional messages printed by the solver This may help identify the cause of the difficulty If the solver messages do not help a perusal of the solver documentation or help from a more experienced user is recommended The solver report from our example follows 10 5 Output Produced by a Solve Statement 103 GAMS MINOS B A Murtagh University of New South Wales and P E Gill W Murray M A Saunders and M H Wright Systems Optimization Laboratory Stanford University Work space allocated 0 04 Mb EXIT OPTIMAL SOLUTION FOUND MAJOR ITNS LIMIT 11 200 FUNOBJ FUNCON CALLS 0 71 SUPERBASICS 4 INTERPRETER USAGE 0 02 NORM RG NORM PI 1 801E 09 Th
269. haracter except the quote character used Single or double quotes can be used but must match Text has to fit on one line and cannot exceed 80 characters in length Text used in unquoted form must follow a number of mild restrictions Unquoted text cannot start with a reserved word or and must not include semicolon commas or slashes End of lines terminate a text These restrictions are a direct consequence of the GAMS syntax and are usually followed naturally by the user Some examples are 32 GAMS Programs this is text final product shipment tpy quoted text containing otherwise illegal characters use single quotes to put a double quote in text 3 4 6 Numbers Numeric values are entered in a style similar to that used in other computer languages t Blanks can not be used in a number GAMS treats a blank as a separator The common distinction between real and integer data types does not exist in GAMS If a number is used without a decimal point it is still stored as a real number In addition GAMS uses an extended range arithmetic that contains special symbols for infinity INF negative infinity INF undefined UNDF epsilon EPS and not available NA One cannot enter UNDF it is only produced by an operation that does not have a proper result such as division by zero All the other special symbols can be entered and used as if they were ordinary numbers The follow
270. hat was previously implemented in MPS format To change the default number of specific column printouts per generic variable the above command can be extended option limrow r limcol c where c is the desired number of columns Setting limrow and limcol to 0 is a good way to save paper after your model has been debugged In nonlinear models the GAMS equation listing shows first order Taylor approximations of the nonlinear equa tions The approximations are taken at the starting values of the variables 2 11 5 Model Statistics The last section of output that GAMS produces before invoking the solver is a group of statistics about the model s size as shown below for the transportation example MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 6 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 7 NON ZERO ELEMENTS 19 The BLOCK counts refer to the number of generic equations and variables The SINGLE counts refer to individual rows and columns in the specific model instance being generated For nonlinear models some other statistics are given to describe the degree of non linearity in the problem 2 11 6 Status Reports After the solver executes GAMS prints out a brief solve summary whose two most important entries are SOLVER STATUS and the MODEL STATUS For our transportation problem the solve summary is as follows SOLVE SUMMARY MODEL TRANSPORT OBJECTIVE Z TYPE LP DIRECTION MINIMIZE SOLVER BDMLP FROM LINE 49 xx SOLVER STAT
271. he Syntax The syntax is for i start toldownto end by incr statements Note that i is not a set but a parameter Start and end are the start and end and incr is the increment by which i is changed after every pass of the loop One cannot make declarations or define equations inside a for statement t The values of start end and incr need not be integer The start and end values can be positive or negative real numbers The value of incr has to be a positive real number 16 5 2 Examples One can use for statements to control the solve statement For instance consider the following bit of GAMS code that randomly searches for a global optimum of a non convex model scalar i scalar globmin globmin inf option bratio 1 for i 1 to 1000 x 1 j uniform 0 1 solve ml using nlp minimizing obj if obj 1 le globmin globmin obj 1 globinit j x 1 j In this example a non convex model is solved from 1000 random starting points and the global solution is tracked The use of real numbers as start end and incr can be understood from the following example for s 3 4 to 0 3 by 1 4 display s The resulting listing file will contain the following lines FERN 2 PARAMETER S 3 400 FERS 2 PARAMETER S 2 000 SESS 2 PARAMETER S 0 600 Notice that the value of s was incremented by 1 4 with each pass of the loop as long as it did not exceed 0 3 The following GAMS code is illega
272. he case that after setting kill i and a are treated as though they have been only defined and have not been initialized or assigned The result of the ki11 statement above is equivalent to i and a being defined as follows set i scalar a Unlike the clear a display statement for i and a after they are killed will trigger an error label id This option marks a line to be jumped to by a goto statement Any number of labels can be used in files and not all of them need to be referenced Re declaration of a label identifier will not generate an error and only the first occurrence encountered by the GAMS compiler will be used for future goto references Consider the following example scalara a 5 3 display a goto next a at5 display a label next a a 10 display a On reaching the goto next option GAMS continues from label next All lines in between are ignored On running the example a finally takes a value of 15 ts The label statement has to be the first dollar control option of multiple dollar control options that appear on the same line libinclude Equivalent to batinclude libinclude file argl arg2 However if an incomplete path is given the file name is completed using the library include directory By default the library include directory is set to the inclib directory in the GAMS system directory The default directory can be reset with the 1dir command line parameter Consider the followin
273. he first dollar control option title sets the title of the pages in the listing file to the text that follows the option name In the second line of the example above two options are set onsymxref and onsymlist Both these options turn of the echoing of the symbol reference table and listings to the listing file D 2 List of Dollar Control Options The Dollar Control Options are grouped into nine major functional categories affecting 204 Dollar Control Options input comment format reference maps environment variables input data format program control macro definitions output format GDX operations Compression and encrypting Table D 1 briefly describes the various options in each of the categories Section D 3 contains a reference list of all dollar control options in alphabetical order with detailed description for each Non default settings are reported before the file summary at the end of a GAMS listing as a reminder for future continued compilations This is only relevant if a restart file has been requested with the GAMS call Options affecting input comment format comment set the comment character eolCom set end of line comment character inlineCom set in line comment character maxCol set right hand margin of input file minCol set left hand margin of input file offEo1Com turn off end of line comments offInline turn off in line comments offMargin turn off margin marking Options affecting inp
274. he function returns iftrue else it returns else relation equal returns 1 if z y else returns 0 another possible command is x eq y relation greater equal returns 1 if x gt y else returns 0 another possible command is x ge y relation greater than returns 1 if x gt y else returns 0 an other possible command is x gt y relation less equal returns 1 if x lt y else returns 0 another possible command is x le y relation less than returns 1 if x lt y else returns 0 another possible command is x 1t y relation not equal returns 1 if x 4 y else returns 0 another possible command is x ne y Time and Calendar functions gday SDAY any gdow SDAY any ghour SDAY any gleap SDAY any gmillisec SDAY any gminute SDAY any gmonth SDAY any gsecond SDAY any gyear SDAY any jdate YEAR MONTH DAY any jnow none jstart none jtime HOUR MIN SEC any returns Gregorian day from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian day of week from a serial day number date time where Jan 1 1900 is day 1 returns Gregorian hour of day from a serial day number date time where Jan 1 1900 is day 1 returns 1 if the year that corresponds to a serial day number date time where Jan 1 1900 is day 1 is a leap year else returns 0 returns Gregorian milli second from a serial day number date time where Jan 1 1900 is day 1 returns
275. he suffix combinations The following is the resulting file out put which shows the value suffix combinations 150 The Put Writing Facility valuel value2 value3 comb1 123 457 0 123 1 2345670E 4 comb2 123 457 0 123 1 2345670E 4 comb3 123 457 0 123 0 000 comb4 1 23457E 2 0 12345670 0 00012346 comb5 123 456700 0 123457 0 000123 Notice that in comb1 the display of values switch to exponential notation when a value becomes smaller than the number of decimal places allowed This is triggered by the suffix nr being set to zero Of particular interest is value3 for comb2 and comb3 Value3 is greater than the zero tolerance level in nz but smaller than the number of decimals allowed by nd In comb2 since nr is set to zero the value is displayed in exponential format In comb3 nr is set to 1 so this small value is rounded to 0 In comb5 valuel is rounded to an integer because of nd being set to 0 15 13 Cursor Control Having described the display of various output items using the put statement this section describes features available to position these items in the output file GAMS has several file suffixes which determine the location of the cursor and the last line of the file These suffixes can also be used to reposition the cursor or reset the last line As such they are instrumental in formatting output items in documents These suffixes are grouped by the title header or window writing area for which they are valid 15 13 1
276. hen restart from the work file when developing the report It is a great relief not to have to solve the model every time F 3 Ways in which a Work File is Useful 255 F 3 3 Tacking Sequences of Difficult Solves In many cases where solves are known to be difficult and expensive it may be too risky to ask GAMS to process a job containing many solve statements The risk is that if one solve does not proceed to normal completion then the following one will be started from a bad initial point and much time and effort will be wasted An alternative is to request one solve at a time and save the work file Then the output is carefully inspected before proceeding If everything is normal the job is restarted with the next solve requested If not the previous solve can be repeated probably with a different initial point or continued if the cause of the trouble was an iteration limit for example This approach is common when doing repeated solves of a model that successively represent several consecutive time periods It uses a work file in a sequential rather than a tree structure way It also produces many files which can be difficult to manage if the solves are especially difficult it is possible to lose track of exactly what was done Great care is needed to avoid losing control of this process F 3 4 Multiple Scenarios The majority of modeling exercises involves a base case and the point of the study is to see how the system changes
277. his case the range is from 0 to 32767 and if the value is above the range then it is set to 32767 parmfile pf text command line parameter include file This option specifies the name of a secondary customization parameter file to use It is used to augment the command line adding more command line parameters from a file It is read from the current directory unless a path is specified plicense plicense text privacy license file name This keyword tells the name of a privacy license file that contains file encryption codes A full path should be used procdir procdir text run or process directory This keyword gives the name of the directory where the work files generated by GAMS will be stored This directory must already exist otherwise an error is triggered If not specified it will be set to 225 with characters a b c attached C 3 Detailed Description of Command Line Parameters 195 profile profile 0 global execution profiling option This option initializes the profile option see Appendix E to the value set and allows the profile of a GAMS run to be printed in the listing file The profile contains the individual and cumulative time required for the various sections of the GAMS model t Setting the profile option through the option statement in the GAMS input file overrides the value of the profile parameter passed through the command line Values O no profiling 1 minimum profiling n profiling depth for nested
278. ht of the sign All numerical facilities available in both standard and extended arithmetic will be covered 56 Data Manipulations with Parameters 6 3 1 Standard Arithmetic Operations The standard arithmetic symbols and operations are exponentiation multiplication and division addition and subtraction unary and binary They are listed above in precedence order which determines the order of evaluation in an expression without parentheses Consider for example x 5 4 3 2 For clarity this could have been written x 5 4 3 2 In both cases the result is 41 ts It is better to use parentheses than to rely on the precedence of operators since it prevents errors and clarifies intentions ts Expressions may be freely continued over many lines an end of line is permissible at any point where a blank may be used Blanks may be used for readability around identifiers parentheses and operator symbols Blanks are not allowed within identifiers or numbers and are significant inside the quote marks used to delimit labels x n is equivalent to the function call rPower x y and is calculated inside GAMS as exp n log x This operation is not defined if x has a negative value and an error will result If the possibility of negative values for x is to be admitted and the exponent is known to be an integer then a function call power x n is available Three additional capabilities are available
279. iable that is being optimized Model_type is one of the model types described before An example of a solve statement in GAMS is shown below Solve transport using lp minimizing cost Solve and using are reserved words Transport is the name of the model 1p is the model type minimizing is the direction of optimization and cost is the objective variable The opposite of minimizing is maximizing both reserved words Note that an objective variable is used instead of an objective row or function ts The objective variable must be scalar and type free and must appear in the least one of the equations in the model The next two sub sections will describe briefly below what happens when a solve statement is processed and more details on how the resulting output is to be interpreted will be given in the next chapter After that sequences of solve statements will be discussed The final section will describe options that are important in controlling solve statements 9 3 2 Requirements for a Valid Solve Statement When GAMS encounters a solve statement the following are verified 1 All symbolic equations have been defined and the objective variable is used in at least one of the equations 2 The objective variable is scalar and of type free 3 Each equation fits into the specified problem class linearity for 1p continuous derivatives for nlp as we outlined above 4 All sets and parameters in the equations have values assigned 9 3
280. ickly and correctly 2 11 3 Reference Maps The next section of output which is the last if errors have been detected is a pair of reference maps that contain summaries and analyses of the input file for the purposes of debugging and documentation The first reference map is a cross reference map such as one finds in most modern compilers It is an alphabetical cross referenced list of all the entities sets parameters variables and equations of the model The list shows the type of each entity and a coded reference for each appearance of the entity in the input The cross reference map for our transportation example is as follows we do not display all tables SYMBOL TYPE REFERENCES A PARAM DECLARED 9 DEFINED 10 REF 42 B PARAM DECLARED 13 DEFINED 14 REF 44 03 PARAM DECLARED 25 ASSIGNED 27 REF 40 COST EQU DECLARED 36 DEFINED 40 IMPL ASN 48 REF 46 D PARAM DECLARED 18 DEFINED 18 REF 27 DEMAND EQU DECLARED 38 DEFINED 44 IMPL ASN 48 REF 46 F PARAM DECLARED 23 DEFINED 23 REF 27 SET DECLARED 4 DEFINED 4 REF 9 18 25 27 30 37 2 40 2 42 44 CONTROL 27 40 42 44 J SET DECLARED 5 DEFINED 5 REF 13 18 25 27 30 38 2 40 42 2 44 CONTROL 27 40 42 44 SUPPLY EQU DECLARED 37 DEFINED 42 IMPL ASN 48 REF 46 TRANSPORT MODEL DECLARED 46 DEFINED 46 IMPL ASN 48 REF 48 X VAR DECLARED 30 IMPL ASN 48 REF 33 40 42 44 2 50 22 A GAMS Tutorial by Richard E Rosenthal Z VAR DECLARED 31 IMPL ASN 48 REF 40 48 For example the cross reference list
281. ification Examples are linear nonlinear and mixed integer programs program A GAMS input file that provides a representation of the model or models relational operator This term may be used in two ways First in an equation definition it describes the type of relationships the equation specifies for example equality as specified with the e symbol Second in a logical expression the symbols eq ne 1t and so on are also called relational operators and are used to specify a required relationship between two values right hand side The value of constant term in a constraint scalar One of the forms of parameter inputs Used for single elements set A collection of elements labels The set statement is used to declare and define a set simplex method The standard algorithm used to solve linear programming problems slack The amount by which an inequality constraint is not binding slack variable An artificial column introduced by a solver into a linear programming problem Makes the implementation of simplex method much easier smooth A classification of a function that has continuous first derivatives solver A computer code used to solve a given problem type An example is GAMS MINOS which is used to solve either linear or nonlinear programming problems statements Sometimes called units The fundamental building block of GAMS programs Statements or sentences that define data structures initial values data modifications and s
282. ile either from its current location or after transfering it to the directory that should contain the GAMS system directory By executing the distribution file the GAMS distribution should be extracted For example if you downloaded the distribution file into your home directory you might execute the following commands mkdir Applications GAMS cd Applications GAMS osx_x64_64_sfx exe Optionally create the license file gamslice txt in the GAMS system directory The license file is nowadays sent via email with instructions If no license file is present GAMS will still function in the demonstration mode but can only solve small problems Student and demonstration systems do not include a license file A license file can easily be added later so if you cannot find a license file you can safely proceed without one Change to the GAMS system directory and run the program gamsinst It will prompt you for default solvers to be used for each class of models If possible choose solvers you have licensed since unlicensed solvers will only run in demonstration mode These solver defaults can be changed or overridden by a rerunning gamsinst and resetting the default values b setting a command line default e g gams trnsport lp bdmlp c an option statement in the GAMS model e g option 1p bdmlp Add the GAMS system directory to your path see below To test the installation log in as a normal user and run a few models f
283. ill be greatly improved and the productivity of modelers enhanced if each generation can stand on the shoulders of the previous generation by beginning with the previous models and enhancing and improving them Thus the GAMS systems includes a large library collectively called GAMSLIB The models included have been selected not only because they collectively provide strong shoulders for new users to stand on but also because they represent interesting and sometimes classic problems For example the trade off between consumption and investment is richly illustrated in the Ramsey problem which can be solved using nonlinear programming methods Examples of other problems included in the library are production and shipment by firms investment planning in time and space cropping patterns in agriculture operation of oil refineries and petrochemical plants macroeconomics stabilization applied general equilibrium international trade in aluminum and in copper water distribution networks and relational databases Another criterion for including models in the library is that they illustrate the modeling capabilities GAMS offers For example the mathematical specification of cropping patterns can be represented handily in GAMS Another example of the system s capability is the style for specifying initial solutions as staring points in the search for the optimal solution of dynamic nonlinear optimization problems Finally some models have been selected
284. ime to execute than this tolerance are not reported in the listing file acp default This option controls the solver used to solve qcp models For details cf option cns reall to real 5 Real communication cell that can contain any real number reslim 1000 This option specifies the maximum time in wall clock seconds that the computer can run during execution of a solver before the solver terminates the run rmip default This option controls the solver used to solve rmip models For details cf option cns rminlp default This option controls the solver used to solve rminlp models For details cf option cns savepoint 0 This option tells GAMS to save a point format GDX file that contains the information on the current solution point E 3 Detailed Description of Options 249 no point GDX file is to be saved 1 a point gdx file from the last solve is to be saved a point gdx file from every solve is to be saved seed 3141 This option resets the seed for the pseudo random number generator solprint on This option controls the printing of the model solution in the listing file Using this specification suppresses the list of the solution following a solve on The solution is printed one line per row and column in the listing file off Solution details are not printed Although this saves paper we do not recommend it unless you understand your model very well and solve it often silent Suppress all solution inform
285. in list and text being optional Labels are used on the top and the left to map out a rectangular grid that contains the data values The order of labels is unimportant but if domain checking has been specified each label must match one in the associated set Labels must not be repeated but can be left out if the corresponding numbers are all zero or not needed At least one blank must separate all labels and data entries Blank entries imply that the default value zero will be associated with that label combination ts Notice also that in contrast to the set scalar and parameter statements only one identifier can be declared and initialized in a table statement 5 4 2 An Illustrative Example The example below adapted from KORPET is preceded by the appropriate set definitions sets i plants inchon ulsan yosu m productive units atmos dist atmospheric distillation unit steam cr steam cracker aromatics aromatics unit hydrodeal hydrodealkylator table ka m i initial cap of productive units 100 tons per yr inchon ulsan yosu atmos dist 3702 12910 9875 steam cr 517 1207 aromatics 181 148 hydrodeal 180 In the example above the row labels are drawn from the set m and those on the column from the set i Note that the data for each row is aligned under the corresponding column headings If there is any uncertainty about which data column a number goes with GAMS will protest with an error message and m
286. in the one dimensional case is replaced by a label tuple for higher dimensions The elements in the n tuple are separated by dots just like in the case of multi dimensional sets The following example illustrates the use of parameter data for higher dimensions parameter salaries employee manager department anderson murphy toy 6000 hendry smith toy 9000 hoffman morgan cosmetics 8000 All the mechanisms using asterisks and parenthesized lists that we introduced in our discussion of sets are available here as well Below is an artificial example in which a very small fraction of the total data points are initialized GAMS will mark an error if the same label combination or label tuple appears more than once in a data list Set row rowi row10 col colix col10 parameter a row col row1 row4 col2 col7 12 row10 col10 17 rowl row7 col10 83 73 In this example the twelve elements row1 co12 to row1 co17 and row4 col2 to row4 col7 are all initialized at 12 the single element row10 co110 at 17 and the seven elements rows1 col10 to row7 col10 at 33 The other 80 elements out of a total of 100 remain at their default value which is 0 This example shows the ability of GAMS to provide a concise initialization or definition for a sparse data structure 5 4 Tables Tabular data can be declared and initialized in GAMS using a table statement For 2 and higher dimensional parameters this provides a more co
287. ing example shows various legal ways of entering numbers 0 156 70 135 095 1 2e10 2e 10 15 e 10 314e5 1 7 0 0 0 0 INF INF EPS NA The letter e denotes the well known scientific notation allowing convenient representation of very large or small numbers For example 1e 5 1 x 107 0 00001 3 56e6 3 56 x 10 3 560 000 GAMS uses a smaller range of numbers than many computers are able to handle This has been done to ensure that GAMS programs will behave in the same way on a wide variety of machines including personal computers A good general rule is to avoid using or creating numbers with absolute values greater than 1 0e 20 t A number can be entered with up to ten significant digits on all machines and more on some 3 4 7 Delimiters As mentioned before statements are separated by a semicolon However if the next statement begins with a reserved word often called keyword in succeeding chapters then GAMS does not require that the semicolon be used The characters comma and slash are used as delimiters in data lists to be introduced later The comma terminates a data element as does an end of line and the slash terminates a data list 3 4 8 Comments A comment is an explanatory text that is not processed or retained by the computer There are three ways to include comments in a GAMS program The first already mentioned above is to start a line with an asterisk in the firs
288. ing the first error and ignore the other The first error detected in line 17 code 97 indicate that GAMS thinks the symbols in line 17 are a continuation of the documentary text at the end of line 16 rather than a direct assignment as we intended The error message also appropriately advises us to check the preceding line for a missing semicolon Unfortunately you cannot always expect error messages to be so accurate in their advice The compiler cannot read your mind It will at times fail to comprehend your intentions so learn to detect the causes of errors by picking up the clues that abound in the GAMS output For example the missing semicolon could have been detected by looking up the c entry in the cross reference list to be explained in the next section and noticing that it was never assigned SYMBOL TYPE REFERENCES 03 PARAM DECLARED 15 REF 17 Example 3 Many errors are caused merely by spelling mistakes and are caught before they can be damaging For example with Seattle spelled in the table differently from the way it was introduced in the set declaration we get the following error message 4 sets 5 i canning plants seattle san diego 6 j markets new york chicago topeka 7 8 table d i j distance in thousand of miles 9 new york chicago topeka 10 seatle 2 5 E 1 8 OK 170 11 san diego 2 5 1 8 1 4 A Error Message 170 DOMAIN VIOLATION FOR ELEMENT Example 4 Similarly if we mistakenly enter dem j instead of
289. inimum value This can be expressed algebraically as Either x 0 or x L U By default this lower bound L is 1 and the upper bound U is 100 The lower and upper bounds are set through lo and up In GAMS a semi integer variable is declared using the reserved phrase semiint variable The following example illustrates its use semiint variable x x lo 2 x up 25 The above slice of code declares the variable x to be semi continuous variable that can either be 0 or can take any integer value between 2 and 25 t Not all MIP solvers allow semi integer variables Please verify that the solver you are interested in can handle semi integer variables by checking the relevant section of the Solver Manual gt The lower bound L has to be less than the upper bound U and both bounds have to be greater than 0 GAMS will flag an error during model generation if it finds that this is not the case t The bounds for semiint variables have to take integer values GAMS will flag an error during model generation if it finds that this is not the case 164 Special Language Features 17 2 6 Setting Priorities for Branching The user can specify an order for picking variables to branch on during a branch and bound search for MIP models through the use of priorities Without priorities the MIP algorithm will determine which variable is the most suitable to branch on The GAMS statement to use priorities for branching during the br
290. instances I 6 Architecture and Customization The current Grid Facility relies on very basic operating system features and does not attempt to offer real and direct job or process control The file system is used to signal the completion of a submitted task and GAMS has currently no other way to interact with the submitted process directly like forcing termination or change the priority of a submitted task This approach has its obvious advantages and disadvantages There are a number of attempts to use grid computing to provide value added commercial remote computing services notably is SUN s recent commercial entry Commercial services require transparent and reliable charge approaches and related accounting and billing features which are still missing or inadequate When GAMS executes a solve under solvelink 3 it will perform the following steps 1 Create a subdirectory in the GridDir with the name gridnnn Where nnn stands for the numeric value of the handle The handle value is the internal symbol ID number x le6 the model instance number For example in the QMEANVAR example the first grid subdirectory was grid137000002 2 Remove the completion signal in case the file already exists Currently the signal is a file called finished For example grid137000002 finished 3 Create or replace a gdx file called gmsgrid gdx which will contain a dummy solution with failed model and solver status This file will be overwritten by the final st
291. ion of Dollar Control Options 231 scalar a 12 a at1 onmulti scalar a 20 display a The two scalar data initialization statements and the onmulti option are processed before the assignment statement a a 1 In the order that it is processed the example above is read by GAMS as compilation step scalar a 12 onmulti scalar a 20 execution step a at1 display a The example results in a taking a value of 21 The display statement in the resulting listing file is as follows 5 PARAMETER A 5 21 000 on off NestCom offNestCom Controls nested in line comments Make sure that the open comment and close comment characters have to match Consider running the following slice of code inlinecom onnestcom nesting is now possible in comments braces have to match on off Order on0rder Lag and lead operations require the reference set to be ordered and constant In some special cases one would want to use those operation on dynamic and or unordered sets The option on offOrder has been added to locally relax the default requirements The use of this option comes with a price the system will not be able to diagnose odd and incorrect formulations and data sets on off Put Causes a block of text to be placed in a put file These commands are used employing the syntax file putfile put putfile onPut Line 1 of text Line 2 of text Line 3 of text Line 4 of text offPut The resul
292. ions 111 11 2 5 Logical Conditions Involving Acronyms Acronyms which are character string values can be used in logical conditions only with the or lt gt operators only Consider the following example of logical conditions involving the use of acronyms dayofweek wednesday dayofweek lt gt thursday where dayofweek is a parameter and wednesday and thursday are acronyms 11 2 6 Numerical Values of Logical Conditions The previous four sub sections have described the various features in GAMS that can be used as logical conditions However GAMS does not have a Boolean data type t GAMS follows the convention that the result of a relational operation is zero if the assertion is False and one if True Consider the following example for illustration x 1 lt 2 2 lt 3 The expression to the right of the assignment evaluates to 2 since both logical conditions within parenthesis are true and therefore assume a value of 1 Note that this is different from the assignment below x 1 lt 2 or 2 lt 3 which evaluates to 1 due to the or operator behaving as explained above 11 2 7 Mixed Logical Conditions Operator Precedence The building blocks discussed in the first four subsections can be used to generate more complex logical conditions The default precedence order in a logical condition used by GAMS in the absence of parenthesis is shown in table 11 2 in decreasing order Operation Operator Exponen
293. ions of dots parentheses and commas are shown in Table 4 1 Construct Result a b c d a c d b c d a b c d e a c e b c e a d e b d e a 1 x3 c a 1 a 2 a 3 cora 1l c a 2 c a 3 c 1x3 1 3 1 3 1 1 1 1 1 2 12113 06 0 3 93 Table 4 1 Examples of the compact representation of sets Note that the asterisk can also be used in conjunction with the dot Recall that the elements of the list 1 4 are 1 2 3 4 4 5 3 Projection and Aggregation of Sets Projection and aggregation operations on sets and parameters can be performed in two different ways a slower and more intuitive way as well as a faster and more compact way The more intuitive way is to use assignment and the sum operator while the faster and more compact way is to use the OPTION statement The OPTION statement can be used as follows Option itemi lt item2 Option itemi lt item2 After the OPTION keyword the left and right items are identifiers with conforming domain declarations The dimensionality of the left symbol has to be equal or less the dimensionality of the right side If the left dimension ality is less than the right one the operation performed is an aggregation or projection depending on the data type of the left side In all cases indices are permuted according to the domain definitions This means that if the domain identifier is unique then the permutation is performed unambiguously However if the domain has identical
294. irectory If no logfile is given but the value of lo is 2 then the file name will be input file name with the extension log To illustrate the use of the logfile option run TRNSPORT with the options lo 2 and 1f myfile log The resulting log file is redirected to myfile log and looks as follows Starting compilation trnsport gms 69 3 Mb Starting execution elapsed 0 00 00 002 trnsport gms 44 4 Mb Generating LP model transport trnsport gms 65 4 Mb 6 rows 7 columns 19 non zeroes Executing CPLEX elapsed 0 00 00 007 IBM ILOG CPLEX Jul 14 2011 23 7 1 WEX 26779 26792 WEI x86_64 MS Windows Cplex 12 3 0 0 Reading data Starting Cplex Tried aggregator 1 time LP Presolve eliminated 1 rows and 1 columns Reduced LP has 5 rows 6 columns and 12 nonzeros Presolve time 0 00 sec Iteration Dual Objective In Variable Out Variable 1 73 125000 x seattle new york demand new york slack 2 119 025000 x seattle chicago demand chicago slack 3 153 675000 x san diego topeka demand topeka slack 4 153 675000 x san diego new york supply seattle slack LP status 1 optimal Optimal solution found Objective 153 675000 Restarting execution trnsport gms 65 2 Mb Reading solution for model transport Executing after solve elapsed 0 00 00 046 trnsport gms 67 3 Mb Status Normal completion Job trnsport gms Stop 11 30 11 05 27 11 elapsed 0 00 00 046 loglin
295. is solve For example the convert solver only reformats the model but does not give a solution SOLVED UNIQUE This is used when a CNS model is solved and the solver somehow can be certain that there is only one solution The simplest examples are a linear model with a non singular Jacobian a triangular model with constant non zero elements on the diagonal and a triangular model where the functions are monotone in the variable on the diagonal SOLVED Locally feasible in a CNS models this is used when the model is feasible and the Jacobian is non singular and we do not know anything about uniqueness SOLVED SINGULAR Singular in a CNS models this is used when the model is feasible all constraints are satisfied but the Jacobian Basis is singular In this case there could be other solutions as well in the linear case a linear ray and in the nonlinear case some curve UNBOUNDED NO SOLUTION The model is unbounded and no solution can be provided INFEASIBLE NO SOLUTION The model is infeasible and no solution can be provided 102 GAMS Output This is the list of possible SOLVER STATUS messages 1 NORMAL COMPLETION This means that the solver terminated in a normal way i e it was not interrupted by a limit resource iterations nodes or by internal difficulties The model status describes the characteristics of the accompanying solution 2 ITERATION INTERRUPT This means that the solver was interrupted because it use
296. ive optimality tolerance Options controlling choice of solver cns sets solver for cns model type mip sets solver for mip model type dnlp sets solver for dnlp model type mpec sets solver for mpec model type lp sets solver for 1p model type nlp sets solver for nlp model type mcp sets solver for mcp model type rminlp sets solver for rminlp model type minlp sets solver for minlp model type rmip sets solver for rmip model type Options affecting input program control seed resets seed for pseudo random number generator solveopt controls return of solution values to GAMS strictsingleton error if assignment to singleton set has multiple elements Other options integer1 integer communication cell reali real communication cell Table E 1 GAMS options E 3 Detailed Description of Options 247 E 3 Detailed Description of Options This section describes each of the options in detail The options are listed in alphabetical order for easy reference In each of the following options the default value if available is bracketed lt identifier gt Display specifier identifier d identifier d r c Defines print formats for identifier when used in a display statement d is the number of decimal places r is the number of index positions printed as row labels c is the number of index positions printed as column labels the remaining index positions if any will be used to index the planes index order plane row column if r is zero list format
297. k s k t k a k K s k t k and i are sets while u k and a i are parameters The assignment will be made only for those members of k that are also members of both s and t Note the position of the parenthesis in the dollar condition The statement above can be rewritten as u k s k and t k a k ts To assist with the readability of statements it is strongly recommended to use the logical and operator instead of nesting dollar operators 11 4 Conditional Assignments The statement comprising the example in the Section before was a conditional assignment In this example the dollar condition was on the left hand side of the assignment ts The effect of the dollar condition is significantly different depending on which side of the assignment it is in ts In many cases it may be possible to use either of the two forms of the dollar condition to describe an assignment In such a case clarity of logic should be used as the criterion for choice The next two subsections describe the use of the dollar condition on each side of the assignment 11 4 1 Dollar on the Left The example illustrated in the section above uses the dollar condition on the left hand side of the assignment statement ts For an assignment statement with a dollar condition on the left hand side no assignment is made unless the logical condition is satisfied This means that the previous contents of the parameter on the left will remain unchanged f
298. king using a dynamic set The following example adapted from the Section 12 2 2 illustrates the use of dynamic sets as domains subitemi item no subiteml subitem2 yes The first assignment ensures that subitem1 is empty Note that this can also be done with parameters For example parameter inventory item inventory subitem1 25 12 3 Using Dollar Controls with Dynamic Sets 121 12 2 5 Equations Defined over the Domain of Dynamic Sets It is sometimes necessary to define an equation over a dynamic set ts The trick is to declare the equation over the entire domain but define it over the dynamic set The following example illustrates its use set allr all regions n s w e n e s w r allr region subset for particular solution scalar price 10 equations prodbal allr production balance variables activity allr first activity revenue allr revenue A prodbal r activity r price e revenue r To repeat the important point the equation is declared over allr but referenced over r Then arbitrary assign ments can be made to r within the membership of allr 12 2 6 Assigning Membership to Singleton Sets Assigning membership to singleton sets is different than to usual sets Since singleton sets can never have more than one element any assignment to a singleton set first clears or empties the set so no explicit clear is necessary This is illustrated in the following example Set i Static Set
299. known identifier entered as set 170 Domain violation for element k 2 ERROR S 0 WARNING S Note that numbers 170 and 120 flag the two errors as they occur but the errors are explained only at the end of the source listing However if the code is run using the option errmsg 1 the resulting listing file contains the following 1 set i 1 10 set j i 10 11 CK 170 xk 170 Domain violation for element 2 parameter a jj 12 25 0 Es RK 120 xk 120 Unknown identifier entered as set 3 k 2 ERROR S 0 WARNING S Note that the explanation for each error is provided immediately following the error marker errnam errnam tezt error message file name Used to change the name GAMSERRS TXT The name text will be used as is error error text Force a parameter error with message text Forces a parameter error with given message string This option is useful if one needs to incorporate GAMS within another batch file and need to have control over the conditions when GAMS is called To illustrate the use of the error option the default GAMS log file from running a model with the option error hullo x ERROR hullo Status Terminated due to parameter errors Erasing scratch files Exit code 6 errorlog er 99 error message lines written to the log file Values O no error messages are written to log file n number of lines for each error written to log file etlim etl inf elapsed time limit This option con
300. l file and acronym The keywords scalar and table do not introduce separate data types but rather comprise a shorthand way to declare a symbol to be a parameter that will use a particular format for specifying initial values declaration The entry of a symbol and the specification of its data type A declaration may include the specification of initial values and then it is more properly called a definition default The value used or the action taken if the user provides no information 170 Glossary definition The definitions of the algebraic relationships in an equation are the assignment of initial values to parameters or of elements to sets as part of the initial declaration of the identifier definition statements Units that describe symbols assign initial values to them and describe symbolic relationships Some examples of the set parameter table and model statements and the equation definition statement direction Either maximization or minimization depending on whether the user is interested in the largest or the smallest possible value for the objective function discontinuous A classification of a function A plot of the function values will be a line with breaks in it discrete A discrete variable type binary or integer may not assume any value between the bounds but must assume integer values dollar control option Directives or options used to control input or output detail associated with the GAMS compiler
301. l R P 1 from the stochastic library J 4 J 5 LINDO Sampling Library 285 poisson MEAN SAMSIZE VARRED Poisson distribution specified by mean Table J 6 LINDO sampling functions The following example illustrates the use of the sample generator and shows how the commands setCorrelation and induceCorrelation work funclibin lsalib lsadclib function normalSample lsalib SampleLSnormal getSampleVal lsalib getSampleValues setCor 1salib setCorrelation indCor 1lsalib induceCorrelation scalar d h k h normalSample 5 2 12 k normalSample 5 2 12 set i i01 i12 parameter sv i loop i sv i getSampleVal k display sv loop i sv i getSampleVal h display sv d setCor h k 1 d indCor 1 loop i sv i getSampleVal k display sv loop i sv i getSampleVal h display sv The resulting output shows that the values of sv are restructured according to the desired correlation aoe 18 PARAMETER sv i01 7 610 102 5 710 103 3 755 104 5 306 105 2 382 106 2 174 107 6 537 108 4 975 109 8 260 i10 3 067 i11 6 216 112 4 349 as 22 PARAMETER sv i01 7 610 102 5 710 103 3 755 104 5 306 105 2 382 106 2 174 107 6 537 108 4 975 109 8 260 i10 3 067 i11 6 216 112 4 349 wees 28 PARAMETER sv i01 2 382 102 4 349 103 6 216 104 4 975 105 7 610 106 8 260 107 3 067 108 5 306 109 2 174 i10 6 537 i11 3 755 112 5 710 a 32 PARAMETER sv 101 7 610 102 5
302. l from the GAMS Model Library contains a more elaborate example of the use of encrypted files Note the use of LICENSE DEMO which overrides the currently installed license with a demo license which has the secure file option enabled Title Input file encryption demo ENCRYPT SEQ 318 ontext Input files can be encrypted and use the save privacy license file mechanism for managing the user password Similar to compression we offer an encrypt utility to lock any file to a specific target license file Once a file has been encrypted it can only be read by a gams program that has the matching license file There is no inverse operation possible you cannot recover the original GAMS file from the encrypted version To create an encrypted file we need a license file which has the security option enabled To allow easy testing and demonstration a special temporary demo license can be created internally and will be valid for a limited time only usually one to two hours In the following example we will use the GAMS option license DEMO to use a demo license with secure option instead of our own license file Also note that we use the same demo license file to read the locked file by specifying the GAMS parameter plicence LICENSE offtext get model ondollar ca amslib q trnsport call gamslib q p encrypt and try to decrypt call rm f t1 gms echo encrypt trnsport gms t1 gms gt s1 gms call gams si license DEMO plic
303. l produced by the solve statement 138 The Display Statement 15 The Put Writing Facility 15 1 Introduction In this chapter the put writing facility of the GAMS language is introduced The purpose of this writing facility is to output individual items under format control onto different files Unlike the display statement the entire set of values for indexed identifiers cannot be output using a single put statement identifiers are the names given to data entities such as the names for parameters sets variables equations models etc While its structure is more complex and requires more programming than is required for the display statement there is much greater flexibility and control over the output of individual items In this chapter the working of the put writing facility is described as well as the syntax for accessing files and globally formatting documents using file suffixes for various attributes of a file The put writing facility enables one to generate structured documents using information that is stored by the GAMS system This information is available using numerous suffixes connected with identifiers models and the system Formatting of the document can be facilitated by the use of file suffixes and control characters The put writing facility generates documents automatically when GAMS is executed A document is written to an external file sequentially a single page at a time The current page is stored in a buffe
304. l since one cannot define equations inside a for statement for s 1 to 5 by 1 eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside a for statement for s 1 to 5 by 1 scalar y y 5 Js 160 Programming Flow Control Features 17 Special Language Features 17 1 Introduction This chapter introduces special features in GAMS that do not translate across solvers or are specific to certain model types These features can be extremely useful for relevant models and are among the most widely used 17 2 Special MIP Features Some special features have been added to GAMS to help in simplifying the modeling of MIP problems Two special types of discrete variables are defined and discussed Finally creating priorities for the discrete variables is discussed The solvers use this information when solving the problem 17 2 1 Types of Discrete Variables The following types of discrete variables have been discussed so far in the book binary variables These can take on values of 0 or 1 only integer variables These can take on integer values between the defined bounds The default lower and upper bounds are 0 and 100 respectively In addition to these two two new types of discrete variables that are introduced in this section Both these variables exploit special structures in MIP models during the solution phase These are the following Special Ordered Sets SOS The preci
305. l that does not do what you want it to do but does not contain errors in the sense that the term is being used in this section The best precaution is to check your work carefully and build in as many automatic consistency checks as possible 106 GAMS Output One mistake that may cause confusion is if a GAMS reserved word is used for a label or an identifier In this case it is impossible to provide helpful messages for technical reasons t In some cases an error may not be detected until the statement following its occurrence where it may produce a number of error conditions whose explanations seem quite silly Always check carefully for the cause of the first error is such a group and look at the previous statement and especially for missing semicolons if nothing seems obvious The following example illustrates the general reporting format for compiler errors 1 set c crops wheat corn wheat longaname CK 172 2 parameter price c wheat 200 cotton 700 OK 170 3 Error Messages 170 Domain violation for element 172 Element is redefined k 2 ERROR S 0 WARNING S 44 USER ERROR S ENCOUNTERED 10 6 2 Compilation Time Errors The reporting format for errors found while analyzing solve statements is more complicated than for normal compilation errors mainly because many things must be checked All identifiers referenced must be defined or assigned the mathematics in the equations must match the model class
306. l type 15 80 dollar dollar control option 209 dollar condition control over the domain of definition 117 example 112 in equations 117 122 in indexed operations 122 nested 112 on the left 113 on the right 114 with dynamic sets 121 within indexed operations 116 within the algebra 117 dollar control option 170 Introduction 203 Syntax 203 dollar operator 112 170 domain checking 38 170 domain definition 170 domain restriction condition 170 domlim GAMS call parameter 181 GAMS option 247 option 100 107 dot in equation definitions 74 in level and marginal listings 104 in many to many mappings 41 in parameter definition 47 in set definition 40 in sets 40 in tables 49 double dollar control option 209 driving set 170 drop dollar control option 210 dropEnv dollar control option 210 dropGlobal dollar control option 210 dropLocal dollar control option 210 dual value m 69 dumpopt GAMS call parameter 181 dumpparms GAMS call parameter 183 dynamic set 170 assigning membership to 119 assigning membership to singleton sets 121 assignments over the domain of 120 dollar assignments 122 equations defined over the domain of 121 example 119 in equations 122 indexed operations 122 introduction 119 syntax 119 using dollar controls with 121 with multiple indices 120 e format 136 170 echo dollar control option 210 echoN dollar control option 210 eDist function 58 eje
307. lable in wall clock seconds to solve in seconds The default value is 1000 savePoint This parameter tells GAMS to save a point format GDX file that contains the information on the current solution point One can save the solution information from the last solve or from every solve Numeric input with the following values is expected e 0 no point gdx file is to be saved e 1 a point gdx file called model_name_p gdx is to be saved from the last solve in the GAMS model e 2 a point gdx file called model_name_pnn gdx is to be saved from every solve in the GAMS model where nn is the solve number as determined internally by GAMS scaleOpt This attribute tells GAMS whether to employ user specified variable and equation scaling factors It must be set to a nonzero value if the scaling factors are to be used solPrint This attribute controls the printing of the model solution to the LST file Note that the corresponding option expects a text while the use of model_name solPrint and the command line expect a numeric value Allowed are e 0 Off remove solution listings following solves e 1 On include solution listings following solves e 2 Silent suppress all solution information The default value is 1 respectively On 9 2 The Model Statement 83 solveLink This attribute controls GAMS function when linking to solve Allowable values are e 0 GAMS operates as always default e 1 the so
308. laration one two three k i offuelxref set j i will not show two onuelxref k one yes 234 Dollar Control Options The resulting listing file will contain the following unique element reference reports ELEMENT REFERENCES ONE DECLARED 2 INDEX 6 THREE DECLARED 2 TWO DECLARED 2 onjoff UNDF offUNDF Controls the use of the special value UNDF which indicates a result is undefined A user may not use this in an assignment unless the onUNDF command has been used The following slice of code scalar x onUNDF x UNDF display x creates the following part at the listing file 4 PARAMETER x UNDF Without the use of 0nUndf an error would be triggered The use of offUNDF will disallow the usage of UNDF in assignments on off Verbatim These commands are used in conjunction with the GAMS parameter DUMPOPT to suppress the input preprocessing for input lines that are copied to the dmp file This feature is mainly used to maintain different versions of related models in a central environment The on offVerbatim commands are only recognized for DUMPOPT gt 10 and apply only to lines in the file the commands appeared The use of goto and on offVerbatim are incompatible and may produce unexpected results Consider the following example set f 123 log f onVerbatim log t offverbatim log 4f The corresponding dmp file contains log 123 onVerbatim log 4f offVerbatim log 123
309. lare variable types The first is to list all variables with domain specifications and explanatory text as a group and later to group them separately as to type The example shown below is adapted from MEXSS The default type is free so phi phipsi etc will be free variables in the example below Note the use of variable names derived from the original mathematical representation variables u c i purchase of domestic materials mill units per yr v c j imports mill tpy e c i exports mill tpy phi total cost mill us phipsi raw material cost mill us positive variables u v e The commas in the list of positive variables are required separators ts It is possible to declare an identifier more than once but that the second and any subsequent declarations should only add new information that does not contradict what has already been entered The second popular way of declaring variables is to list them in groups by type We rewrite the example above using this second method 7 3 Variable Attributes 69 free variables phi total cost mill us phipsi raw material cost mill us positive variables u c i purchase of domestic materials mill units per yr v c j imports mill typ e c i exports mill typ The choice between the two approaches is best based on clarity 7 3 Variable Attributes Another important difference between parameters and variables is that an additional set of keywords
310. le to the LST file Note that the cor responding option expects a text while the use of model_name solPrint and the command line expect a numeric value Allowed are e 0 Off suppress additional solver generated output default e 1 On include additional solver generated output threads This attribute controls the number of threads or CPU cores to be used by a solver Allowable values are e n number of cores to leave free for other tasks e 0 use all available cores e n use n cores will be reduced to the available number of cores if n is too large tolInfeas Infeasibility tolerance for an empty row of the form a 0 x e 0 0001 By default this tolerance is set close to the machine precision tolInfRep This attribute sets the tolerance for marking infeasible in the equation listing The default value is 1 0e 6 tolProj This attribute controls the tolerance for filtering marginals i e setting marginals within the tolerance to 0 and projecting levels to the lower or upper bound that are within the tolerance when reading a solution default is le 8 84 Model and Solve Statements tryInt Signals the solver to make use of a partial or near integer feasible solution stored in current variable values to get a quick integer feasible point If or how tryint is used is solver dependent tryLinear Examine empirical NLP model to see if there are any NLP terms active If ther
311. lems gt An easy way of making performance comparisons between solvers gt The guarantee that a user has not somehow provided an illegal input specification gt Elaborate documentation particularly of input formats is not needed gt Access to the existing community of GAMS users for marketing or testing This completes the discussion of the model and solve statements In the next chapter the various components of GAMS output are described in some detail 90 Model and Solve Statements 10 GAMS Output 10 1 Introduction The output from GAMS contains many aids for checking and comprehending a model In this chapter the contents of the output file are discussed Ways by which the amount of diagnostic output produced can be controlled will also be discussed although complete lists of all these controls are not given until later A small nonlinear model ALAN by Alan S Manne is used to illustrate the output file and list it piece by piece as we discuss the various components The possibilities for extension to large models with voluminous output which is when the diagnostics are really useful should be apparent The output from a GAMS run is produced on one file which can be read using any text editor The default name of this output file depends on the operating system but Appendix C describes how this default can be changed The display statement described in detail in Chapter 14 can be used to export information from
312. level 1 abort model t3 failed call gdxdiff trnsport t3 system redirlog if errorlevel 1 abort results for trnsport and t3 are not equal check for hidden output call grep this is hidden t3 1st gt system nullfile if not errorlevel 1 abort did not hide in listing call grep this is hidden t3 dmp gt system nullfile if not errorlevel 1 abort did not hide in dump file The GAMS Grid Computing Facility I 1 Introduction As systems with multiple CPUs and High Performance Computing Grids are becoming available more widely the GAMS language has been extended to take advantage of these new environments New language features facilitate the management of asynchronous submission and collection of model solution tasks in a platform independent fashion A simple architecture relying on existing operating system functionality allows for rapid introduction of new environments and provides for an open research architecture A typical application uses a coarse grain approach involving hundreds or thousands of model solutions tasks which can be carried out in parallel For example gt Scenario Analysis gt Monte Carlo Simulations gt Lagrangian Relaxation gt Decomposition Algorithms gt Advanced Solution Approaches The grid features work on all GAMS platforms and have been tailored to many different environments like the Condor Resource Manager a system for high throughput computing from the University of Wisconsi
313. ll intermediate points is by adding bounds to the variable concerned Consider the following function reference from RAMSEY preceded by the bounding of the variables 8 5 Data Handling Aspects of Equations 77 c lo t 0 01 util utility e sum t beta t log c t The bounding on c t away from 0 prevents the log function from being undefined 8 5 Data Handling Aspects of Equations The previous section dealt with the algebraic nature of equations This section deals with the other aspect of an equation it also serves as data As with variables four data values are associated with each unique label tuple unique label combination of every equation In practice these are used mainly for reporting purposes after a solve and so the discussion will be brief The suffixes associated with the four values are 1 m 1o and up as with variables They may be assigned values in assignments this is rare or referenced in expressions or displayed which is more common especially for the marginal m The meanings of the attributes 1o 1 and up will be described with respect to an individual constraint rather than the symbolic equation After a solution has been obtained there is a value associated with the unknown terms on the left and this is by definition 1 The meaning of 1o and up are shown in table 8 2 in terms of the constant right hand side rhs and the variable left hand side 1 for each of the equation types The r
314. ll strip and makes the name short gmsrerun cmd will resubmit runit cmd echo echo off gt 3runit cmd echo 1 2 gt gt 3runit cmd echo gmscr_nx exe 2 gt gt 3runit cmd echo echo OK gt 3finished gt gt 3runit cmd echo exit gt gt 3runit cmd echo start b 3runit cmd gt nul gt 3gmsrerun cmd start b 3runit cmd gt nul exit 1 6 1 Grid Submission Testing The grid submission process can be tested on any GAMS program without having to change the source text The solvelink 4 option instructs the solve statement to use the grid submission process and then wait until the results are available and then loads the solution into the GAMS data base The solvelink option can be set via a GAMS command line parameter or via assignment to a the model attribute Once the model instance has been submitted for solution GAMS will check if the job has been completed It will keep checking twice the reslim seconds allocated for this optimization job and report a failure if this limit has been exceed After successful or failed retrieval of the solution gams will remove the grid directory unless we have used gamskeep or have set the gams keep parameter 1 7 Glossary and Definitions 277 1 7 Glossary and Definitions BCH Condor GAMS GDX HPC SUN Grid Compute Utility Branch amp Cut amp Heuristic High throughput computing system General Algebraic Modeling System GAMS Data Exchange High Performance
315. low DECLARED This is where the identifier is declared as to type This must be the first appearance of the identifier DEFINED This is the line number where an initialization a table or a data list between slashes or symbolic definition equation starts for the symbol ASSIGNED This is when values are replaced because the identifier appears on the left of an assignment statement IMPL ASN This is an implicit assignment an equation or variable will be updated as a result of being referred to implicitly in a solve statement CONTROL This refers to the use of a set as the driving index in an assignment equation loop or other indexed operation sum prod smin or smax REF This is a reference the symbol has been referenced on the right of an assignment in a display in an equation or in a model or solve statement 10 3 Compilation Output 95 10 3 3 The Symbol Listing Map The next map is called the Symbol Listing All identifiers are grouped alphabetically by type and listed with their explanatory texts This is another very useful aid to have handy when first looking into a large model prepared by someone else The symbol listing map can be turned on by entering a line containing onsymlist at the beginning of the program Symbol Listing SETS I securities J Aliased with I PARAMETERS HIGHRISK variance of highest security risk LOWYIELD yield of lowest yielding security MEAN mean annual returns on individual securities
316. ls gt and gt gt have the usual meaning of starting at the beginning or appending to an existing file There is also a variant onEchoS that permits parameter substitution as onEcho also does and another variant onEchoV that forbids parameter substitution Consider the following example set it TEST OnechoS gt externalfilel send it to external file line 2 to send Offecho The created file contains send TEST to external file line 2 to send while the file created by set it TEST OnechoV gt externalfilel send it to external file line 2 to send Offecho contains send it to external file line 2 to send In contrast to the second case in the first case it is substituded by TEST Note that when there is no path included the file by default will be placed in the working directory on off Embedded offEmbedded Enables or disables the use of embedded values in parameter and set data statements For sets the final text is concatenated with blank separators For example the element texts for the set i and j will be identical set k a b 1 a set i k 1 a a aaaa cccc dddd b a bbbb cccc dddd onEmbedded set j x 1 a aaaa b bbbb a cccc dddd onjoff Empty offEmpty This option allows empty data statements for list or table formats By default data statements cannot be empty Consider running the following slice of code set i 1 2 3 set jG parameter x i empty
317. lselfE does the same as elself but evaluates numerical values of the control variables elseIfI elseIfI does the same as elseIf but is case insensitive encrypt Causes a file to be converted into an encrypted file The syntax is encrypt source target where source is the name of the source file to be encrypted and target is the name for the resulting encrypted file Note that encryption requires a special GAMS license The use of the Plicense parameter specifies the target license to be used as a user key for decrypting This must be done with the same license as was used in encryption Decryption is done when reading the GAMS system files GAMS recognizes whether a file is compressed or encrypted and will process the files accordingly endIf endIf must be matched with an ifThen ifThenE or ifThenI eolcom This option redefines the end of line comment symbol which can be a one or two character sequence By default the system is initialized to but not active The oneolcom option is used to activate the end of line comment The eo1com option sets oneolcom automatically Consider the following example eolcom gt set i 1 2 gt set declaration parameter a i gt parameter declaration The character set gt serves as the end of line comment indicator t GAMS requires that one does not reset the eolcom option to the existing symbol The following code is illegal since eolcom is being reset to the same
318. luded therein The syntax is set varname expression where varname is any user chosen variable name and expression is optional and can contain text or a number These variables are destroyed using drop varname In contrast to eval the set command does not evaluate the expression at compile time For differences to setGlobal and setLocal consider the following example setGlobal Anumber 3 2 2 setLocal Bnumber 44 2 set Cnumber min 33 34 ife Anumber 11 display Anumber equals 11 ife Bnumber 22 display Bnumber equals 22 ife Cnumber 33 display Cnumber equals 33 include test2 gms if Dnumber 44 display Dnumber equals 44 if NOT Dnumber 44 display Dnumber does NOT equal 44 if Enumber 55 display Enumber equals 55 if NOT Enumber 55 display Enumber does NOT equal 55 if Fnumber 66 display Fnumber equals 66 if NOT Fnumber 66 display Fnumber does NOT equal 66 where test2 gms is D 3 Detailed Description of Dollar Control Options 237 ife Anumber 11 display Anumber equals 11 in test2 gms ife NOT Anumber 11 display Anumber does NOT equal 11 in test2 gms if Bnumber 22 display Bnumber equals 22 in test2 gms if NOT Bnumber 22 display Bnumber does NOT equal 22 in test2 gms ife Cnumber 33 display Cnumber equals 33 in test2 gms ife NOT Cnumber 33 display Cnumber does NOT equal 33 in test2 gms setGlobal Dnumber 44 setLocal Enumber 55 set Fnumber
319. lver is called from a shell and GAMS remains open e 2 the solver is called with a spawn if possible as determined by GAMS or a shell if the spawn is not possible and GAMS remains open 3 GAMS starts the solution and continues in a Grid computing environment 4 GAMS starts the solution and waits same submission process as 3 in a Grid computing environment e 5 the problem is passed to the solver in core without use of tempo rary files solveOpt This attribute tells GAMS how to manage the model solution when only part of the variables and equations are in the particular problem being solved Note that the corresponding option expects a text while the use of model_name solveOpt and the command line expect a numeric value Allowed are e 0 replace the solution information for all equations appearing in the model is completely replaced by the new model results variables are only replaced if they appear in the final model e 1 merge the solution information for all equations and variables is merged into the existing solution information default e 2 clear the solution information for all equations appearing in the model is completely replaced in addition variables appearing in the symbolic equations but removed by conditionals will be removed There is an example called solveopt in the model library sysOut This attribute controls the incorporation of additional solver generated output that in the solver status fi
320. lverdict 178 solverinst 178 solvermatr 178 solversolu 178 solverstat 178 stepsum 178 strictsingleton 178 stringchk 178 subsys 178 suppress 178 symbol 178 sys11 178 sysdir 178 sysincdir 178 sysout 178 tabin 178 tformat 178 threads 178 timer 178 trace 178 traceopt 178 userl 178 warnings 178 workdir 178 workfactor 178 workspace 178 xsave 178 zerores 178 zeroresrep 178 GAMS coordinator 171 GAMS execution output column listing 98 equation listing 97 Model statistics 98 solve summary 99 GAMS output echo print 92 example 91 introduction 91 report summary 104 solution listing 103 symbol listing map 95 symbol reference map 93 GAMS call Introduction 177 specifying options 177 GAMS language items Characters 30 GAMS language items 29 Comments 32 declarative statements 28 Delimiters 32 identifiers 30 Labels 31 Numbers 32 reserved words 30 text 31 GAMSLIB 175 gamsRelease function 61 gamsVersion function 61 gday function 61 gdow function 61 gdx GAMS call parameter 187 gdxcompress GAMS call parameter 187 gdxconvert GAMS call parameter 187 gdxIn dollar control option 214 gdxOut dollar control option 214 ge relational operator 30 109 geometric distribution 282 ghour function 61 gleap function 61 gmillisec function 61 gminute function 61 gmonth function 61 goto dollar control option 214 grid computing 269 griddir GAMS
321. m as follows new york chicago topeka seattle 50 000 300 000 san diego 275 000 275 000 You will also receive the marginal costs simplex multipliers below chicago topeka seattle 0 036 san diego 0 009 These results indicate for example that it is optimal to send nothing from Seattle to Topeka but if you insist on sending one case it will add 036 K or 36 00 to the optimal cost Can you prove that this figure is correct from the optimal shipments and the given data 2 2 Structure of a GAMS Model For the remainder of the tutorial we will discuss the basic components of a GAMS model with reference to the example above The basic components are listed in table 2 2 There are optional input components such as edit checks for bad data and requests for customized reports of results Other optional advanced features include saving and restoring old models and creating multiple models in a single run but this tutorial will discuss only the basic components Before treating the individual components we give a few general remarks 1 A GAMS model is a collection of statements in the GAMS Language The only rule governing the ordering of statements is that an entity of the model cannot be referenced before it is declared to exist 2 GAMS statements may be laid out typographically in almost any style that is appealing to the user Multiple lines per statement embedded blank lines and multiple statements per line are allowed You
322. m3 is set equal to all elements that are members of subitem1 but subitem2 The operation above is equivalent to the following longer way of representation subitem3 item yes subitem1 item subitem3 subitem2 no 12 5 Summary The purpose of set assignments is to make calculations based on given data the static sets for use in exception handling It is one more example of the principle of entering a small amount of data and building a model up from the most elemental information 13 Sets as Sequences Ordered Sets 13 1 Introduction In our original discussion of sets in Chapter 4 we said that unless there is a special need to do things differently a one dimensional set should be regarded as an unordered collection of labels In this chapter we will discuss special features that can be used when you need to be able to deal with a set as if it were a sequence For example in economic models that explicitly represent conditions in different time periods it is necessary to refer to the next or previous time period because there must be links between the periods As another example stocks of capital are normally tracked through such models by equations of the form stocks at the end of period n are equal to stocks at the end of period n 1 plus net gains during period n Location problems where the formulation may require a representation of contiguous areas as in a grid representation of a city and scheduling problems are othe
323. mber offdigit can be used to ignore trailing digits Note that the error occurs in the 17th significant digit of y toolarge However after the o0ffdigit line y ignored is accepted without any errors even though there are more than 16 significant digits on off Dollar offDollar This option controls the echoing of dollar control option lines in the listing file Consider running the following slice of code hidden this line will not be displayed ondollar hidden this line will be displayed offdollar hidden this line will not be displayed The listing file that results looks like 2 ondollar 3 hidden this line will be displayed Note that all lines between the ondollar and offdollar are echoed in the listing file Also note that this action of this option is immediate i e the ondollar line is itself echoed on the listing file while the offdollar line is not onjoff DotL offDotL Activates or deactivates the automatic addition of L to variables on the right hand side of calculations as described at macro onjofF Echo Sends multiple subsequent lines to an external file These commands are used employing the syntax Onecho gt externalfilel line 1 to send line 2 to send 0ffecho or 226 Dollar Control Options Onecho gt gt externalfile2 line 1 to send line 2 to send Offecho In both cases the created file contains line 1 to send line 2 to send The redirection symbo
324. mber 66 display Fnumber does NOT equal 66 where test gms is if Anumber 11 display Anumber equals 11 in test gms if NOT Anumber 11 display Anumber does NOT equal 11 in test gms if Bnumber 22 display Bnumber equals 22 in test gms if NOT Bnumber 22 display Bnumber does NOT equal 22 in test gms if Cnumber 33 display Cnumber equals 33 in test gms if NOT Cnumber 33 display Cnumber does NOT equal 33 in test gms evalGlobal Dnumber 44 evalLocal Enumber 55 eval Fnumber 66 The resulting listing file contains SaaS 4 Anumber equals 11 5 Bnumber equals 22 ead 6 Cnumber equals 33 Baas 9 Anumber equals 11 in test gms saa 12 Bnumber does NOT equal 22 in test gms a 13 Cnumber equals 33 in test gms o 20 Dnumber equals 44 ate 23 Enumber does NOT equal 55 25 Fnumber does NOT equal 66 Note that GAMS allows one to define scoped local and global variables with the same name and has to prioritize under some cases Consider the following slice of code evalglobal notunique 11 evallocal notunique 22 eval notunique 33 log notunique log will echo 22 the current value of notunique to the log file evalGlobal evalGlobal evaluates a numerical expression at compile time and places it into a global control variable In turn one can use if and ife to do numeric testing on the value of this variable The format is evalGlobal varname expression where the expression must consist of constan
325. me periods 1985 1995 parameter s s card t As a result of the statement above s will be assigned the value 11 A common use of card is to specify some condition only for the final period for example to fix a variable An artificial example is c fx t ord t card t demand t which fixes the variable for the last member only no assignment is made for other members of t The advantage of this way of fixing c is that the membership of t can be changed safely and this statement will always fix c for the last one 13 4 Lag and Lead Operators The lag and lead operators are used to relate the current to the next or previous member of a set In order to use these operators the set in question must of course be ordered GAMS provides two forms of lag and lead operators gt Linear Lag and Lead Operators gt Circular Lag and Lead Operators The difference between these two types of operators involves the handling of endpoints in the sequence GAMS provides some built in facilities to deal with this issue but in any work involving sequences the user must think carefully about the treatment of endpoints and all models will need special exception handling logic to deal with them In the linear case the members of the set that are endpoints are left hanging In other words there are no members preceding the first member or following the last one This may cause the use of non existent elements The next secti
326. me solutions to complete by putting the GAMS program to sleep Note that we have assumed that there will be no errors in any of those steps This of course will not always be the case and elaborate mechanisms are in place to make the operation fail safe 13 A First Example The model QMEANVAR form the GAMS model library will be used to illustrate the use of the basic grid facility This model traces an efficiency frontier for restructuring an investment portfolio Each point on the frontier requires the solution of independent quadratic mixed integer models The original solution loop is shown below Loop p pp ret fx rmin rmax rmin card pp 1 ord pp Solve minvar min var using miqcp xres i p x 1 i report p i inc xi 1 i report p i dec xd 1 i This loop will save the solutions to the model MINVAR for different returns RET Since the solutions do not depend on the order in which they are carried out we can rewrite this loop to operate in parallel The first step is to write the submit loop parameter h pp model handles minvar solvelink 3 Loop p pp ret fx rmin rmax rmin card pp 1 ord pp Solve minvar min var using miqcp h pp minvar handle The model attribute solvelink controls the behavior of the solve statement A value of 3 tells GAMS to generate and submit the model for solution and continue without waiting for the completion of the solution step There is
327. ment has several effects Again they may be self evident but it is worthwhile to analyze them in detail The statement declares the existence of two parameters gives them the names a and b and declares their domains to be i and j respectively A domain is the set or tuple of sets over which a parameter variable or equation is defined The statement also gives documentary text for each parameter and assigns values of a i and b j for each element of i and j It is perfectly acceptable to break this one statement into two if you prefer as follows Parameters a i capacity of plant i in cases seattle 350 san diego 600 Parameters b j demand at market j in cases new york 325 chicago 300 topeka 275 Here are some points to remember when using the list format 1 The list of domain elements and their respective parameter values can be laid out in almost any way you like The only rules are that the entire list must be enclosed in slashes and that the element value pairs must be separated by commas or entered on separate lines 2 There is no semicolon separating the element value list from the name domain and text that precede it This is because the same statement is being used for declaration and assignment when you use the list format An element value list by itself is not interpretable by GAMS and will result in an error message 3 The GAMS compiler has an unusual feature called domain checking which verifies tha
328. model instance instance not ready minvar handle h instance execute_loadhandle minvar display x 1 xi 1 xd 1 gt gams qanalyze r submit gdir c test grid instance p4 Once all jobs are completed we can continue with the second part which will contain the collection loop for simplicity without the repeat loop because we would not run the final collection program unless we are satisfied that we got most of what we wanted Then the qreport gms file could look like loop pp handlestatus h pp minvar handle h pp execute_loadhandle minvar xres i pp zilli report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 xres i pp h pp na We would restart the above program from the save file that was created by the submitting job like gt gams qreport r submit gdir c test grid Note that it would not be necessary to run the job out of the same directory we did the initial submission We don t even have to run the same operating system 1 5 Summary of Grid Features To facilitate the asynchronous or parallel execution of the solve solution steps we have introduced three new functions a new model attribute a new gdx load procedure and a new GAMS option GridDir 274 The GAMS Grid Computing Facility 1 5 1 Grid Handle Functions HandleCollect handle collects loads the solution if ready 0 the model instance was not re
329. mpilation errors All other features are the same as discussed under load Consider the following example where transsol is the GDX file of the model trnsport gms which can be found in the GAMS Model Library set i j parameter b i a j gdxin transsol load i b loadDC j a gdxin transsol Note that in transsol a depends on i and b depends on j in contrast to this example While load i b works and b is just empty after that line loadDC j a triggers a domain violation error because in transsol a depends on i loadDCM loadDCM does the same as loadM plus domain checking like loadDC loadDCR loadDCR does the same as loadR plus domain checking like loadDC loadM loadM is an alternative form of load Instead of replacing an item or causing a domain violation error if the item was already initialized it merges the contents Consider the following example where transsol is the GDX file of the model trnsport gms which can be found in the GAMS Model Library set j 1 5 gdxin transsol loadm j display j gdxin transsol The resulting listing file contains 4 SET j markets 1 2 A 3 y 4 4 5 3 new york chicago topeka loadR loadR iteml item2 will replace the parameters or sets item1 item2 by the data stored in the current GDX file It must be used in conjunction with the command gdxIn Consider the following example where transsol is the GDX file of the model trnsport gms which can be found in the GAMS Model Libr
330. mpparms parameter provides more detailed information about the parameters changed or set by the user GAMS or the IDE during the current run Values O no logging 1 lists accepted parameters 2 log of file operations plus parameters Note that with dp 2 all the file operations are listed including the full path of each file on which any operation is performed emp emp tezt default EMP solver eolonly ey 0 single key value pair option By default any number of keyword value pairs can be present on the same line This parameter is an immediate switch that forces only one keyword value pair to be read on a line If there are more than one such pairs on a line then this option will force only the first pair to be read while all the other pairs are ignored Values O any number of keys or values 1 only one key value pair on a line errmsg errmsg 0 error message option This option controls the location in the listing file of the messages explaining the compilation errors Values O error messages at the end of compiler listing 1 error messages immediately following error line 2 no error messages To illustrate the option consider the following slice of GAMS code set i 1 10 set j i 10 11 parameter a jj 12 25 0 fis The listing file that results from running this model contains the following section 184 The GAMS Call 1 set i 1 10 set j i 10 11 CK 170 2 parameter a jj 12 25 0 143 RK 120 3 120 Un
331. mpress the file and compare it to the original file gt echo Decompress ti gms t3 org gt t4 gms gt gams t4 gt diff ti gms t3 org Finally we may want to encrypt the input file in a way to hide the equation definitions To do this we just insert Offlisting and Onlisting around the blocks of GAMS code we want to hide We now can encrypt the modified model file by using a privacy or target license file to lock the new encrypted file to this license key gt echo encrypt trnsport gms t1 gms gt t2 gms gt gams t2 plicense target This new version of tl gms can only be used with the target license file To simulate the target environment we can force the target license to be used instead of the installed one gt gams ti license target dumpopt 19 Note the use of dumopt 19 which is sometimes used for debugging and maintenance writes a clean copy of the input to the file t1 dmp all include files and macros are expanded In the file t1 dmp you will see that the input text between offlisting and Sonlisting is suppressed An attempt to Decompress and decrypt the file will fail as well Once a file has been encrypted it cannot be decrypted any more For example trying to decompress as in the example before will fail gt gams t4 Decompress Source C support 28Dec t1 gms Decompress Target C support 28Dec t3 org Decompress Error Security violation H 3 The CEFILES Gamslib Model The CEFILES model from th
332. must be entered on separate lines recognized by a symbol in the first column A dollar control option line may be placed anywhere within a GAMS program and it is processed during the compilation of the program The symbol is followed by one or more options identified by spaced Since the dollar control options are not part of the GAMS language they do not appear on the compiler listing unless an error had been detected Dollar control option lines are not case sensitive and a continued compilation uses the previous settings D 1 1 Syntax In general the syntax in GAMS for dollar control options is as follows option_name argument_list option_name argument_list where option_name is the name of the dollar control option while argument_list is the list of arguments for the option Depending on the particular option the number of arguments required can vary from 0 to many t No blank space is permitted between the character and the first option that follows ts In most cases multiple dollar control options can be processed on a line However some dollar control options require that they be the first option on a line ts The effect of the dollar control option is felt immediately after the option is processed An example of a list of dollar control options is shown below title Example to illustrate dollar control options onsymxref onsymlist Note that there is no blank space between the character and the option that follows T
333. n variables and equations onupper will cause all echo print to be in upper case ontext Sofftext ontext offtext pairs are used to create block comments that are ignored by GAMS Every ontext must have a matching offtext in the same file The 0fftext must be on a line by itself title text The text can have up to 80 characters This causes every page of the output to have the title specified t In all dollar control directives the symbol must be in the first character position on the line t Dollar control directives are dynamic they affect only what happens after they are encountered and they can be set and reset wherever appropriate They are remembered in continued compilations started from work files The directives that do not have following text can be entered many to a line as shown below for the map controls 10 4 Execution Output The only output to the listing file while GAMS is executing performing data manipulations is from the display statement All the user controls available to change the format will be discussed in detail later The output from the display statement on line 41 of the example is shown below Note the wrap of the explanatory text FREF 32 PARAMETER LOWYIELD 7 000 yield of lowest yielding security 10 000 variance of highest security risk PARAMETER HIGHRISK If errors are detected because of illegal data operations a brief message indicating the cause and the line number of the offendi
334. n control the last line suffix is updated continuously Last line suffixes are especially useful for modifying the various writing areas of a page gt The t111 and hd11 suffixes may not hold values applicable to the current page because when the title or header blocks are modified they correspond to the title or header blocks of the next page whenever the window has been written to on the current page t Not only can this suffix be used to determine the last line used in a writing area but it can also be used to delete lines within this area In the following example the header section will be completely deleted by resetting the hd11 suffix to 0 file out puthd out This header statement will be eliminated out hdll 0 In this example a header is initially written By changing the hd11 suffix to 0 the cursor is reset to the top of the header block Consequently the header will not be written unless something new is added to the header block 152 The Put Writing Facility 15 14 Paging Control In addition to the automatic paging which occurs when the bottom of the page is reached a page can also be written to file early The keyword putpage is used to do this Putpage forces the current page to immediately be written to file making a new page available for put statements In its simplest form the keyword putpage is used by itself to eject the current page Additionally it can be used with output items When it is used
335. n or the Sun Grid Engine Researchers using Condor reported a delivery of 5000 CPU hours in 20 hours wall clock time Disclaimer The use of the term grid computing may be offensive to some purists in the computer science world We use it very loosely to refer to a collection of computing components that allow us to provide high throughput to certain applications One may also think of it as a resurrection of the commercial service bureau concept of some 30 years ago Caution Although these features have been tested on all platforms and are part of our standard release we may change the approach and introduce alternative mechanisms in the future Acknowledgments Prof Monique Guignard Spielberg from the Wharton School at U Penn introduced us to parallel Lagrangian Relaxation on the SUN Grid Environment Prof Michael Ferris from the University of Wisconsin at Madison adopted our original GAMS grid approach to the high throughput system Condor and helped to make this approach a practical proposition 1 2 Basic Concepts The grid facility separates the solution into several steps which then can be controlled separately We will first review what happens during the synchronous solution step and then introduce the asynchronous or parallel solution steps When GAMS encounters a solve statement during execution it proceeds in three basic steps 270 The GAMS Grid Computing Facility 1 Generation The symbolic equations of the model are used to i
336. n the program gamsinst It will prompt you for default solvers to be used for each class of models If possible choose solvers you have licensed since unlicensed solvers will only run in demonstration mode These solver defaults can be changed or overridden by a rerunning gamsinst and resetting the default values b setting a command line default e g gams trnsport lp bdmlp c an option statement in the GAMS model e g option 1p bdmlp Add the GAMS system directory to your path see below To test the installation log in as a normal user and run a few models from your home directory but not the GAMS system directory LP trnsport objective value 153 675 NLP chenery objective value 1058 9 MIP bid optimal solution 15210109 512 MINLP procsel optimal solution 1 9231 MCP scarfmcp no objective function MPSGE scarfmge no objective function If you move the GAMS system to another directory remember to rerun gamsinst It is also good practice to rerun gamsinst when you add or change your license file if this has changed the set of licensed solvers K 4 Access to GAMS To run GAMS you must be able to execute the GAMS programs located in the GAMS system directory There are several ways to do this Remember that the GAMS system directory in the examples below may not correspond to the directory where you have installed your GAMS system 1 2 4 If you are using the C shell csh and its variants you
337. n worse if solvelink 0 is set the GAMS process terminates in order to execute the solve statement and restarts a new GAMS process after the solve which again starts up with a fresh function library instance so the function library s memory is lost also in this case The GAMS Test Library model trilib04 demonstrates this problem 6 3 4 Extended Range Arithmetic and Error Handling GAMS uses an extended range arithmetic to handle missing data the results of undefined operations and the representation of bounds that solver systems regard as infinite The special symbols are listed in table 6 2 with the brief explanation of the meaning of each Special symbol mapval Description inf 6 Plus infinity A very large positive number inf 7 Minus infinity A very large negative number na 5 Not available Used for missing data Any Operation that uses the value NA will produce the result NA undf 4 Undefined The result of an undefined or illegal operation A user cannot directly set a value to UNDF eps 8 Very close to zero but different from zero Table 6 2 Special symbols for extended arithmetic GAMS has defined the results of all arithmetic operations and all function values using these special values The results can be inspected by running the model library problem CRAZY As one would expect 1 INF evaluates to INF and 1 EPS to 1 ts The mapval function should be used in comparisons involving extended range arithmetic Only the
338. nStrictSingleton maxGoto phantom shift stop sysInclude terminate warning loadDCR loadM loadR unload set setArgs setComps setDDList setEnv setGlobal setLocal setNames show onDotL onExpand onLocal onMacro hide protect purge take first record if data statement for singleton set has multiple elements turns on global options turn on redefinition of data lag and lead operations on constant and ordered sets only enable recursive include files error if data statement for singleton set has mul tiple elements maximum number of jumps to the same label defines a phantom element DOS shift operation stop compilation include file from system directory terminate compilation and execution issue compilation warning load symbols from GDX file domain checked replace load symbols from GDX file domain filtered merge load symbols from GDX file domain filtered replace unload symbols into GDX file define a scoped environment variable define local environment variables using argu ment list unpack dotted names into local variables check double dash GAMS parameters define an OS environment variable define a global environment variable define a local environment variable unpack a filename into local environment vari ables show current GAMS environment variables assume l for variables in assignments expand macros when processing macro argu ments no limit on local nesting
339. ncise and easier method of data entry than the list based approach since each label appears only once at least in small tables 5 4 1 The Syntax In general the syntax in GAMS for a table declaration is table table_name text EOL element element element signed_num signed_num EOL element signed_num signed_num EOL 48 Data Entry Parameters Scalars amp Tables Table_name is the internal name of the table also called an identifier in GAMS The accompanying text is used to describe the parameter immediately preceding it Signed_num is a signed number and is declared to be the value of the entry associated with the corresponding element t The table statement is the only statement in the GAMS language that is not free format The following rules apply gt The relative positions of all entries in a table are significant This is the only statement where end of line EOL has meaning The character positions of the numeric table entries must overlap the character positions of the column headings gt The column section has to fit on one line gt The sequence of signed numbers forming a row must be on the same line gt The element definition of a row can span more than one line gt A specific column can appear only once in the entire table The rules for forming simple tables are straightforward The components of the header line are the by now familiar keyword identifier domain_list text sequence the doma
340. nerating LP model transport trnsport gms 66 4 Mb 6 rows 7 columns 19 non zeroes Executing CPLEX elapsed 0 00 00 114 IBM ILOG CPLEX 24 3 1 DEG Mac x86_64 Darwin Cplex 12 6 0 0 Reading data Starting Cplex Space for names approximately 0 00 Mb Use option names no to turn use of names off Tried aggregator 1 time LP Presolve eliminated 1 rows and 1 columns Reduced LP has 5 rows 6 columns and 12 nonzeros Presolve time 0 02 sec 0 00 ticks Iteration Dual Objective In Variable Out Variable 1 73 125000 x seattle new york demand new york slack 2 119 025000 x seattle chicago demand chicago slack 3 153 675000 x san diego topeka demand topeka slack 4 153 675000 x san diego new york supply seattle slack LP status 1 optimal Cplex Time 0 03sec det 0 01 ticks Optimal solution found Objective 153 675000 Restarting execution trnsport gms 66 2 Mb Reading solution for model transport trnsport gms 68 3 Mb Status Normal completion Job trnsport gms Stop 06 26 14 11 24 57 elapsed 0 00 00 487 298 Installation and System Notes Index circular operator 127 circular operator 127 after equation name 74 cursor control 144 n cursor control 144 n cursor control 144 abort dollar control option 206 abs function 58 acronym 28 169 action GAMS call parameter 179 activity level 1 or L 69 70 87 97 ALAN example fr
341. ng language and that programs must be written in the language to use it A GAMS program is contained in a disk file which is normally constructed with a text editor of choice When GAMS is run the file containing the program the input file is submitted to be processed After this processing has finished the results which are in the output file s can be inspected with a text editor On many machines a few terse lines appear on the screen while GAMS runs keeping the user informed about progress and error detection But it is the responsibility of the user to inspect the output file carefully to see the results and to diagnose any errors The first time or casual reader can skip this chapter the discussion of specific parts of the language in the next Chapters does not assume an understanding of this chapter 3 2 The Structure of GAMS Programs GAMS programs consist of one or more statements sentences that define data structures initial values data modifications and symbolic relationships equations While there is no fixed order in which statements have to be arranged the order in which data modifications are carried out is important Symbols must be declared as to type before they are used and must have values assigned before they can be referenced in assignment statements Each statement is followed by a semicolon except the last statement where a semicolon is optional 3 2 1 Format of GAMS Input GAMS input is free format A s
342. ng statement will appear 10 5 Output Produced by a Solve Statement 97 10 5 Output Produced by a Solve Statement In this section the content of the output produced when a solve statement is executed will be explained In Chapter 9 all the actions that are triggered by a solve were listed All output produced as a result of a solve is labeled with a subtitle identifying the model its type and the line number of the solve statement 10 5 1 The Equation Listing The first output is the Equation Listing which is marked with that subtitle on the output file By default the first three equations in every block are listed If there are three or fewer single equations in any equation block then all the single equations are listed The equation listing section from the example is listed below This model has three equation blocks each producing one single equation A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a Equation Listing SOLVE PORTFOLIO USING NLP FROM LINE 48 FSUM E fractions must add to 1 0 FSUM X hardware X software X show biz X t bills E 1 LHS 0 INFES 1 DMEAN E definition of mean return on portfolio DMEAN 8 X hardware 9 X software 12 X show biz 7 X t bills i t i p o LHS 0 INFES 10 xxx DVAR E definition of variance DVAR 0 X hardware 0 X software 0 X show biz VARIANCE E O LHS 0 ts The equation listing
343. ns the following statement display x 1 x m that calls for a printout of the final levels x 1 and marginal or reduced costs x m of the shipment variables x i j GAMS will automatically format this printout in to dimensional tables with appropriate headings 2 10 The lo l up m Database GAMS was designed with a small database system in which records are maintained for the variables and equations The most important fields in each record are lo lower bound 1 level or primal value up upper bound m marginal or dual value The format for referencing these quantities is the variable or equation s name followed by the field s name followed if necessary by the domain or an element of the domain GAMS allows the user complete read and write access to the database This may not seem remarkable to you now but it can become a greatly appreciated feature in advanced use Some examples of use of the database follow 2 10 1 Assignment of Variable Bounds and or Initial Values The lower and upper bounds of a variable are set automatically according to the variable s type free positive negative binary or integer but these bounds can be overwritten by the GAMS user Some examples follow capacity i j 10 0 new york 1 2 capacity seattle new york x up i j x 1o i j x up seattle 2 10 The lo l up m Database 17 It is assumed in the first and third exam
344. nstantiate the model using the current state of the GAMS data base This instance contains all information and services needed by a solution method to attempt a solution This representation is independent of the solution subsystem and computing platform 2 Solution The model instance is handed over to a solution subsystem and GAMS will wait until the solver subsystem terminates 3 Update The detailed solution and statistics are used to update the GAMS data base In most cases the time taken to generate the model and update the data base with the solution will be much smaller than the actual time spent in a specific solution subsystem The model generation takes a few seconds whereas the time to obtain an optimal solution may take a few minutes to several hours If sequential model solutions do not depend on each other we can solve in parallel and update the data base in random order All we need is a facility to generate models submit them for solution and continue At a convenient point in our GAMS program we will then look for the completed solution and update the data base accordingly We will term this first phase the submission loop and the subsequent phase the collection loop Submission Loop In this phase we will generate and submit models for solutions that can be solved indepen dently Collection Loop The solutions of the previously submitted models are collected as soon a solution is available It may be necessary to wait for so
345. nt capacity loop i put 3 i tl 15 a i put Market demand loop j put 3 j tl 15 b j put results put Transportation Model Results loop i j put i tl 12 j tl 24 x 1 i j 8 4 In the first line the internal file names factors and results are defined and connected to the external file names factors dat and results dat These internal file names are used inside the model to reference files which are external to the model The second line of this example assigns the file factors dat as the current file that is the file which is currently available to be written to In the third line of the example writing to the document begins using a put statement with the textual item Transportation Model Factors Notice that the text is quoted The slashes following the quoted text represent carriage returns The example continues with another textual item followed by the scalar f Notice that these output items are separated with commas Blanks commas and slashes serve as delimiters for separating different output items As mentioned above the slash is used as a carriage return Commas and blank spaces serve as item delimiters These delimiters leave the cursor at the next column position in the document following the last item written In most cases the blank and the comma can be used interchangeably however the comma is the stronger form and will eliminate any ambiguities In the fifth line of the pr
346. ntil and files minimizing parameter set using assign for model parameters sets variable binary free models positive smax variables card ge na prod smin while diag gt ne putpage solve xor display if negative puttl sos1 yes else inf no repeat sos2 The reserved non alphanumeric symbols are g e n x c s Table 3 3 Reserved words and symbols 3 4 3 Identifiers Identifiers are the names given to sets parameters variables models etc GAMS requires an identifier to start with a letter followed by more letters or digits The length of an identifier is currently limited to 63 characters 3 4 Language Items 31 Identifiers can only contain alphanumeric characters letters or numbers Examples of legal identifiers are a a15 revenue x0051 whereas the following identifiers are incorrect 15 casg milk amp meat t A name used for one data type cannot be reused for another 3 4 4 Labels Labels are set elements They may be up to 63 characters long and can be used in quoted or unquoted form The unquoted form is simpler to use but places restrictions on characters used in that any unquoted label must start with a letter or digit and can only be followed by letters digits or the sign characters and Examples of unquoted labels are Phos Acid 1986 1952 53 A September H2504 Line 1 In quoted labels quotes are used to delimit the label which may begin with and or include any legal charact
347. number L formed by these digits in the left and R in the right then a label is constructed for every integer in the sequence L to R Any non numeric differences or other inconsistencies cause errors The following example illustrates the most general form of the asterisked definition set g albc a20bc Note that this is not the same as set g a0ibc a20bc although the sets which have 20 members each have 11 members in common As a last example the following are both illegal because they are not consistent with the rule given above for making lists set illegali alx1 a9x9 illegal2 al b9 y Note one last time that set elements often referred to as labels can contain the sign characters and as well as letters and numbers 4 2 6 Declarations for Multiple Sets The keyword set if you prefer say sets instead the two are equivalent does not need to be used for each set rather only at the beginning of a group of sets It is often convenient to put a group of set declarations together 38 Set Definitions at the beginning of the program When this is done the set keyword need only be used once If you prefer to intermingle set declarations with other statements you will have to use a new set statement for each additional group of sets The following example below shows how two sets can be declared together Note that the semicolon is used only after the last set is declared se
348. numerical values to be encountered by the optimizer have relatively small absolute orders of magnitude The symbol K here means thousands of dollars The names of the types of entities may differ among modelers For example economists use the terms exogenous variable and endogenous variable for given data and decision variable respectively In GAMS the terminology adopted is as follows indices are called sets given data are called parameters decision variables are called variables and constraints and the objective function are called equations The GAMS representation of the transportation problem closely resembles the algebraic representation above The most important difference however is that the GAMS version can be read and processed by the computer Plants Shipping Distances to Markets 1000 miles Supplies New York Chicago Topeka Seattle 2 5 1 7 1 8 350 San Diego 2 5 1 8 1 4 600 Demands 325 300 275 Table 2 1 Data for the transportation problem adapted from Dantzig 1963 As an instance of the transportation problem suppose there are two canning plants and three markets with the data given in table 2 1 Shipping distances are in thousands of miles and shipping costs are assumed to be 90 00 per case per thousand miles The GAMS representation of this problem is as follows Sets i canning plants seattle san diego j markets new york chicago topeka Parameters a i capacity of plant i in cases
349. o DJ This can be written in GAMS as follows dj d 2 75 da d This assignment is known technically as an indexed assignment and set d will be referred to as the controlling index or controlling set ts The index sets on the left hand side of the assignment are together called the controlling domain of the assignment The extension to two or more controlling indices should be obvious There will be an assignment made for each label combination that can be constructed using the indices inside the parenthesis Consider the following example of an assignment to all 100 data elements of a Set row r 1x r 10 col c 1x c 10 sro row xr 7 r 10 parameters a row col a row col 13 2 r row c col The calculation in the last statement is carried out for each of the 100 unique two label combinations that can be formed from the elements of row and col The first of these is explicitly a r 1 c 1 13 2 r r 1 x c c 1 6 2 3 Using Labels Explicitly in Assignments It is often necessary to use labels explicitly in assignments This can be done as discussed earlier with parameters by using quotes around the label Consider the following assignment a r 7 c 4 2 36 This statement assigns a constant value to one element of a All other elements of a remain unchanged Either single or double quotes can be used around the labels 6 2 4 Assignments Over Subsets In general wherever a set name can
350. o annotate the solution output Note the use of per instead of in the text above slashes are illegal in all unquoted text 7 2 2 Variable Types There are five basic types of variables that may be used in variable statements These are shown in table 7 1 Keyword Default Default Description Lower Upper Bound Bound free default inf inf No bounds on variable Both bounds can be changed from the default values by the user positive 0 inf No negative values are allowed for variable The user can change the upper bound from the default value negative inf O No positive values are allowed for variables The user can change the lower bound from the default value binary 0 1 Discrete variable that can only take values of 0 or 1 integer 0 100 Discrete variable that can only take integer values between the bounds The user can change bounds from the default value Table 7 1 Variable types and default bounds The default type is free which means that if the type of the variable is not specified it will not be bounded at all The most frequently used types are free and positive for descriptions of variables for which negative values are meaningless such as capacities quantities or prices Four additional although more exotic variable types sos1 sos2 semicont and semiint are available in GAMS These are explained in Section 17 2 1 7 2 3 Styles for Variable Declaration Two styles are commonly used to dec
351. o define or alter values associated with any sets parameters variables or equations A simple assignment is written in the style associated with many other computer languages GAMS uses the traditional symbols for addition subtraction multiplication and division We will use them in the examples that follow and give more details in Section 6 3 page 55 6 2 1 Scalar Assignments Consider the following artificial sequence scalar x 1 5 x 1 2 x 2 x The scalar x is initialized to be 1 5 The second statement changes the value to 1 2 and the third changes it to 3 2 The second and third statement assignments have the effect of replacing the previous value of x if any with a new one Note that the same symbol can be used on the left and right of the sign The new value is not available until the calculation is complete and the operation gives the expected result rt An assignment cannot start with a reserved word A semicolon is therefore required as a delimiter before all assignments 6 2 2 Indexed Assignments The syntax in GAMS for performing indexed assignments is extremely powerful This operation offers what may be thought of as simultaneous or parallel assignment and it provides a concise way of specifying large amounts of data Consider the mathematical statement DJa 2 75D Ag for all d 54 Data Manipulations with Parameters This means that for every member of the set d a value is assigned t
352. o es aa ae ae RRR A Red Saha eee Rees 74 i Tho GIE IN EE 74 53 2 An Illustrative Example 00 0464 5 ea mes na a ee ee E A 74 Bass Dealer Eguations o a cas aaa s Ge Goel ae ea A Oe eo ee 75 Soe Indexed Mquaens gt o oe sa cas eala aala a hd adthaaneeags 248 Se ee eH 75 6 3 5 Using Labels Explicitly in Equations 66 645404 a p e bbe ee we ee a 75 Ba Expressions ia Equation Definitions o e c 04 4666 ee Bee eee PERE eS 76 8 4 1 Arithmetic Operators in Equation Definitions o e e ee 76 84 2 Functions in Equation Dellartio0s lt lt voca RD ee es 76 8 43 Preventing Undefined Operations in Equations e e 76 8 5 Data Handling Aspects of Equations aoao 77 9 Model and Solve Statements 79 TL a se se sss eae Ge aI eee ee ha eke ew eben bE ele ae ee 79 9 2 The Model Statement aowa coe saamari tadaa a A eae eee a 79 Cae o 2 a a A A 79 42 2 Classification of Models cc ce aceae e d a heen Baw e as 80 aa Modal ATIDI e e A a A i A A a 81 9a The Solve Statement cca sas ke ea GRE eR ea ee PEE Be ee ER Ee 85 Mok The A eo ke Oe ae ee Bi Ee Goes ea Go dhe ele ee 85 9 3 2 Requirements for a Valid Solve Statement 2 0 ee 86 9 3 3 Actions Triggered by the Solve Statement 0000 eee eee ee 86 TABLE OF CONTENTS 9 4 Programs with Several Solve Statements 9 4 1 Several Models ccioooosos sens 9 4 2 Sensitivity or Scenario Analysis
353. ocessing a solve statement preparing a problem description for the solver model list A list of equations used in a model as specified in a model statement nonbasic A column that is not basic and in nonlinear problems not superbasic Its value will be the same as the one of the finite bounds or zero if there are no finite bounds if the solution is feasible nonlinear nonzero In a linear programming problem the nonzero elements are constant In a nonlinear problem one or more of them vary because their values depend on that of one or more columns The ratio of nonlinear varying to linear constant non linear zero elements is a good indicator of the pervasiveness of non linearities in the problem nonoptimal There are two contexts First describing a variable a non basic variable that would improve the objective value if made basic The sign of the marginal value is normally used to test for non optimality Second for a solution other solutions exists with better objective values nonsmooth A classification of function that does not have continuous first derivatives but has continuous function values A plot of the function values will be a line with kinks in it nonzero element The coefficient of a particular column in a particular row if it is not zero Most mathematical programming problems are sparse meaning that only a small proportion of the entries in the full tableau of dimensions number of rows by number of columns is differ
354. ock puthd write to header block put write to window The size of any area within a given page is based entirely on the number of lines put into it Note that the total number of lines for all areas must fit within the specified page size If the total number of lines written to the title and header block equals or exceeds the page size an overflow error will be displayed in the program listing When this occurs this means there is no room remaining on the page to write to the window As mentioned above the syntax for writing an output item to any of the three possible writing areas of the page is basically the same the only difference being the choice of put keyword This is illustrated by writing to the title block of our report dat file puttl class2 GAMS Put Example In this case the text GAMS Put Example has been placed in the first column of the first row of the title block Any subsequent pages in the report dat file will now start with this information ts If the title block was modified or the header block was started after the window of the current page has been written to these modifications would appear in the next page and not the current page 15 6 2 Paging Paging occurs automatically whenever a page is full However note that the window must be used in order for the page to be written to the output file When a page has no output in its window the page is not written to file regardless of whether there are output i
355. od example of this is the assignment problem t Not all MIP solvers allow SOS1 variables Furthermore among the solvers that allow their use the precise definition can vary from solver to solver Any model that contains these variables may not be transferable among solvers Please verify how the solver you are interested in handles SOS1 variables by checking the relevant section of the Solver Manual 17 2 3 Special Order Sets of Type 2 SOS2 At most two variables within a SOS2 set can have non zero values The two non zero values have to be adjacent The most common use of SOS2 sets is to model piece wise linear approximations to nonlinear functions t The default bounds for SOS2 variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required Special ordered sets of type 2 are defined as follows 17 2 Special MIP Features 163 sos2 Variable s2 i t2 k j w2 i j k The members of the innermost the right most index belongs to the same set For example in the sets defined above s2 represents one special ordered set of type 2 with i elements t2 defines k sets of j elements each and w2 defines i j sets with k elements each PRODSCHX shows SOS type formulations with binary SOS1 and S0S2 sets The default bounds for SOS variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required t Not all MIP solvers allow SOS2 variables Furthermore
356. odels For details cf option cns domlim 0 This controls the maximum number of domain errors undefined operations like division by zero a nonlinear solver will perform while calculating function and derivative values before it terminates the run Nonlinear solvers have difficulty recovering after attempting an undefined operation eject Advances output in the listing file to the next page integerl to integerb Integer communication cell that can contain any integer number iterlim 2000000000 This option will cause the solver to interrupt the solution process after iterlim iterations and return the current solution values to GAMS limcol 3 This controls the number of columns that are listed for each variable in the COLUMN LISTING section of the listing file Specify zero to suppress the COLUMN LISTING altogether limrow 3 This controls the number of rows that are listed for each equation in the EQUATION LISTING section of the listing file Specify zero to suppress the EQUATION LISTING altogether 248 The Option Statement lp default This option controls the solver used to solve 1p models For details cf option cns mcp default This option controls the solver used to solve mcp models For details cf option cns minlp default This option controls the solver used to solve minlp models For details cf option cns mip default This option controls the solver used to solve mip models For details cf option cns
357. of Type L SOS cc ce ee eee ee 161 17 2 3 Special Order Sets of Type 2 SOS2 2 a md eae ee a 162 1 24 Dem Contmupus Variables c as s sonu Dae wa we ae a Re ee eo ee a 163 17 2 5 Semi Integer Variables eee P E 163 17 26 Setting Priorities for Branching su oori es Pe ee ee ee Ee a ee 164 17 3 Model Scala The Seale Option os poora meci ee A ERT ES 164 TABLE OF CONTENTS 9 7 04 The scale Option coo a A ae A A we e e G 164 e a II ee E A pa 165 liad Eguation Scaling isaac a a e e A A A Le eS 165 I7 34 Sealing ar Deriyatiyos o xoa he oo ee eee hE a we oP ee eRe ee eS 166 Appendix 168 A Glossary 169 B The GAMS Model Library 175 C The GAMS Call 177 C 1 The Generic no frills GAMS Call 2 20 00 0200 00000 ee ee 177 C 1 1 Specifying Options through the Command Line o a 177 C2 List of Command Line Parameters cococpnraca trineos crasas aaa 178 C 3 Detailed Description of Command Line Parameters e 179 D Dollar Control Options 203 DAL INTUOAUCUOR lt span ra a a ade a a 203 PA AE E 203 DZ List of Dollar Control Options c e cc ere sa REE EERE EE a 203 D 3 Detailed Description of Dollar Control Options 0 ea pidua ea 206 E The Option Statement 245 E1 Tatroduction oa o cori eaaa 040200544 bee dd e dd denn de ews 245 A ToM a a II a ee a a me Gm Ee 245 E2 List ot Options lt se 4046 2 dosie ee ee ee a Pe ee a A G 246 E3 Detailed Description of Options soc ca a
358. ogram above the cursor is repositioned to the first column of the sixth row of the output file where another textual item is written The cursor control characters and serve to reposition the cursor to a specific row or column as designated by the row or column number following the cursor control character Lastly the put statement is terminated with a semicolon Next the parameters a and b are written along with their corresponding set labels Only one element of the index set can be written using a put To write the entire contents of the parameters a and b the put statement is embedded inside a loop which iterates over the index set In the example above the set element labels are identified using their set identifier and the suffix t1 As can be seen the set element labels are located starting in the third column and the parameter a at column 15 The example continues with the display of another quoted textual item followed by the parameter b When executed the factors dat file will look like Transportation Model Factors Freight cost 90 00 Plant capacity seattle 350 00 san diego 600 00 Market demand new york 325 00 chicago 300 00 topeka 275 00 This output has been formatted using the default file format values The methods to change these defaults will be described later in this chapter In the last two lines of the example the file results dat is made current and the values associated with the variable x along with their co
359. ogramming Flow Control Features 16 4 The While Statement The while statement is used in order to loop over a block of statements 16 4 1 The Syntax The syntax of the while statement is while condition statements e t One cannot make declarations or define equations inside a while statement 16 4 2 Examples One can use while statements to control the solve statement For instance consider the following bit of GAMS code that randomly searches for a global optimum of a non convex model scalar count count 1 scalar globmin globmin inf option bratio 1 while count le 1000 x 1 j uniform 0 1 solve ml using nlp minimizing obj if obj 1 le globmin globmin obj 1 globinit j x 1 j Y count count 1 In this example a non convex model is solved from 1000 random starting points and the global solution is tracked The model PRIME from the model library illustrates the use of the while statement through an example where the set of prime numbers less than 200 are generated The following GAMS code is illegal since one cannot define equations inside a while statement while s gt 0 eq sum i x i g 2 The following GAMS code is illegal since one cannot make declarations inside a while statement while s gt 0 scalar y y 5 16 5 The For Statement The for statement is used in order to loop over a block of statements 16 5 The For Statement 159 16 5 1 T
360. olumn that is in the basis maintained by solution methods that use linear programming iterations binding An inequality constraint is binding when the value of the associated slack is zero bounds Upper and lower limits on the possible values that a column may assume in a feasible solution May be infinite meaning that no limit is imposed column An individual decision variable in the model seen by a solver program Many may be associated with one GAMS variable compilation The initial phase of GAMS processing when the program is being checked for syntax and consistency constant set A set is constant if it remains unchanged It has to be initialized with a set definition statement and cannot be changed using assignment statement Sets used in domain definitions must be constant Sets used in lag operations must be ordered as well Sometimes the word static is used instead of constant constraint A relationship between columns that must hold in a feasible solution There may be many constraints associated with one GAMS equation continuous There are two contexts First a classification of a function A plot of the function values will be a line without breaks in it Second a classification of variables A continuous variable may assume any value within its bounds controlling sets See driving sets data types Each symbol or identifier has to be declared to be one of the seven data types which are set parameter variable equation mode
361. olver minlp default MINLP solver mip default MIP solver miqcp default MIQCP solver mpec default MPEC solver nlp default NLP solver parmfile command line parameter include file plicense privacy license file name putdir sets put directory qcp default QCP solver reference symbol reference file rminlp default RMINLP solver rmip default RMIP solver rmiqcp default RMIQCP solver rmpec default RMPEC solver scrdir sets scratch directory scrext scratch extension for temporary files scriptexit script executed at the end of a GAMS run scriptfrst first line written to gamsnext scriptnext script mailbox file name scrnam scratch name solvelink solver link options solvercntr solver control file name solverdict solver dictionary file name solverinst solver instruction file name solvermatr solver matrix file name solversolu solver solution file name solverstat solver status file name subsys sets configuration file name symbol symbol file name sys11 dynamic resorting sysdir sets system directory sysincdir sets system library directory trace trace file name traceopt trace file format option userl strings passed to subsystems workdir sets working directory Parameters affecting input file processing g205 sets version compatibility input sets input file name multipass controls multiple pass facility on115 generate certain errors optdir option file directory optfile option file indicator stringchk controls string substitution check tabin sets tab spacing
362. om GAMSLIB 91 93 algorithm 169 Implementation of non standard 88 alias 28 169 statement 38 all defining a model 98 ALUM example from GAMSLIB 39 and relational operator 110 ANDEAN example from GAMSLIB 56 appendexpand GAMS call parameter 179 appendlog GAMS call parameter 179 appendout GAMS call parameter 180 arccos function 58 arcsin function 58 arctan function 58 arctan2 function 58 arithmetic operations 56 65 107 addition 56 division 56 exponentiation 56 multiplication 56 prod 56 smax 56 smin 56 subtraction 56 sum 56 assigned reference type 94 assignment 70 169 conditional 113 indexed 53 issues with controlling indices 54 over subsets 54 scalar 53 statement 53 to dynamic sets 120 using labels explicitly 54 asterisk in set definitions 37 marking errors 98 105 use in comments 32 basic 169 batinclude dollar control option 206 beta distribution 281 283 Beta function 58 betaReg function 58 binary operator 111 134 binding 169 binomial distribution 282 284 binomial function 58 bool_and function 60 bool_eqv function 60 bool imp function 60 bool_not x function 60 bool_or function 60 bool_xor function 60 boolean operations 116 bounds 169 on variables 69 branching priority value prior 69 bratio GAMS call parameter 180 GAMS option 247 call dollar control option 207 call Async dollar control op
363. ome dynamic because of assignments They are also domain checked the only members they will ever be able to have must also be members of item And item is a static set and henceforth its membership is frozen The first two assignments each add one new element to subiteml The third is an example of the familiar indexed assignment subitem2 is assigned all the members of item The output caused by the display statement that will reveal the membership of the sets is shown below for verification See 7 SET SUBITEM1 first subset of item INK P LIPSTICK PEN r PENCIL 7 SET SUBITEM2 second subset of item DISH gt INK gt LIPSTICK PEN 7 PENCIL ts The elements are displayed in the order specified in the declaration of item 12 2 3 Dynamic Sets with Multiple Indices Dynamic sets like static sets can have up to 20 dimensions The following example illustrates assignments for multi dimensional sets Sets item items sold pencil pen sup suppliers bic parker waterman supply item sup supply pencil bic yes supply pen sup yes All the mechanisms using asterisks and parenthesized lists that we introduced in the discussion on static sets in chapter 4 are available for dynamic sets as well 12 2 4 Assignments over the Domain of Dynamic Sets One can make an assignment over the domain of a dynamic set because dynamic sets are known to be proper subsets of static sets This is not the same as doing domain chec
364. on This option suppresses the echoing of the contents of the input file s to the listing file This parameter is similar in functionality to the 0fflisting dollar control option 200 The GAMS Call Values O standard compiler listing 1 suppress compiler listing ts The offlisting and onlisting dollar control options effect the listing file only if suppress is set to 0 If suppress is set to 1 the input file s is not echoed to the listing file and these dollar control options have no effect on the listing file symbol symbol tezt symbol file name Writes a partial symbol table to be used in conjunction with reference files sys11 sys11 0 dynamic resorting Speed up for expressions containing constant indices or indices that are not in the natural order at the cost of increased memory use Values O automatic optimization restructuring of data 1 no optimization 2 always optimize restructure sysdir sysdir texwt system directory This option sets the GAMS system directory This option is useful if there are multiple systems installed on the machine or when GAMS is called from an external system like Visual Basic sysincdir sdir text system library search directory Used to complete a file name for sysinclude If the sdir option is not set the GAMS system directory is searched ts Unlike idir additional directories cannot be set with sdir The string passed will be treated as one directory Passing additional dire
365. on domlim nn in the program before the solve statement where nn is the required limit on the evaluation errors allowed The SOLVER STATUS and MODEL STATUS require special explanation The status for the solver the state of the program and the model what the solution looks like are characterized and a complete list of possible MODEL STATUS and SOLVER STATUS messages is given below Here is a list of possible MODEL STATUS messages 1 OPTIMAL This means that the solution is optimal that is it is feasible within tolerances and it has been proven that no other feasible solution with better objective value exists Note that the latter criterion is not influenced by the optcr and optca options 2 LOCALLY OPTIMAL This message means that a local optimum has been found that is a solution that is feasible within tolerances and it has been proven that there exists a neighborhood of this solution in which no other feasible solution with better objective value exists 10 5 Output Produced by a Solve Statement 101 3 10 11 12 13 14 15 16 17 18 19 UNBOUNDED This means that the solution is unbounded This message is reliable if the problem is linear but occasionally it appears for difficult nonlinear problems that are not truly unbounded but that lack some strategically placed bounds to limit the variables to sensible values INFEASIBLE This means that the problem has been proven to be infeasible If this
366. on sets the GAMS syntax to that of first version of Release 2 25 This is mainly used for backward compatibility New keywords have been introduced in the GAMS language since the first version of Release 2 25 Models developed earlier that use identifiers that have since become keywords will cause errors when run with the latest version of GAMS This option will allow one to run such models Consider the following example use225 set for 1 2 3 scalar x The word for is a keyword in GAMS introduced with the later versions of Release 2 25 The setting of the use225 option allows for to be used as an identifier since it was not a keyword in the first version of Release 2 25 use999 This option sets the GAMS syntax to that of the latest version of the compiler This option is the default Consider the following example use225 set for 1 2 3 scalar x use999 for x 1 to 3 display x The word for is used as a set identifier by setting the option use225 and later the keyword for is used as a looping construct by setting the language syntax to that of the latest version by setting use999 version version nnn issues a compilation error if nnn is greater than the current GAMS version D 3 Detailed Description of Dollar Control Options 243 warning warning issues a compilation warning but continues compilation and execution 244 Dollar Control Options E The Option Statement E 1 Introduction The option statement is
367. on will describe how this is handled in GAMS This form of the lag and lead operators is useful for modeling time periods that do not repeat A set of years say 1990 to 1997 is an example The operators are and GAMS is able to distinguish linear lag and lead operators from arithmetic operators by context To avoid ambiguity GAMS does not allow to mix lag and lead operators with arithmetic operators For example i 1 1 is not allowed but writing i 1 1 would work In the circular case the first and last members of the set are assumed to be adjacent so as to form a circular sequence of members The notion is that first 1 isareference to last and last 2 is the same as first 1 and so on All references and assignments are defined This is useful for modeling time periods that repeat such as months of the year or hours in the day It is quite natural to think of January as the month following December Agricultural farm budget models and workforce scheduling models are examples of applications where circular leads occur naturally The operators are and The next two sections will describe the use of these lag and lead operators in assignment statements and in equations respectively 13 5 Lags and Leads in Assignments One use of the lag and lead operator is in assignment statements The use of a lag and lead operator on the right hand side of an assignment is called a reference while its use in the
368. onditional Expressions Assignments and Equations shipcost i j ij i j factor congestfac j distance i j This cannot be re written as shipcost ij factor congestfac j distance ij The above representation has the index j on the right hand side but not on the left hand side As explained before GAMS will flag this assignment as an error However the following representation will work shipcost ij i j factor congestfac j distance ij In the above assignment ij is specifically denoted as a tuple of i and j which then appear on the left hand side 11 5 Conditional Indexed Operations Another important use of the dollar condition is to control the domain of operation of indexed operations This is conceptually similar to the dollar on the left described in Section 11 3 1 Consider the following example adapted from GTM tsubc sum i supc i ne inf supc i This statement evaluates the sum of the finite values in supc t A common use of dollar controlled index operations is where the control is itself a set This importance of this concept will become apparent with the discussion of dynamic sets A set has been used to define the mapping between mines and ports in Chapter 4 Another typical example is a set to set mapping defining the relationship between states and regions used for aggregating data obtained by state to the models requirements by region sets r west east s florida texas v
369. ons sulfur sulfur million tons Notice that text may have embedded blanks and may include special characters such as parentheses There are however restrictions on special characters in text Include slashes commas or semicolons only if the text is enclosed in quotes A set definition like set prices prices of commodities in dollars ounce gold price sil price will cause errors since the slash between dollars and ounce will signal the beginning of the set declaration and the GAMS compiler will treat ounce as the name of the first element Further the slash before gold price will be treated as the end of the set definition and gold price will be treated as a new set However by enclosing the explanatory text in quotes this problem is avoided The following text is valid set prices prices of commodities in dollars ounce 4 2 5 Sequences as Set Elements The asterisk plays a special role in set definitions It is used to relieve the tedium of typing a sequence of elements for a set and to make intent clearer For example in a simulation model there might be ten annual time periods from 1991 to 2000 Instead of typing ten years the elements of this set can be written as set t time 1991 2000 which means that the set includes the ten elements 1991 1992 2000 GAMS builds up these label lists by looking at the differences between the two labels If the only characters that differ are digits with the
370. or labels that do not satisfy the condition ts If the parameter on the left hand side of the assignment has not previously been initialized or assigned any values zeroes will be used for any label for which the assignment was suppressed Consider the following example adapted from CHENERY rho i sig i ne 0 1 sig i 1 The parameter sig i has been previously defined in the model and the statement above is used to calculate rho i The dollar condition on the statement protects against dividing by zero If any of the values associated with sig i turn out to be zero no assignment is made and the previous values of rho i remain As it happens rho i was previously not initialized and therefore all the labels for which sig i is 0 will result in a value of 0 Now recall the convention explained in Section 11 2 1 that non zero implies True and zero implies False The assignment above could therefore be written as rho i sig i 1 sig i 1 114 Conditional Expressions Assignments and Equations 11 4 2 Dollar on the Right t For an assignment statement with a dollar condition on the right hand side an assignment is always made If the logical condition is not satisfied the corresponding term that the logical dollar condition is operating on evaluates to 0 Consider the following example which is a slight modification to the one described in Section 11 3 1 x 2 y gt 1 5 Expressed in words this is
371. ords will cause errors when run with the latest version of GAMS This option will allow one to run such models Values O latest syntax 1 syntax from Release 2 05 only 2 syntax from the first version of Release 2 25 only For example the word if is a key word in GAMS introduced with the first version of Release 2 25 Setting the g205 1 option allows if to be used as an identifier since it was not a keyword in Release 2 05 As another C 3 Detailed Description of Command Line Parameters 187 example the word for is a key word in GAMS introduced with the later versions of Release 2 25 Setting the g205 2 option allows for to be used as an identifier since it was not a keyword in the first version of Release 2 25 t Using values of 1 or 2 for g205 will not permit the use of enhancements to the language introduced in the later versions gdx gdx tewt GAMS data exchange file name This option specifies the name of the GAMS data exchange file and causes such a file a gdx file to be written containing all data in the model at the end of the job Setting gdx to the string default causes GAMS to create a gdx file with the gms file root name and a gdx extension Thus gams trnsport with gdx default will cause GAMS to write the gdx file trnsport gax gdxcompress gdxcompress 0 compression of generated gdx file This option specifies whether the files are compressed or not Values O do not compress gdx files 1 compress gdx files Note
372. ourth tt gt 18 fifth DOIT E 19 sixth 4tt 8 and it put contains display one 08 10 11 display two amp system dateZ amp display third 08 10 11 display fourth system date display fifth 08 10 11 display sixth Z amp system dateZ amp This is really only present to allow one to be able to write GAMS instructions from GAMS as one would not be able to use a put to write the symbols gams ps otherwise eval eval evaluates a numerical expression at compile time and places it into a scoped control variable In turn one can use if and ife to do numeric testing on the value of this variable The format is eval varname expression where the expression must consist of constants functions or other control variables with numerical values No whitespace is allowed in the expression For differences to evalGlobal and evalLocal consider the following example evalGlobal Anumber 3 2 2 evalLocal Bnumber abs 22 eval Cnumber min 33 34 ife ZAnumber 11 display Anumber equals 11 ife Bnumber 22 display Bnumber equals 22 ife Cnumber 33 display Cnumber equals 33 include test gms if Dnumber 44 display Dnumber equals 44 if NOT Dnumber 44 display Dnumber does NOT equal 44 if Enumber 55 display Enumber equals 55 D 3 Detailed Description of Dollar Control Options 213 if NOT Enumber 55 display Enumber does NOT equal 55 if Fnumber 66 display Fnumber equals 66 if NOT Fnu
373. ow much we can benefit from relaxing the linear constraint to y i j 25 q j l 1 0 18 A GAMS Tutorial by Richard E Rosenthal Unfortunately this relaxed constraint has no realistic significance The constraint we are interested in relaxing or tightening is the nonlinear form of the ration constraint For example we would like to know the marginal benefit arising from changing the ratio constraint to y i j a 3 1 26 We can in fact obtain the desired marginals by entering the following transformation on the undesired marginals parameter amr i j appropriate marginal for ratio constraint amr i j ratio m i j 0 01 q 1 j display amr Notice that the assignment statement for amr accesses both m and 1 records from the database The idea behind the transformation is to notice that ydi p q j 1 26 is equivalent to y i j 25 q j 1 0 01 q j 2 11 GAMS Output The default output of a GAMS run is extensive and informative For a complete discussion see Chapter 10 page 91 This tutorial discusses output partially as follows Echo Print Reference Maps Status Reports Error Messages Model Statistics Solution Reports A great deal of unnecessary anxiety has been caused by textbooks and users manuals that give the reader the false impression that flawless use of advanced software should be easy for anyone with a positive pulse rate GAMS is designed with the understanding that even the most experience
374. ow sets are declared and initialized There are some more advanced set concepts such as assignments to sets as well as lag and lead operations but these are not introduced until much later in the book However the topics covered in this chapter will be enough to provide a good start on most models 4 2 Simple Sets A set S that contains the elements a b and c is written using normal mathematical notation as S a b c In GAMS notation because of character set limitations the same set must be written as set S a b c The set statement begins with the keyword set or sets S is the name of the set and its members are a b and c They are labels but are often referred to as elements or members 4 2 1 The Syntax In general the syntax in GAMS for simple sets is as follows set set_name text element text element text set_name text element text element text set_name is the internal name of the set also called an identifier in GAMS The accompanying text is used to describe the set or element immediately preceding it 4 2 2 Set Names The name of the set is an identifier An identifier has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long This is enough to construct meaningful names and explanatory text can be used to provide more details Examples of legal identifiers are 36 Set Definitions
375. parameter table y i i headers only 1 2 3 onempty set k i parameter xx i empty parameter table yy i i 1 2 3 The listing file that results looks like 1 set i 1 2 3 3 2 set j i 2K 460 3 parameter x i empty parameter RK 460 D 3 Detailed Description of Dollar Control Options 227 4 table y i i headers only 5 1 2 3 AK 462 8 set k i 9 parameter xx i empty parameter 10 table yy i i 11 1 2 3 12 gt Error Messages 460 Empty data statements not allowed You may want to use 0N OFFEMPTY 462 The row section in the previous table is missing Note that empty data statements are not allowed for sets parameters or tables These are most likely to occur when data is being entered into the GAMS model by an external program Using the onempty dollar control option allows one to overcome this problem t The empty data statement can only be used with symbols which have a known dimension If the dimension is also derived from the data the phantom dollar control option should be used to generate phantom set elements onjoff End offEnd Offers alternative syntax for flow control statements Endloop endif endfor and endwhile are introduced as key words with the use of the onend option that then serves the purpose of closing the loop if for and while language constructs respectively The following example provides the alternate syntax for the four language constructs men
376. parameter has already been declared and the right hand side parameters have already been assigned values in previous statements csquared sqr c 12 A GAMS Tutorial by Richard E Rosenthal e m csquared W 1 lamda eoq i sqrt 2 demand i ordcost i holdcost i t i min p i q i r i log s i euclidean i j qrt sqr xi i xi j sqr x2 i x2 3 present j future j exp interest time j The summation and product operators to be introduced later can also be used in direct assignments 2 5 Variables The decision variables or endogenous variables of a GAMS expressed model must be declared with a Variables statement Each variable is given a name a domain if appropriate and optionally text The transportation model contains the following example of a Variables statement Variables x i j shipment quantities in cases Z total transportation costs in thousands of dollars This statement results in the declaration of a shipment variable for each i j pair You will see in Chapter 8 page 73 how GAMS can handle the typical real world situation in which only a subset of the i j pairs is allowable for shipment The z variable is declared without a domain because it is a scalar quantity Every GAMS optimization model must contain one such variable to serve as the quantity to be minimized or maximized Once declared every variable must be assigned a type The permissible types are given in tabl
377. particular it returns e 0 if the model associated with HANDLE had not yet finished solution or could not be loaded e 1 if the solution has been loaded deletes the grid computing problem identified by the HANDLE calling argument and returns a numerical indicator of the sta tus of the deletion as follows e 0 if the the model instance has been removed e 1 if the argument HANDLE is not a legal handle e 2 if the model instance is not known to the system e 3 if the deletion of the model instance encountered errors A nonzero return indicates a failure in the deletion and causes an execution error tests if the solve of the problem identified by the calling ar gument HANDLE is done and if so loads the solution into a GDX file A numerical indication of the result is returned as follows e 0 if a model associated with HANDLE is not known to the system e 1 the model associaed with HANDLE exists but the solution process is incomplete e 2 the solution process has terminated and the solution is ready for retrieval e 3 the solution process signaled completion but the solu tion cannot be retrieved An execution error is triggered if GAMS cannot retrieve the status of the handle resubmits a previously created instance of the model identified by the HANDLE for solution A numerical indication of the result is returned as follows e 0 the model instance has been resubmitted for solution e 1 if the argument HANDLE is not a legal handle
378. ping limit fsave force workfile to be written heaplimit maximum Heap size allowed in Mb holdfixed treat fixed variables as constants integer1 integer communication cell iterlim iteration limit keep keep scratch files nodlim node limit in branch and bound tree optca absolute optimality criterion optcr relative optimality criterion procdir run or process directory reslim solve time limit seed random number seed strictsingleton Error if assignment to singleton set has multiple elements threads number of threads to be used by a solver timer instruction timer threshold in milli seconds warnings number of warnings permitted workfactor work space multiplier workspace work space in Mb zerores set results of certain operations to zero zeroresrep report use of zerores as a warning Parameters controlling system settings charset extended character set cns default CNS solver curdir sets current directory dnlp default DNLP solver emp default EMP solver errnam error message file name errorlog error message lines written to the log file execerr execution time error limit griddir grid file directory gridscript grid submission script ide Integrated Development Environment inputdir sets input search path inputdir1 sets individual input search path jobtrace string written at the end of a trace libincdir sets library include directory license sets license file name lp default LP solver maxprocdir maximum number of process directories mcp default MCP s
379. placed in the bottom margin of the page These lines are in addition to the number of lines specified in the ps file suffix This is functional with pc option 0 only Default value is 0 alphabetic case case Used to specify the case in which alphabetic characters are displayed in the output file 0 default Causes mixed case to be displayed 1 Causes the output to be displayed in upper case regardless of the case used for the input To illustrate the use of these file suffixes the following example involves formatting report txt so that the pages are 72 spaces wide with 58 lines of output an additional top margin of 6 lines using ASCII page control characters inserted every 64 lines and with the output displayed in upper case file class2 report txt class2 pw 72 class2 ps 58 class2 tm 6 class2 pc 3 class2 case 1 t Using a value of 4 5 or 6 for the print control suffix pc will cause data to be squeezed and therefore will ignore spacing information provided by the user through the character However these values can be used to pass data on to be read by spreadsheets 15 6 Page Sections There are three independent writing areas on each page of a document These areas are the title block the header block and the window This is quite useful when there are sections of a page which remain relatively constant throughout a document Title and header blocks are often used to provide organizational information
380. plate of an exit script can be found in the GAMS system directory gmsxitnt cmd Windows or gmsxitus run Unix 198 The GAMS Call scriptfrst sf text first line written to gamsnext The default is an empty string and the first line is not written scriptnext script gamsnext script mailbox file name scrnam sn tezt scratch name Name stem used to complete the names of intermediate work files This name stem has to have at least one Name will be completed with the scratch directory and the standard scratch name extension seed seed 3141 random number seed This option specifies the seed used for the pseudo random number generator solprint solprint 1 solution report print option This option controls the printing of the model solution to the listing file Values O remove solution listings following solves 1 include solution listings following solves 2 suppress all solution information solvelink sl 0 solver link options This option controls GAMS function when linking to solve Values O GAMS operates as always 1 the solver is called from a shell and GAMS remains open 2 the solver is called with a spawn if possible as determined by GAMS or a shell if the spawn is not possible and GAMS remains open 3 GAMS starts the solution and continues in a Grid computing environment 4 GAMS starts the solution and waits same submission process as 3 in a Grid computing environment 5 the problem is passed to the solve
381. ples that capacity i j is a parameter that was previously declared and assigned values These statements must appear after the variable declaration and before the Solve statement All the mathematical expressions available for direct assignments are usable on the right hand side In nonlinear programming it is very important for the modeler to help the solver by specifying as narrow a range as possible between lower and upper bound It is also very helpful to specify an initial solution from which the solver can start searching for the optimum For example in a constrained inventory model the variables are quantity i and it is known that the optimal solution to the unconstrained version of the problem is a parameter called eoq i As a guess for the optimum of the constrained problem we enter quantity 1 i 0 5 eoq i The default initial level is zero unless zero is not within the bounded range in which case it is the bound closest to zero It is important to understand that the 1o and up fields are entirely under the control of the GAMS user The l and m fields in contrast can be initialized by the user but are then controlled by the solver 2 10 2 Transformation and Display of Optimal Values This section can be skipped on first reading if desired After the optimizer is called via the solve statement the values it computes for the primal and dual variables are placed in the database in the 1 and m fields We can then read
382. ports SYMBOL TYPE REFERENCES i SET declared 2 defined 2 k SET declared 2 assigned 7 SETS i k on off Text The onText offText pair encloses comment lines Line numbers in the compiler listing are suppressed to mark skipped lines Consider the following standard comment line ontext Everything here is a comment until we encounter the closing offtext like the one below offtext another standard comment line The resulting listing file is as follows 1 standard comment line Everything here is a comment until we encounter the closing offtext like the one below 7 another standard comment line t GAMS requires that every ontext has a matching offtext and vice versa on off UEIList offUElList This option controls the complete listing of all set elements that have been entered in the listing file The unique element listing in the listing file generated by running TRNSPORT with onUE1List is as follows Unique Element Listing Unique Elements in Entry Order 1 SEATTLE SAN DIEGO NEW YORK CHICAGO TOPEKA Unique Elements in Sorted Order 1 CHICAGO NEW YORK SAN DIEGO SEATTLE TOPEKA Note that the sorted order is not the same as the entry order This is explained in Section 12 2 onjoff UEIXRef offUElXRef This option controls the collection and listing in the listing file of cross references of set elements Consider the following slice of code onuelxref set i this is set dec
383. program because they are illegal or ambiguous on some machines Generally all unprintable and control characters are illegal The only place where any character is legal is in an Sontext Sofftext block as illustrated in the section on comments below For completeness the full set of legal characters are listed in table 3 2 Most of the uncommon punctuation characters are not part of the language but can be used freely in text or comments AtoZ alphabet atoz alphabet Oto9 numerals amp ampersand double quote pound sign asterisk equals question mark at gt greater than semicolon back slash lt less than 7 single quote colon minus slash A comma parenthesis space dollar square brackets underscore dot braces exclamation mark plus percent circumflex Table 3 2 Legal characters 3 4 2 Reserved Words GAMS like computer languages such as C and Pascal uses reserved words often also called keywords that have predefined meanings It is not permitted to use any of these for one s own definitions either as identifiers or labels The complete list of reserved words are listed in table 3 3 In addition a small number of symbols constructed from non alphanumeric characters have a meaning in GAMS abort eps integer not sameas sum acronym eq le option scalar system acronyms equation loop options scalars table alias 1t or semicont then equations AA o all file maximizing ord semiint u
384. provided that it is qualified with one of the four suffixes The only places where a variable name can appear without a suffix is in a variable declaration as shown here or in an equation definition which is discussed in the next chapter 72 Variables 8 Equations 8 1 Introduction Equations are the GAMS names for the symbolic algebraic relationships that will be used to generate the constraints in the model As with variables one GAMS equation will map into arbitrarily many individual constraints depending on the membership of the defining sets 8 2 Equation Declarations A GAMS equation like all identifiers must be declared before it can be used 8 2 1 The Syntax The declaration of an equation is similar to a set or parameter declaration in that domain lists and explanatory text are allowed and recommended and several equations can be declared in one statement Equation s eqn_name text eqn_name text Eqn_name is the internal name of the equation an identifier in GAMS An identifier has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long The accompanying text is used to describe the set or element immediately preceding it This must not exceed 254 characters and must all be contained on the same line as the identifier it describes There are no modifying keywords as there are with variables and no initializing data list
385. ps equation listings solution reports and optional displays GAMS saves the documentary text and parrots it back throughout the output to help keep the model well documented 2 12 Summary This tutorial has demonstrated several of the design features of GAMS that enable you to build practical opti mization models quickly and effectively The following discussion summarizes the advantages of using an algebraic modeling language such as GAMS versus a matrix generator or conversational solver gt By using an algebra based notation you can describe an optimization model to a computer nearly as easily as you can describe it to another mathematically trained person gt Because an algebraic description of a problem has generality most of the statements in a GAMS model are reusable when new instances of the same or related problems arise This is especially important in environments where models are constantly changing gt You save time and reduce generation errors by creating whole sets of closely related constraints in one statement gt You can save time and reduce input errors by providing formulae for calculating the data rather than entering them explicitly gt The model is self documenting Since the tasks of model development and model documentation can be done simultaneously the modeler is much more likely to be conscientious about keeping the documentation accurate and up to date gt The output of GAMS is easy to read and
386. py txt call copy myfile txt mycopy txt 208 Dollar Control Options The first call will work on a PC but the second will not The copy command can only be used from a command line shell The system is not aware of this command Try this command after clicking Run under the Start menu in Windows You will find that it does not work call Async Works like ca11 but allows asynchronous job handling This means you can start a job without waiting for the result You can continue in your model and collect the return code of the job later The function JobHandle can be used to get the Process ID pid of the last job started With JobStatus pid one could check for the status of a job Possible return values are e 0 error input is not a valid PID or access is denied e 1 process is still running is e 2 process is finished with return code which could be accessed by errorlevel 3 process not running anymore or was never running no return code available With JobTerminate pid an interrupt signal can be sent to a running job If this was successful the return value is one otherwise it is zero With JobKill pid a kill signal can be sent to a running job If this was successful the return value is one otherwise it is zero clear This option resets all data for an identifier to its default values clear idi id2 id1 id2 are the identifiers whose data is being reset Note that this is carried out during compile
387. r which is automatically written to an external file whenever the page length attribute is exceeded Consequently the put writing facility only has control of the current page and does not have the ability to go back into the file to alter former pages of the document However while a particular page is current information placed on it can be overwritten or removed at will 15 2 The Syntax The basic structure of the put writing facility in its simplest form is file fname s put fname put item s where fname represents the name used inside the GAMS model to refer to an external file Items are any type of output such as explanatory text labels parameters variable or equation values In the basic structure shown above the first line defines the one or more files which you intend to write to The second line assigns one of these defined files as the current file that is the file to be written to Lastly the third line represents the actual writing of output items to the current file 140 The Put Writing Facility 15 3 An Example It is instructive to use a small example to introduce the basics of the put writing facility The example will be based on the transportation model TRNSPORT The following program segment could be placed at the end of the transportation model to create a report file factors factors dat results results dat put factors put Transportation Model Factors Freight cost f 1 6 Pla
388. r 7 calls soe ERRORS S IN EQUATION ONE 2 INSTANCES OF DIVISION BY ZERO RESULT SET TO 0 1E 05 x4 REPORT SUMMARY NONOPT NOPT INFEASIBLE UNBOUNDED ERRORS NOOR Note that the solver status returned with a value of 5 meaning that the solver has been interrupted because more than domlim evaluation errors have been encountered The type of evaluation error and the equation causing the error are also reported If the solver returns an intermediate feasible solution because of evaluation errors the following solve will still be attempted The only fatal GAMS error that can be caused by a solver program is the failure to return any solution at all If this happens as mentioned above all possible information is listed on the GAMS output file and any solves following will not be attempted 10 7 Summary This is the end of the sequential discussion of the basic features of the GAMS language All further chapters are geared towards more advanced use of GAMS 11 Conditional Expressions Assignments and Equations 11 1 Introduction This chapter deals with the way in which conditional assignments expressions and equations are made in GAMS The index operations already described are very powerful but it is necessary to allow for exceptions of one sort or another For example heavy trucks may not be able use a particular route because of a weak bridge or some sectors in an economy may not produce exportable product The use o
389. r c y 1988 these two retain their previous values of 1 The lag or lead value does not have to be an explicit constant it can be arbitrary expression provided that it evaluates to an integer If it does not error messages will be produced A negative result causes a switch in sense from lag to lead for example The following is guaranteed to set d t to all zero d t d t ord t 13 5 3 Circular Lag and Lead Operators The following example illustrates the use of circular lag and lead operators set seasons spring summer autumn winter parameter val s spring 10 summer 15 autumn 12 winter 8 lagval2 s leadval s lagval2 s 1 lagval2 s val s 2 leadval s 1 leadval s 1 val s option decimals 0 display val lagval2 leadval The results are shown below TERR 7 PARAMETER VAL SPRING 10 SUMMER 15 AUTUMN 12 WINTER 8 s 7 PARAMETER LAGVAL2 SPRING 12 SUMMER 8 AUTUMN 10 WINTER 15 5 7 PARAMETER LEADVAL SPRING 8 SUMMER 10 AUTUMN 15 WINTER 12 The parameter lagval2 is used for reference while lagval1 if used for assignment Notice that the case of circular lag and lead operators does not lead to any non existent elements The difference between reference and assignment is therefore not important Note that the following two statements from the example above lagval2 s val s 2 leadval s 1 val s are equivalent to lagval2 s 2 val s leadval s
390. r classes of problems in which sets must also have the properties of sequences ts Models involving sequences of time periods are often called dynamic models because they describe how conditions change over time This use of the word dynamic unfortunately has a different meaning from that used in connection with sets but this is unavoidable 13 2 Ordered and Unordered Sets As with sets used in domain checking restrictions are imposed when the set needs to be referred as if it were a sequence The notion of static sets was introduced already the set must be initialized with a list of labels enclosed in slashes at the time the set is declared and never changed afterwards ts Ordered sets must be static sets In other words no order is possible for dynamic sets t GAMS maintains one list of unique elements the labels that are used as elements in one or more sets The order of the elements in any one set is the same as the order of those elements in that unique element list This means that the order of a set may not be what it appears to be if some of the labels were used in an earlier definition t The map of your labels in the GAMS order can be seen by putting the compiler directive onuellist somewhere before the first set declaration t A good rule of thumb is that if the labels in a set one wants to be ordered have not been used already then they will be ordered The map is shown with the other compiler maps after the listing of
391. r example the definition for the demand constraint will result in the creation of one constraint for each element of the domain j as shown in the following excerpt from the GAMS output DEMAND new york X seattle new york X san diego new york G 325 DEMAND chicago X seattle chicago X san diego chicago G 300 DEMAND topeka X seattle topeka X san diego topeka G 275 The key idea here is that the definition of the demand constraints is exactly the same whether we are solving the toy sized example above or a 20 000 node real world problem In either case the user enters just one generic equation algebraically and GAMS creates the specific equations that are appropriate for the model instance at hand Using some other optimization packages something like the extract above would be part of the input not the output In many real world problems some of the members of an equation domain need to be omitted or differentiated from the pattern of the others because of an exception of some kind GAMS can readily accommodate this loss of structure using a powerful feature known as the dollar or such that operator which is not illustrated here The domain restriction feature can be absolutely essential for keeping the size of a real world model within the range of solvability The relational operators have the following meanings 1 less than or equal to g greater than or equal to e equal to It is important to und
392. r in between e When load is not followed by arguments this causes a listing of the GDX file contents to be generated e If the same symbol names as in the underlying GDX file should be used the symbols are listed as arguments after load e g load i j e Symbols can also be loaded with a new name e g load inew i j_new j e The universal set can be loaded using load uni Consider the following example where transsol is the GDX file of the model trnsport gms which can be found in the GAMS Model Library gdxin transsol Sets i jj uni load i jj j Parameters a i bb jj load a load bb b Scalar f load f uni gdxin display i jj a bb f uni The resulting listing file contains gt 11 SET i canning plants seattle san diego gt 11 SET jj markets new york chicago topeka zess 11 PARAMETER a capacity of plant i in cases seattle 350 000 san diego 600 000 gt 11 PARAMETER bb demand at market j in cases D 3 Detailed Description of Dollar Control Options 221 new york 325 000 chicago 300 000 topeka 275 000 11 PARAMETER f 90 000 freight in dollars pe r case per thousand m iles gt 11 SET uni Universe seattle san diego new york chicago topeka loadDC loadDC is an alternative form of load but checks to see if the set element names being loaded are in the associated sets i e checks the domain Any domain violations will be reported and flagged as co
393. r in core without use of temporary files solvercntr scntr text solver control file name default name override Name completed with scratch directory and scratch extension solverdict sdict text solver dictionary file name default name override Name completed with scratch directory and scratch extension solverinst sinst tezxt solver instruction file name default name override Name completed with scratch directory and scratch extension solvermatr smatr text solver matrix file name default name override Name completed with scratch directory and scratch extension solversolu ssolu text solver solution file name default name override Name completed with scratch directory and scratch extension C 3 Detailed Description of Command Line Parameters 199 solverstat sstat texwt solver status file name default name override Name completed with scratch directory and scratch extension stepsum stepsum 0 step summary option This option controls the generation of a step summary of the processing times taken by GAMS during a given run Values O no step summary 1 step summary printed To illustrate the use of the stepsum option the default GAMS Ist file from running TRNSPORT with the option stepsum 1 contains the following step summaries STEP SUMMARY 0 000 0 000 STARTUP 0 000 0 000 COMPILATION 0 000 0 000 EXECUTION 0 000 0 000 CLOSEDOWN 0 000 0 000 TOTAL SECONDS 0 008 0 008 ELAPSED SECONDS 3 949 3 949 MAX
394. rameter variable or equation and d value must be as before in the range 0 and 8 Exactly d value places of decimals will be shown on all displays of ident that follow This form can be extended to control layout of the data The general form is option ident d value r value c value Here r value means the number of index positions that are combined to form the row label and c value means the number on the column headers The example discussed in the previous section is further extended in order to illustrate the local display control option x 5 3 1 display x and the output 12 PARAMETER X a four dimensional structure 14 5 Display Controls 137 first one b 5 63559 first two a 2 93930 first two b first three b 6 31610 second one a INF second one b second two a second two b 19 83500 0 02873 10 34570 1 00370 17 29948 INF Five places of decimals are shown and three labels are used to mark the rows and one on the column Since this is a four dimensional structure there are no remaining indices to be used as sub table labels on the plane and we now have the results in one piece The option statement is checked for consistency against the dimensionality of the identifier and error messages issued if necessary Here is an example that puts two indices on each of the row and column labels and retains five decimal places option x 5 2 2 display x The output is 12 PARAMETER X
395. rative Example Consider the following example adapted from MEXSS The associated declarations are also included Variables phi phipsi philam phipi phieps equations obj obj phi e phipsi philam phipi phieps Obj is the name of the equation being defined The e symbol means that this is an equality Any of the following forms of the equation are mathematically equivalent 8 3 Equation Definitions 75 obj phipsi philam phipi phieps e phi obj phieps phipsi e philam phi phipi obj phi phieps phipsi philam phipi e 0 obj 0 e phi phieps phipsi philam phipi ts The arrangement of the terms in the equation is a matter of choice but often a particular one is chosen because it makes the model easier to understand 8 3 3 Scalar Equations A scalar equation will produce at most one equation in the associated optimization problem The equation defined in the last Section is an example of a scalar equation which contains only scalar variables Note that in general scalar equations may contain indexed variables operated on by index operators Consider the following example from CHENERY dty td e sum i y i 8 3 4 Indexed Equations All the set references in scalar equations are within the scope of index operations many references can therefore be included in one equation However GAMS allows for equations to be defined over a domain thereby developing a compact
396. referencing a symbol of dimensionality one or more i e a vector or a matrix inequality constraint A constraint in which the imposed relationship between the columns is not fixed but must be either greater than or equal to or less than or equal to a constant The GAMS symbols g and 1 are used in equation definitions to specify these relationships infeasible Used to describe either a model that has no feasible solution or an intermediate solution that is not feasible although feasible solutions may exist See feasible above initialization Associating initial values with sets or parameters using lists as part of the declaration or definition or for parameters only using table statements list One of the ways of specifying initial values Used with sets or parameters most often for one dimensional but also for two and higher dimensional data structures list format One of the ways in which sets and parameters can be initialized and all symbol classes having data can be displayed Each unique label combination is specified in full with the associated non default value alongside marginal Often called reduced costs or dual values The values which are meaningful only for non basic rows or columns in optimal solutions contain information about the rate at which the objective value will change of if the associated bound or right hand side is changed matrix element See nonzero element model generation The initial phase of pr
397. representation for constraints The index sets to the left of the are called the domain of definition of the equation t Domain checking ensures that the domain over which an equation is defined must be the set or a subset of the set over which the equation is declared Consider the following example of a singly indexed equation meaning one that produces a separate constraint for each member of the driving or controlling set dg t g t e mew t xsi t m t As t has three members three constraints will be generated each one specifying separately for each member of t the dependence of g on m Mew and xsi are parameters the data associated with them are used in building up the individual constraints These data do not have to be known when the equation is defined but do have to be when a model containing the equation is solved The extension to two or more index positions on the left of the should be obvious There will be one constraint generated for each label combination that can constructed using the indices inside the parenthesis Here are two examples from AIRCRAFT a scheduling model bd j h b j h yd j m y j h dd j h y j h sum i p i j x i j e 1 The domain of definition of both equations is the Cartesian product of j and h constraints will be generated for every label pair that can be constructed from the membership of the two sets 8 3 5 Using Labels Explicitly in Equ
398. rginal are zero for basic variables and not zero for others t EPS is used with non basic variables whose marginal values are very close to or actually zero or in nonlinear problems with superbasic variables whose marginals are zero or very close to it A superbasic variable is one between its bounds at the final point but not in the basis There are brief explanations of technical terms used in this section in the Glossary For models that are not solved to optimality some constraints may additionally be marked with certain flags The list of these flags and their description is given below INFES The row or column is infeasible This mark is made for any entry whose level value is not between the upper and lower bounds NOPT The row or column is non optimal This mark is made for any non basic entries for which the marginal sign is incorrect or superbasic ones for which the marginal value is too large UNBND The row or column that appears to cause the problem to be unbounded 10 5 7 Report Summary The final section of the solution listing is the report summary marked with four asterisks as are all important components of the output It shows the count of rows or columns that have been marked INFES NOPT or UNBND in the solution listing section The sum of infeasibilities will be shown if it the reported solution is infeasible The error count in is only shown if the problem is nonlinear k REPORT SUMMARY 0 NONOPT O INFEASIBLE
399. riables so they contain the components of a period delimited string The syntax is setcomps perioddelimstring vi v2 v3 where perioddelimstring is any period delimited string like the set specification of a multidimensional parameter and 238 Dollar Control Options vi is the name of a control variable that will contain the name of the set element in the first position v2 is the name of a control variable that will contain the name of the set element in the second position v3 is the name of a control variable that will contain the name of the set element in the third position The items may be recombined back into the original filename string by using v1 v27 v3 Consider the following example setcomps period delim string vi v2 v3 display vi v1 display v2 v2 display v3 v3 set name v17 v27 v37 display name name The resulting listing file contains 2 vi period 3 v2 delim 4 v3 string ni 6 name period delim string setDDList Causes GAMS to look for misspelled or undefined double dash GAMS parameters Consider the following example The following double dash parameters are defined in the command line one 11 three 33 four 44 and the corresponding gms file contains display one display two setDDList three display three display four setDDList three checks if all double dash parameters have been used so far except
400. rings so the elements of t are not numbers Another convenient feature is the alias statement which is used to give another name to a previously declared set In the following example Alias t tp the name tp is like a in mathematical notation It is useful in models that are concerned with the interactions of elements within the same set The sets i j t and m in the statements above are examples of static sets i e they are assigned their members directly by the user and do not change GAMS has several capabilities for creating dynamic sets which acquire their members through the execution of set theoretic and logical operations Dynamic sets are discussed in Chap ter 12 page119 Another valuable advanced feature is multidimensional sets which are discussed in Section 4 5 page 39 2 4 Data The GAMS model of the transportation problem demonstrates all of the three fundamentally different formats that are allowable for entering data The three formats are e Lists e Tables e Direct assignments The next three sub sections will discuss each of these formats in turn 10 A GAMS Tutorial by Richard E Rosenthal 2 4 1 Data Entry by Lists The first format is illustrated by the first Parameters statement of the example which is repeated below Parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 This state
401. rks J 8 2 Multi variate Normal Distributions The CPP Library implements the PDF and CDF for the univariate bivariate and trivariate standard normal distributions We use the standard normal mean of 0 standard deviation of 1 since intrinsic functions are limited to 20 arguments The functions for the univariate case are included as convenient examples and should give results nearly identical to the pdfNormal and cdfNormal functions from the stochastic extrinsic library J 5 For the multivariate cases we based our implementation on the TVPACK code from Alan Genz with modifications to allow for proper computation of derivatives Again the number of arguments allowed is a consideration so we chose to implement functions taking correlation coefficients as arguments not a covariance matrix The conversion from the latter case to the former is relatively straightforward Here we describe it with some R code making use of the mnormt package that computes the multivariate CDF using similar code from Genz start with a mean mu and variance covariance matrix S1 x lt c 1 0 3 0 3 0 mu lt c 0 0 1 0 1 0 Si lt matrix c 1 0 1 1 5 1 4 1 5 1 5 1 5 9 3 3 2Alan Genz http www math wsu edu faculty genz homepage J 8 CPP Library 289 vi lt pmnorm x x mean mu varcov S1 convert to std normal with 3 correlation coeffs R lt cov2cor S1 sd lt sqrt diag S1 xn lt x mu sd v2 lt pmnorm x xn mean 0
402. rnal file name used in a put statement remains as the current file until a subsequent put statement uses an internal file name 142 The Put Writing Facility 15 4 3 Closing a File The keyword putclose is used to close a file during the execution of a GAMS program The syntax is as follows putclose myfile item s where myfile is the internal name of the file to be closed and item s are the final entries into the file before it is closed If the internal file name is omitted from the putclose statement the current put file is closed Note that after using the putclose command the file does not have to be redefined in order to use it again Simply make the file current and use put statements as would be done normally Of course the existing file will either be overwritten or appended to depending on the value of the append file suffix t One application where this is useful is to write the solver option file from within the GAMS model Option file statements can be written using put and the file closed with a putclose prior to the solve statement This makes the option file available for use by the solver The following example shows the creation and closing of an option file for the MINOS solver file opt Minos option file minos opt put opt put Iteration limit 500 Feasibility tolerance 1 0E 7 gt putclose opt This program segment would be placed inside the GAMS model prior to the solve statement 15 4 4 Appendin
403. ro level The marginal is marked with EPS rather than zero to facilitate restarting the optimizer from the old basis If the solvers results contain either infeasibilities or marginal costs of the wrong sign then the offending entries are marked with INFES or NOPT respectively If the problem terminates unbounded then the rows and columns corresponding to extreme rays are marked UNBND At the end of the solvers solution report is a very important report summary which gives a tally of the total number of non optimal infeasible and unbounded rows and columns For our example the report summary shows all zero tallies as desired xxx REPORT SUMMARY 0 NONOPT O INFEASIBLE O UNBOUNDED After the solver s report is written control is returned from the solver back to GAMS All the levels and marginals obtained by the solver are entered into the GAMS database in the 1 and m fields These values can then be transformed and displayed in any desired report As noted earlier the user merely lists the quantities to be displayed and GAMS automatically formats and labels an appropriate array For example the input statement 2 12 Summary 25 display x l x m results in the following output Lan 50 VARIABLE X L shipment quantities in cases new york chicago topeka seattle 50 000 300 000 san diego 275 000 275 000 ER 50 VARIABLE X M shipment quantities in cases chicago topeka seattle 0 036 san diego 0 009 As seen in reference ma
404. rom the label 1 Each element in a set must be separated from other elements by a comma or by an end of line In contrast each element is separated from any associated text by a blank Consider the following example from the Egyptian fertilizer model FERTS where the set of fertilizer nutrients could be written as set cq nutrients N P205 or as set cq nutrients N P205 The order in which the set members are listed is normally not important However if the members represent for example time periods then it may be useful to refer to next or previous member There are special operations to do this and they will be discussed in Chapter 13 For now it is enough to remember that the order in which set elements are specified is not relevant unless and until some operation implying order is used At that time the rules change and the set becomes what we will later call an ordered set 4 2 4 Associated Text It is also possible to associate text with each set member or element Explanatory text must not exceed 254 char acters and must all be contained on the same line as the identifier or label it describes For example label text for the set of final products in SHALE contains details of the units of measurement 4 2 Simple Sets 37 Set f final products yncrude refined crude million barrels lpg liquified petroleum gas million barrels ammonia ammonia million tons coke coke million t
405. rom your home directory but not the GAMS system directory LP trnsport objective value 153 675 NLP chenery objective value 1058 9 MIP bid optimal solution 15210109 512 K 6 Access to GAMS 295 MINLP procsel optimal solution 1 9231 MCP scar mcp no objective function MPSGE scarfmge no objective function 9 If you move the GAMS system to another directory remember to rerun gamsinst It is also good practice to rerun gamsinst when you add or change your license file if this has changed the set of licensed solvers K 6 Access to GAMS To run GAMS you must be able to execute the GAMS programs located in the GAMS system directory There are several ways to do this Remember that the GAMS system directory in the examples below may not correspond to the directory where you have installed your GAMS system 1 If you are using the C shell csh and its variants you can modify your cshrc file by adding the second of the two lines given below set path set path your previous path setting path Applications GAMS gams24 3_osx_x64_64_sfx new 2 Those of you using the Bourne sh or Korn ksh shells and their variants can modify their profile file by adding the second of the three lines below PATH your previous path setting PATH PATH Applications GAMS gams24 3_osx_x64_64_sfx new export PATH If the profile file does not exist yet it needs to be created You should log out and log in again
406. rresponding set element index labels are written line by line The output results of 15 4 Output Files 141 the variable x are formatted by specifying a field width of eight spaces with four of these spaces reserved for the decimal Notice that the local formatting options are delimited with colons The results dat file will look like Transportation Model Results seattle new york 0 0000 seattle chicago 300 0000 seattle topeka 0 0000 san diego new york 325 0000 san diego chicago 0 0000 san diego topeka 275 0000 With just this brief introduction to the put writing facility it is easy to envision its many uses such as report writing providing output to a file for use by another computer program or simply the display of intermediate calculations But the surface of the put writing facility has just barely been scratched In the sections that follow the many features and structure of the put writing facility are described in more detail along with examples 15 4 Output Files As noted earlier the put statement allows the user to write to external files This section describes the various features related to the use of external files 15 4 1 Defining Files The complete syntax for defining files is file fname text external file name where file is the keyword used to define files Fname is the internal file name and is used inside the GAMS model to refer to an external file External files are the actual files that output is wri
407. ry GAMS provides powerful facilities for data manipulation with parallel assignment statements built in functions and extended range arithmetic 7 Variables 7 1 Introduction This chapter covers the declaration and manipulation of GAMS variables Many of the concepts covered in the previous Chapters are directly applicable here A variable is the GAMS name for what are called endogenous variables by economists columns or activities by linear programming experts and decision variables by industrial Operations Research practitioners They are the entities whose values are generally unknown until after a model has been solved A crucial difference between GAMS variables and columns in traditional mathematical programming terminology is that one GAMS variable is likely to be associated with many columns in the traditional formulation 7 2 Variable Declarations A GAMS variable like all other identifiers must be declared before it is referenced 7 2 1 The Syntax The declaration of a variable is similar to a set or parameter declaration in that domain lists and explanatory text are allowed and recommended and several variables can be declared in one statement var type variable s var_name text 1 var_name text Var_type is the optional variable type that is explained in detail later Var_name is the internal name of the variable also called an identifier in GAMS An identifier has to start with a letter followed by more let
408. ry inclib in the GAMS system directory is searched t Unlike idir additional directories cannot be set with 1dir The string passed will be treated as one directory Passing additional directories will cause errors ts Note that if the ldir parameter is set the default library include directory is not searched Consider the following illustration gams myfile ldir mydir GAMS searches for any referenced libinclude file in the directory mydir license license text license file name This option should only be used by advanced users attempting to override internal license information The file name is used as given The default license file is gamslice txt in the GAMS system directory limcol limcol 3 default column listing This controls the number of columns that are listed for each variable in the COLUMN LISTING section of the listing file Specify zero to suppress the COLUMN LISTING altogether Values n first n columns listed limrow limrow 3 default row listing This controls the number of rows that are listed for each equation in the EQUATION LISTING section of the listing file Specify zero to suppress the EQUATION LISTING altogether Values n first n rows listed 190 The GAMS Call logfile lf tezt log file name This option is used in conjunction with the lo option If lo is set to 2 then this option will specify the name of the log file name The name provided by the option is completed using the current d
409. s 1 1 0 000 0 003 ExecInit 45 6 0 000 0 004 Assignment c 66 1 0 000 0 004 Solve Init transport 58 1 0 000 0 004 Equation cost 60 2 0 000 0 004 Equation supply 62 3 0 000 0 004 Equation demand 66 19 0 015 0 004 Solve Fini transport 66 1 0 000 0 004 GAMS Fini 1 1 0 000 0 002 ExecInit 66 1 0 000 0 002 Solve Read transport 68 f 0 000 0 003 Display 68 f 0 000 0 003 GAMS Fini profiletol ptol 0 0 profile time tolerance This option sets profile tolerance in seconds All statements that take less time to execute than this tolerance are not reported in the listing file putdir pdir text put directory This option specifies the directory where the put files are generated and saved If not specified it will be set to the working directory This option does not work if an absolute file name is provided through the file statement qcp qcp text default QCP solver reference r text symbol reference file If specified all symbol references will be written to this file Setting rf or Reference to the string default causes GAMS to create a reference file with the GMS file root name and a REF extension Thus gams trnsport with rf default will cause GAMS to write the reference file trnsport ref reslim reslim 1000 solve time limit This option specifies the maximum time in wall clock seconds that the computer can run during execution of a solver before the solver terminates the run restart r text restart file name Thi
410. s ts When complex sets like this are created it is important to check that the desired set has been obtained The checking can be done by using a display statement The hash sign followed by the set name is a shorthand for referring to all the elements in a set The matching operator can be used to map ordered sets The operator is similar to the product operator however in this case elements are matched pairwise by mapping elements with the same order number The below example demonstrates the two concepts set i a b j c d e ijta i j a j ij4b i j a c a d a e ij5a i j i j ij5b i j a c a d a e b c b d b e ij6a i j i j ij6b i j a c b d ij7a i j i d e ij7b i j a d b e Sets which name differ only by the last letter map to the same elements Consider set ij6a i j where the element with the highest order number in set i is element b with order number 2 Similarly the element with the highest order number in set j is element e with order number 3 Hence element e is without a match and therefore not mapped 4 5 Multi dimensional Sets 41 The concepts may be generalized to sets with more than two labels per set element Mathematically these are called 3 tuples 4 tuples or more generally n tuples This section ends with some examples to illustrate definitions of multi label set elements Some examples of the compact representation of sets of n tuples using combinat
411. s Most of them are caught at the compilation stage which behaves like the proofreading stage of the modeling process Once a problem has passed through the rigorous test of this stage the error rate drops almost to zero Most of the execution runs which are much more expensive than compilation proceed without difficulties because GAMS knows about modeling and has anticipated problems Many of the typical errors made with conventional programming languages are associated with concepts that do not exist in GAMS Those error sources such as address calculations storage assignment subroutine linkages input output and flow control create problems at execution time are difficult to locate often lead to long and frustrating searches and leave the computer user intimidated GAMS takes a radically different approach Errors are spotted as early as possible are reported in a way understandable to the user including clear suggestions for how to correct the problem and a presentation of the source of the error in terms of the user s problem t All errors are marked with four asterisks at the beginning of a line in the output listing As soon as an error is detected processing will be stopped at the next convenient opportunity A model will never be solved after an error has been detected The only remedy is to fix the error and repeat the run Errors are grouped into the three phases of GAMS modeling compilation execution and model
412. s indicating existence is used instead of values t Only the non default values are displayed for all data types The default value is generally zero except for the lo and up subtypes of variables and equations The default values for these are shown in table 14 1 143 An Example An example of a display statement is given below set s si s4 t t5 t7 parameter p s si 0 33 s3 0 67 parameter q t t5 0 33 t7 0 67 variable v s t v 1 5 t p s q t display first a set s then a parameter p then the activity level of a variable v 1 The resulting listing file will contain the following section that corresponds to the display statement 134 The Display Statement lo Up Variable positive 0 INF free INF INF negative INF 0 integer 0 100 binary 0 1 Equation g 0 INF n INF INF c 0 INF INF 0 e 0 0 Table 14 1 Default values for lo and up subtypes Sas 5 first a set 5 SET S si 82 3 s4 a5 5 then a parameter gt 5 PARAMETER P si 0 330 S3 0 670 sess 5 then the activity level of a variable Sass 5 VARIABLE V L T5 T7 S1 0 109 0 221 s3 0 221 0 449 Note that the only the non zero values are displayed In the case of multi dimensional identifiers the data is reported in a tabular form that is easy to read 14 4 The Label Order in Displays The default layout of a display for identifiers of different dimensionality is
413. s Associated with the Put Statement There are two types of errors that can occur when using the put writing facility syntax errors and put errors The following subsections discuss each of these types of errors 15 16 1 Syntax Errors Syntax errors are caused by the incorrect usage of the GAMS language These errors are the same or are similar to what one finds elsewhere with GAMS such as unmatched parentheses undefined identifiers uncontrolled sets or the incorrect use of a keyword or suffix These errors are detected during program compilation and are always fatal to program execution Errors of this kind are identified in the program listing at the location of the error with a symbol and corresponding error numbers The program listing includes a brief description of the probable cause of the error 15 16 2 Put Errors Put errors are unique to the put writing facility This type of error occurs during program execution and is caused when one or more of the file or page attributes are violated These errors are non fatal and are listed at the end of the program listing They typically occur when a put statement attempts to write outside of a page such as moving the cursor with the character to a location beyond the page width Other typical errors are the inability 15 17 Simple Spreadsheet Database Application 153 to open a specified file the overflow of a page or an inappropriate value being assigned to a suffix For many of these
414. s doe cd Applications GAMS doe mac Applications GAMS osx_x64_64_sfx exe UnZipSFX 5 52 of 28 creating inflating inflating inflating inflating inflating inflating inflating inflating inflating inflating inflating gams24 gams24 gams24 gams24 gams24 gams24 gams24 gams24 gams24 gams24 gams24 gams24 February 2005 by Info ZIP http www info zip org 3_osx_x64_64_sfx 3_058x_x64_64_sfx sp2full m 3_058x_x64_64_sfx optpathnlp def 3_osx_x64_64_sfx MessageReceiverWindow exe 3_0sx_x64_64_sfx hexdump 3_osx_x64_64_sfx datalib 3_0sx_x64_64_sfx empsyntax txt 3_0sx_x64_64_sfx optlindoglobal html 3_0sx_x64_64_sfx apifiles CSharp DomainChecking DomainChecking cs 3_osx_x64_64_sfx apifiles CSharp DomainChecking DomainChecking csproj 3_osx_x64_64_sfx apifiles CSharp xp_example2 cs 3_0sx_x64_64_sfx optdicopt html doe mac Applications GAMS cd gams24 3_osx_x64_64_sfx doe mac Applications GAMS gams24 3_osx_x64_64_sfx cp gamslice txt doe mac Applications GAMS gams24 3_osx_x64_64_sfx gamsinst gamsinst run on Wed Jun 25 19 25 29 2014 GAMS sysdir is Applications GAMS gams24 3_osx_x64_64_sfx LP Linear Programming models can be 1 NO PWD BDMLP CBC CONOPT CPLEX GUROBI IPOPT IPOPTH Installed defaults LP MIP RMIP NLP MCP MPEC RMPEC CNS DNLP RMINLP MINLP QCP MIQCP RMIQCP EMP CPLEX CPLEX CPLEX CONOPT PATH NLPEC NLPEC CONOPT CONOPT CONOPT
415. s forbidden to use the uniform and normal functions in an equation definition Functions with endogenous arguments can be further classified into types listed in table 8 1 Type Function Derivative Examples Smooth Continuous Continuous exp sin log Non Smooth Continuous Discontinuous max min abs Discontinuous Discontinuous Discontinuous ceil sign Table 8 1 Classification of functions with endogenous arguments Smooth functions can be used routinely in nonlinear models but non smooth ones may cause numerical problems and should be used only if unavoidable and only in a special model type called dnlp However the use of the dnlp model type is strongly discouraged and the use of binary variables is recommended to model non smooth functions Discontinuous functions are not allowed at all with variable arguments A fuller discussion is given in Chapter 9 page 79 For convenience all the available functions are classified in table 6 1 8 4 3 Preventing Undefined Operations in Equations Certain operations can be undefined at particular values for the arguments For example the log function is undefined when the argument is 0 Division by 0 is another example While this can easily be determined for exogenous functions and expressions it is a lot more difficult when the operands are variables The expression may be evaluated many times when the problem is being solved One way of preventing an expression from becoming undefined at a
416. s have keys for curly braces Note also that multiword names like New York are not allowed so hyphens are inserted The lowercase words in the sets statement above are called text Text is optional It is there only for internal documentation serving no formal purpose in the model The GAMS compiler makes no attempt to interpret the text but it saves the text and parrots it back to you at various times for your convenience It was not necessary to combine the creation of sets i and j in one statement We could have put them into separate statements as follows Set i canning plants seattle san diego Set j markets new york chicago topeka The placement of blank spaces and lines as well as the choice of upper or lowercase is up to you Each GAMS user tends to develop individual stylistic conventions The use of the singular set is also up to you Using set in a statement that makes a single declaration and sets in one that makes several is good English but GAMS treats the singular and plural synonymously A convenient feature to use when you are assigning members to a set is the asterisk It applies to cases when the elements follow a sequence For example the following are valid set statements in GAMS Set t time periods 1991 2000 Set m machines machi mach24 Here the effect is to assign t 1991 1992 1993 2000 m mach machg macho Note that set elements are stored as character st
417. s in which a Work File is Useful The basic function of a work file is to preserve information that has been expensive to produce Several reasons for wanting to do this are described in this section F 3 1 Separation of Model and Data The separation of model and data is one of the core principles of the GAMS modeling paradigm The use of save and restart features helps to exploit this separation Let us re arrange the contents of file1 gms and file2 gms to separate the model from the data The modified version of file1 gms is shown below Sets i canning plants j markets Parameters a i capacity of plant i in cases 254 The Save and Restart Feature b j demand at market j in cases c i j transport cost in 1000 case d i j distance in 1000 miles Scalar f freight in case per 1000 miles Variables x i j shipment quantities in cases z total transportation costs in 1000 Positive Variable x Equations cost define objective function supply i observe supply limit at plant i demand j satisfy demand at market j cost z e sum i j c i j x i j supply i sum j x i j l a i demand j sum i x i j g b j Model transport all Note that this representation does not contain any data and is a purely algebraic representation of the trans portation problem Running this model and saving the resulting work file will allow the model to be used with the data stored in a separ
418. s option provides the name of the save files to restart from The final name is composed by completing the file name with the current directory and the standard workfile extension The name provided for the restart file follows the same convention as that of the save file see command line parameter save C 3 Detailed Description of Command Line Parameters 197 rminlp rminlp text default RMINLP solver rmip rmip text default RMIP solver rmigcp rmiqcp tezt default RMIQCP solver rmpec rmpec tezt default RMPEC solver save s tezt save file name The final name is composed by completing the save file name with the current directory and the standard workfile extension Eight save files are generated so the name provided by the user for the save file should be such that GAMS can generate eight names from it GAMS distinguishes file names from their extensions If no extension is provided by the user GAMS adds the extensions g01 through g08 to name the eight saved work files The presence of a character in the save file name is used by GAMS to substitute the numbers 1 through 8 in its place The following table illustrates through examples the generation of names for the save files by GAMS from the name provided through the save parameter myfile myfile g01 myfile g02 myfile g08 myfile myfile1 g01 myfile2 g02 myfile8 g08 myfile 007 myfile 001 myfile 002 myfile 008 myfile wrk myfilel wrk myfile2 wrk myfile myfile1
419. s that are passed on to the batch include file These arguments are treated as character strings that are substituted by number inside the included file These arguments can be single unbroken strings quoted or unquoted or quoted multi part strings The syntax has been modeled after the DOS batch facility Inside the batch file a parameter substitution is indicated by using the character followed immediately by an integer value corresponding to the order of parameters on the list where 1 refers to the first argument 42 to the second argument and so on If the integer value is specified that does not correspond to a passed parameter then the parameter flag is substituted with a null string The parameter flag 0 is a special case that will substitute a fully expanded file name specification of the current batch included file The flag is the current symbol see dollar Parameters are substituted independent of context and the entire line is processed before it is passed to the compiler The exception to this is that parameter flags appearing in comments are not substituted t GAMS requires that processing the substitutions must result in a line of less than or equal to the maximum input line length currently 255 characters ts The case of the passed parameters is preserved for use in string comparisons Consider the following slice of code batinclude filel inc abcd bbbb cccc dddd In this case file1 inc is included with ab
420. s therefore exactly one number associated with the parameter 5 2 1 The Syntax In general the syntax in GAMS for a scalar declaration is scalar s scalar_name text signed_num scalar_name text signed_num Scalar_name is the internal name of the scalar also called an identifier in GAMS The accompanying text is used to describe the element immediately preceding it Signed_num is a signed number and is assigned to be the value of scalar_name As with all identifiers scalar_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 characters long Explanatory text must not exceed 254 characters and must all be contained on the same line as the identifier or label it describes 46 Data Entry Parameters Scalars amp Tables 5 2 2 An Illustrative Example An example of a scalar definition in GAMS is shown below Scalars rho discount rate 15 irr internal rate of return life financial lifetime of productive units 20 The statement above initializes rho and life but not irr Later on another scalar statement can be used to initialize irr or looking ahead to a notion that will be developed later an assignment statement could be used to provide the value irr 0 07 5 3 Parameters While parameter is a data type that encompasses scalars and tables the discussion in this chapter will focus on the use of parameters in da
421. sage that gives the valid range of input columns For example the dollar control option mincol 20 maxcol 110 will trigger the message NEW MARGIN 20 110 tw GAMS requires that the right margin set by maxcol is greater than 15 te GAMS requires that the right margin set by maxcol is greater than the left margin set by mincol maxGoto 100 Sets the maximum number of jumps to the same label Once the maximum number is reached an error is triggered Consider the following example scalar a 1 maxgoto 5 label label1 a a 10 display a goto label1 When goto label1 is called for the fifth time an error is triggered mincol n 1 Sets the left margin for the input file All valid data is after and including column n in the input file All text before column n is treated as comment and ignored Consider the following example mincol 30 set definition set i vienna rome scalar definition scalar a 2 3 The text strings set definition and scalar definition are treated as comments and ignored since they begin before column 30 Any changes in the margins via maxcol or mincol will be reported in the listing file with the message that gives the valid range of input columns For example the dollar control option mincol 20 maxcol 110 will trigger the message NEW MARGIN 20 110 te GAMS requires that the left margin set by mincol is smaller than the right margin set by maxcol onjoff Delim offD
422. scratch directory This file contains the following lines 0 0 0 O D GAMS NEW LST 1 1 170 31 D GAMS NEW GMS 2 2 120 14 D GAMS NEW GMS 186 The GAMS Call The first column refers to the global row number of the error in the listing file The second column refers to the row number of the error in the individual file where the problem occurs This will be different from the first column only if the error occurs in an include file In this case the second column will contain the line number in the include file where the error occurs while the first number will contain the global line number as reported in the listing file where the error occurs The number in the third column refers to the error number of the error The fourth number refers to the column number of the error in the source file The fifth column contains the individual file in which the error occurred filecase filecase 0 casing of new file names put gdx ref etc This option allows one to alter the file name casing GAMS uses in saving put gdx ref etc files It only works with new file names but for example it won t create trnsport REF if TRNSPORT ref already exists Values O causes GAMS to use default casing 1 causes GAMS to uppercase filenames 2 causes GAMS to lowercase filenames forcework fw 0 force workfile translation Most of the work files generated by GAMS using the save option are in binary format The information inside these files will change from v
423. se definition of special ordered sets differ from one solver to another and the development of these features has been driven more by internal algorithmic consideration than by broader modeling concepts GAMS offers sos1 and sos2 variables as two types of compromise features that model special ordered sets Sections 17 2 2 and 17 2 3 discuss these two types of variables in greater detail Semi continuous variables GAMS offers semicont and semiint variables to model this class of variables These are explained in Sections 17 2 3 and 17 2 4 The presence of any of the above types of discrete variables requires a mixed integer model and all the discreteness is handled by the branch and bound algorithm in the same way as binary and general integer variables are handled 17 2 2 Special Order Sets of Type 1 SOS1 At most one variable within a SOS1 set can have a non zero value This variable can take any positive value Special ordered sets of type 1 are defined as follows 162 Special Language Features sosi Variable si i t1 k j wi i j k The members of the innermost the right most index belongs to the same set For example in the sets defined above s1 represents one special ordered set of type 1 with i elements t1 defines k sets of j elements each and wi defines i j sets with k elements each t The default bounds for SOS1 variables are 0 to 00 As with any other variable the user may set these bounds to whatever is required
424. sed on in this manner The number appended to inputdir is important because the earlier inputdir directories are searched first The example used to illustrate the inputdir option can also be equivalently called as gams myfile idiri mydiri idir2 mydir2 Note that the search order in this case is as follows 1 current directory 2 mydirt 3 mydir2 However if the command was altered to be gams myfile idir3 mydir1 idir2 mydir2 then the search order is altered to be as follows 1 current directory 2 mydir2 3 mydirl Note that it is not the order in which they are specified that matters but the number of the inputdir that they have been assigned to C 3 Detailed Description of Command Line Parameters 189 integer1 to integer5 integerl number integer communication cell This integer communication cell that can contain any integer number iterlim iterlim 2000000000 iteration limit This option specifies the maximum number of allowable solver iterations before the solver terminates the run jobtrace jt text string written at the end of a trace The string is written to the trace file at the end of a GAMS job keep keep 0 keep scratch files This parameter tells GAMS whether to keep the temporary files generated during a run Values O delete all files 1 keep intermediate files libincdir Idir text library include directory Used to complete a file name for libinclude If the 1dir option is not set the sub directo
425. signed for many purposes especially in linear models the default bounds are sufficient In nonlinear models on the other hand bounds play a far more important role It may be necessary to provide bounds to prevent undefined operations such as division by zero It is also often necessary to define a reasonable solution space that will help to make the nonlinear programming problem be solved more efficiently ts The lower bound cannot be greater than the upper if you happen to impose such a condition GAMS will exit with an error condition 7 3 2 Fixing Variables GAMS allows the user to set variables through the fx variable suffix This is equivalent to the lower bound and upper bound being equal to the fixed value Fixed variables can subsequently be freed by changing the lower and upper bounds 70 Variables 7 3 3 Activity Levels of Variables GAMS allows the user to fix the activity levels of variables through the 1 variable suffix These activity levels of the variables prior to the solve statement serve as initial values for the solver This is particularly important for nonlinear programming problems 7 4 Variables in Display and Assignment Statements GAMS allows the modeler to use the values associated with the various attributes of each variable in assignment and display statements The next two sub sections explain the use of variables in the left and right hand sides of assignment statements respectively Later we
426. solved again However before the second solve statement the option iterlim is changed to 50 The effect of the sequence above is to limit the first solve to less than 100 iterations and the second to less than 50 E 2 List of Options The options available through the option statement are grouped into the following functional categories affecting output detail solver specific parameters input program control choice of solver Table E 1 briefly describes the various options in each of the categories Section E 3 contains a reference list of all options available through the option statement in alphabetical order with detailed description for each Options controlling output detail lt identifier gt controls print format profile lists program execution profile decimals global control of print format profiletol sets tolerance for execution profile eject advances output to next page solprint controls printing of solution limcol number of columns listed solslack controls type of equation information limrow number of rows listed sysout controls printing of solver status file Options controlling solver specific parameters bratio use of advanced basis reslim limits amount of solver time domlim limits number of domain errors savepoint save solver point in GDX file iterlim limits number of solver iterations solvelink solver link options optca sets absolute optimality tolerance threads number of threads to be used by a solver optcr sets relat
427. some documentary text The second statement assigns to c i j the product of the values of the parameters f and d i j Naturally this is legal in GAMS only if you have already assigned values to f and d i j in previous statements The direct assignment above applies to all i j pairs in the domain of c If you wish to make assignments for specific elements in the domain you enclose the element names in quotes For example c Seattle New York 0 40 is a valid GAMS assignment statement The same parameter can be assigned a value more than once Each assignment statement takes effect immediately and overrides any previous values In contrast the same parameter may not be declared more than once This is a GAMS error check to keep you from accidentally using the same name for two different things The right hand side of an assignment statement can contain a great variety of mathematical expressions and built in functions If you are familiar with a scientific programming language such as FORTRAN or C you will have no trouble in becoming comfortable writing assignment statements in GAMS Notice however that GAMS has some efficiencies shared by neither FORTRAN nor C For example we were able to assign c i j values for all i j pairs without constructing do loops The GAMS standard operations and supplied functions are given later Here are some examples of valid as signments In all cases assume the left hand side
428. ss 1 hh mm ss threads threads 1 number of threads to be used by a solver This option controls the number of threads or CPU cores to be used by a solver Values n number of cores to leave free for other tasks O use all available cores n use n cores will be reduced to the available number of cores if n is too large timer timer 0 instruction timer threshold in milli seconds Only details about internal GAMS intructions that took more than n milli seconds are echoed to the log Values O interpreted as inf no details echoed n echo all details about internal GAMS intructions that took more than n milli seconds to the log trace trace tezt trace file name The trace file name is completed using the current directory traceopt traceopt 0 trace file format option Values solver and GAMS step trace without headers solver and GAMS step trace solver step trace only trace file format used for GAMS performance world trace file with all available trace fields OwWnNr O userl to user ul tezt u5 text strings passed to the subsystems This options permit user entry of text for up to 5 user defined options warnings warnings MAXINT number of warnings permitted This option specifies the maximum number of allowable warnings before the run terminates workdir wdir curdir sets working directory This option sets the working directory This option is useful when GAMS is called from an external system like Visual Basi
429. st be matched with an endIf endIf must be matched with an ifThen ifThenE or ifThenI else is followed by an instruction which is executed if the matching ifThen statement is not true elseIf has another comparison behind it elseIfI is a case insensitive variant of elseIf elseIfE is a numerical value evaluating variant of elseIf The statements following directly an ifThen elseIf or else on the same line can be a sequence of other dollar control statements or contain proper GAMS syntax The statements following directly a endif can only contain another dollar control statement A NOT may be used in the commands One may add a tag to the ifThen and endIf Then for example ifThen tagone has to match with endif tagone as shown below Consider the following example which illustrates the use of ifThen and elseIf set x a label two ifthen x a set x c log ifthen with x x elseif x f b set x k log elseif 1 with x x elseif x f c set x b log elseif 2 with x x else set x e log else with x x endif if NOT x e goto two the resulting log file contains ifthen with x a elseif 2 with x c elseif 1 with x b else with x k The next examples illustrates the use of tags ifThen one x y display it1 elseIf one a a display it2 ifThen two c c 218 Dollar Control Options display it3 endIf two elseIf one b
430. sting file input lines echoed to listing file reset line logging start of block put without substitution start of block put with substitution start of block put without substitution start verbatim copy if dumpopt gt 10 comment line with suppressed line number single spaced listing follows set characters in listing file set subtitle and reset page set title reset subtitle and page on symbol list on symbol cross reference listing on unique element listing on unique element cross listing include file kill data connected with identifier label name as entry point from goto include file from library directory turns off global options turns off redefinition of data allow lag and lead opereations on dynamic or unordered sets disable recursive include files D 2 List of Dollar Control Options 205 elself elselfE elselIfI endif error exit funcLibIn goto hiddenCall if ifE if ifThen ifThenE ifThenI elself structure with case sensitive compare elself structure with expression evaluation elself structure with case insensitive compare closing of ifThen ifThenE ifThenI control struc ture issue an error message exit from compilation load extrinsic function library go to line with given label name executes another program hidden conditional processing case sensitive if statement with expression evaluation conditional processing case insensitive ifThen elself structur
431. sting file append option Setting this option to 1 will ensure that the listing file is appended to and not rewritten Values O reset listing file 1 append to listing file bratio bratio 0 25 basis acceptance threshold Certain solution procedures can restart from an advanced basis that is constructed automatically This option is used to specify whether or not basis information probably from an earlier solve is used The use of this basis is rejected if the number of basic variables is smaller than bratio times the size of the basis Setting bratio to 1 will cause all existing basis information to be discarded which is sometimes needed with nonlinear problems A bratio of 0 accepts any basis and a bratio of 1 always rejects the basis Setting bratio to 0 forces GAMS to construct a basis using whatever information is available If bratio has been set to 0 and there was no previous solve an all slack sometimes called all logical basis will be provided This option is not useful for MIP solvers Range 0 1 case case 0 output case option Values O write listing file in mixed case 1 write listing file in upper case only cerr cerr 0 compile time error limit The compilation will be aborted after n errors have occurred By default there is no error limit and GAMS compiles the entire input file and collects all the compilation errors that occur If the file is too long and the compilation process is time consuming cerr coul
432. ston chicago houston sandiego phoenix baltimore j newyork detroit losangeles atlanta set ij i j boston newyork baltimore newyork miami atlanta houston atlanta chicago detroit sandiego losangeles phoenix losangeles table distance i j distance in miles newyork detroit losangeles atlanta miami 1327 1387 2737 665 boston 216 699 3052 1068 chicago 843 275 2095 695 houston 1636 1337 1553 814 sandiego 206 phoenix 2459 1977 398 1810 parameter factor shipcost i j factor 0 009 The set ij denotes the regional transportation hub for each collection site Factor is the cost estimate per unit mile The cost of transporting parcels shipcost from a local collection site i to a regional hub j is then provided by the following assignment shipcost i j ij i j factor distance i j Note that i and j do not appear separately in the assignment for shipcost The assignment can then be simply written as shipcost ij factor distance ij If i or j appear separately in any assignment the above simplification cannot be made For example consider that travelcost depended not only on factor and the distance between collection sites and regional hubs but also the load on the regional hub Parameter congestfac j newyork 1 5 detroit 0 7 losangeles 1 2 atlanta 0 9 Congestfac is a parameter used to model the congestion at each regional hub The unit cost of shipment is then computed as follows 116 C
433. sts of specialized discussions of advanced topics and can be studied as needed Users with large complex or expensive models will find much useful material in this part Introduction A GAMS Tutorial by Richard E Rosenthal 2 1 Introduction The introductory part of this book ends with a detailed example of the use of GAMS for formulating solving and analyzing a small and simple optimization problem Richard E Rosenthal of the Naval Postgraduate School in Monterey California wrote it The example is a quick but complete overview of GAMS and its features Many references are made to other parts of the book but they are only to tell you where to look for more details the material here can be read profitably without reference to the rest of the book The example is an instance of the transportation problem of linear programming which has historically served as a laboratory animal in the development of optimization technology See for example Dantzig 1963 It is a good choice for illustrating the power of algebraic modeling languages like GAMS because the transportation problem no matter how large the instance at hand possesses a simple exploitable algebraic structure You will see that almost all of the statements in the GAMS input file we are about to present would remain unchanged if a much larger transportation problem were considered In the familiar transportation problem we are given the supplies at several plants and
434. summarized in table 14 2 The figures in the table refer to the index position in the domain list of the identifier As an example if we display c where c has been declared as c i j k 1 then the i labels the first index will be associated with the planes or individual sub tables the j and k with the row labels and the 1 the fourth and last index with the column headings Numbers of Indices Plane Index Position s on the Row Column 1 List Format 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 Table 14 2 Default layout of display output For 7 to 10 indices the natural progression is followed The labels vary slowest for the first index position and 14 5 Display Controls 135 quickest for the highest Within each index position the order is the GAMS entry order of the labels The order of the indices is always as in the declaration statement for the symbol One can declare them in the order that is found appealing or make an assignment to a new identifier with a different order t The only way to change the order in which the labels for each index position appear on display output is to change the order of appearance of the labels in the GAMS program This is most easily done by declaring a set whose only purpose is to list all the labels in the order that is needed Make this set the very first declaration in the GAMS program 14 4 1 Example Consider the following example X has four dimensions or inde
435. t CijTij The last expression could also have been written as a nested summation as follows Sum i Sum j c i j x i j In Section 11 3 page 112 we describe how to use the dollar operator to impose restrictions on the summation operator so that only the elements of i and j that satisfy specified conditions are included in the summation Products are defined in GAMS using exactly the same format as summations replacing Sum by Prod For example prod j x i j is equivalent to Ijz Summation and product operators may be used in direct assignment statements for parameters For example scalar totsupply total supply over all plants totsupply sum i a i 14 A GAMS Tutorial by Richard E Rosenthal 2 6 3 Equation Definition Equation definitions are the most complex statements in GAMS in terms of their variety The components of an equation definition are in order The name of the equation being defined The domain Domain restriction condition optional The symbol Left hand side expression Relational operator 1 e or g Right hand side expression The transportation example contains three of these statements cost z e sum i j c i j x i j supply i sum j x i j 1 a i demand j sum i x i j g b j Here are some points to remember gt The power to create multiple equations with a single GAMS statement is controlled by the domain Fo
436. t character position The remaining characters on the line are ignored but printed on the output file The second is to use special block delimiters that cause GAMS to ignore an entire section of the program The symbol must be in the first character position The choice between the two ways is a matter of individual taste or utility The example below illustrates the use of the block comment 3 5 Summary 33 ontext Following a ontext directive in column 1 all lines are ignored by GAMS but printed on the output file until the matching offtext is encountered also in column 1 This facility is often used to logically remove parts of programs that are not used every time such as statements producing voluminous reports Every ontext must have a matching offtext in the same file Sofftext The third style of comment allows embedding a comment within a line It must be enabled with the compiler option inlinecom or eolcom as in the following example eolcom inlinecom x 1 this is a comment y 2 this is also a comment z 3 3 5 Summary This completes the discussion of the components of the GAMS language Many unfamiliar terms used in this chapter have been further explained in the Glossary 34 GAMS Programs 4 Set Definitions 4 1 Introduction Sets are fundamental building blocks in any GAMS model They allow the model to be succinctly stated and easily read In this chapter we will discuss h
437. t each domain element in the list is in fact a member of the appropriate set For example if you were to spell Seattle correctly in the statement declaring Set i but misspell it as Seatle in a subsequent element value list the GAMS compiler would give you an error message that the element Seatle does not belong to the set i 4 Zero is the default value for all parameters Therefore you only need to include the nonzero entries in the element value list and these can be entered in any order 5 A scalar is regarded as a parameter that has no domain It can be declared and assigned with a Scalar statement containing a degenerate list of only one value as in the following statement from the transportation model Scalar f freight in dollars per case per thousand miles 90 If a parameters domain has two or more dimensions it can still have its values entered by the list format This is very useful for entering arrays that are sparse having few non zeros and super sparse having few distinct non zeros 2 4 Data 11 2 4 2 Data Entry by Tables Optimization practitioners have noticed for some time that many of the input data for a large model are derived from relatively small tables of numbers Thus it is very useful to have the table format for data entry An example of a two dimensional table or matrix is provided in the transportation model Table d i j distance in thousands of miles new york chicago topeka sea
438. t parameter is given as a file name without an absolute path using the current directory composes the final name If the absolute path is included in the file name then the name is used as given Consider the following examples gams trnsport gams trnsport o trnsport out gams trnsport o c test trnsport out The first call will create an output file called trnsport 1st for PC and Unix platforms in the current directory The second call will create a file called trnsport out in the current directory The last call will create the file as listed If the directory c test does not exist GAMS will exit with a parameter error pagecontr pc 3 page control This option affects the page control in the listing file Values O no page control with padding 1 Fortran style line printer format 2 no page control no padding 3 Form feed character for new page pagesize ps 58 page size This is the number of lines that are used on a page for printing the listing file The lower bound is 0 which is interpreted as inf That means that everything is printed to one page pagewidth pw 255 print width This option sets the print width on a page in the listing file with a possible range from 72 to 32767 Note that under the IDE the default is set to 80 If the value is outside the allowed range the default value will be used The option can also be used to specify the pagewidth for the put facility i e file f myfile txt put f f pw 80 In t
439. tInclude include file with substitution arguments call executes program during compilation call Async executes another program asynchronously clear reset all data for an identifier to its default values clearError clear compilation errors clearErrors clear compilation errors else else clause offNestCom offText onEo1Com onInline onMargin onNestCom onText onEmbedded onEmpty onEnd onEps onGlobal onUNDF onWarning use205 use225 use999 version onEcho onEchoS onEchoV onInclude onListing onLog onPut onPutS onPutV onVerbatim remark single stars sTitle title onSymList onSymXRef onUEl1List onUE1XRef include kill label libInclude offGlobal of fMulti of fOrder offRecurse turn off nested comments off text mode turn on end of line comments turn on in line comments turn on margin marking turn on nested comments on text following lines are comments allow embedded text or data in set and parame ter statements allow empty data initialization statements allow alternate program control syntax interpret EPS as 0 force inheritance of parent file settings allow UNDF as input convert certain domain errors into warnings Release 2 05 language syntax Release 2 25 Version 1 language syntax latest language syntax test GAMS compiler version number start of block echo with substitution start of block echo with substitution start of block echo without substitution include file name echoed to li
440. ta entry List oriented data can be read into GAMS using the parameter statement 5 3 1 The Syntax In general the syntax in GAMS for a parameter declaration is parameter s param_name text element signed_num element signed num param_name text element signed_num element signed num Param_name is the internal name of the parameter also called an identifier in GAMS The accompanying text is used to describe the parameter immediately preceding it Signed_num is a signed number and is declared to be the value of the entry associated with the corresponding element As with all identifiers param_name has to start with a letter followed by more letters or digits It can only contain alphanumeric characters and can be up to 63 long Explanatory text must not exceed 254 characters and must all be contained on the same line as the identifier or label it describes A parameter may be indexed over one or more sets the maximum number being 20 The elements in the data should belong to the set that the parameter is indexed over t The default value of a parameter is 0 Parameter initialization requires a list of data elements each consisting of a label and a value Slashes must be used at the beginning and end of the list and commas must separate data elements entered more than one to a line An equals sign or a blank may be used to separate the label tuple from its associated value A parameter can be d
441. tatement above 10 6 Error Reporting 107 soex 3 ERROR S 0 WARNING S USER ERROR S ENCOUNTERED 10 6 3 Execution Errors Execution time errors are usually caused by illegal arithmetic operations such as division by zero or taking the log of a negative number GAMS prints a message on the output file with the line number of the offending statement and continues execution A GAMS program should never abort with an unintelligible message from the computer s operating system if an invalid operation is attempted GAMS has rigorously defined an extended algebra that contains all operations including illegal ones The model library problem CRAZY contains all non standard operations and should be executed to study its exceptions Recall that GAMS arithmetic is defined over the closed interval INF INF and contains values EPS small but not zero NA not available and UNDF the result of an illegal operation The results of illegal operations are propagated through the entire system and can be displayed with standard display statements However remember that one cannot solve a model or save a work file if errors have been detected previously 10 6 4 Solve Errors The execution of a solve statement can trigger additional errors called MATRIX ERRORS which report on problems encountered during transformation of the model into a format required by the solver Problems are most often caused by illegal or inconsistent bounds or an extended r
442. tatement can be placed anywhere on a line multiple statements can appear on a line or a statement can be continued over any number of lines as follows statement statement statement statement statement the words that you are now reading is an example of a very long statement which is stretched over two lines Blanks and end of lines can generally be used freely between individual symbols or words GAMS is not case sensitive meaning that lower and upper case letters can be mixed freely but are treated identically Up to 255 characters can be placed on a line and completely blank lines can be inserted for easier reading Not all lines are a part of the GAMS language Two special symbols the asterisk and the dollar symbol can be used in the first position on a line to indicate a non language input line An asterisk in column one means 28 GAMS Programs that the line will not be processed but treated as a comment A dollar symbol in the same position indicates that compiler options are contained in the rest of the line Multiple files can be used as input through the use of the include facility described in Appendix D In short the statement include filel inserts the contents of the specified file filel in this case at the location of the call A more complex versions of this is the batinclude which is described in Appendix D 3 2 2 Classification of GAMS Statements Each statement in GAMS is classifie
443. tells us that the symbol A is a parameter that was declared in line 10 defined assigned value in line 11 and referenced in line 43 The symbol I has a more complicated entry in the cross reference list It is shown to be a set that was declared and defined in line 5 It is referenced once in lines 10 19 26 28 31 38 45 and referenced twice in lines 41 and 43 Set I is also used as a controlling index in a summation equation definition or direct parameter assignment in lines 28 41 43 and 45 For the GAMS novice the detailed analysis of the cross reference list may not be important Perhaps the most likely benefit he or she will get from the reference maps will be the discovery of an unwanted entity that mistakenly entered the model owing to a punctuation or syntax error The second part of the reference map is a list of model entities grouped by type and listed with their associated documentary text For example this list is as follows sets i canning plants j markets parameters a capacity of plant i in cases b demand at market j in cases c transport cost in 1000s of dollars per case d distance in thousands of miles f freight in dollars per case per thousand miles variables x shipment quantities in cases z total transportation costs in 1000s of dollars equations cost define objective function demand satisfy demand at market j supply observe supply limit at plant i models transport 2 11 4 Equation Listings Once
444. tems in the title or header blocks To force a page that has an empty window out to file simply write something innocuous to the window such as put Now the window of the page has been initiated and it will be written 15 7 Positioning the Cursor on a Page The cursor is positioned at the space immediately following the last character written unless the cursor is specif ically moved using one of the following cursor control characters n Move cursor position to row n of current page 15 8 System Suffixes 145 On Move cursor position to column n of current line Move cursor to first column of next line Also acts as a delimiter between output items In addition to numerals any expression or symbol with a numeric value can be used to follow the and characters The following example illustrates the use of these position controls to write out the value of a parameter a i j in a tabular form file out put out scalar col column number 1 loop i loop j put col a i j col co1 10 put Js 15 8 System Suffixes The complete list of system suffixes that can be used to recover information about the GAMS run are date program execution date ifile input file name ofile output file name page current file page rdate restart file date rfile restart file name rtime restart file time sfile save file name time program execution time title title of the model as specified by title
445. ters or digits It can only contain alphanumeric characters and can be up to 63 characters long The accompanying text is used to describe the set or element immediately preceding it This must not exceed 254 characters and must all be contained on the same line as the identifier it describes One important difference between variable and parameter declarations is that values cannot be initialized in a variable declaration A typical variable statement adapted from RAMSEY is shown below for illustration variables k t capital stock trillion rupees c t consumption trillion rupees per year i t investment trillion rupees per year utility utility measure The declaration of k above implies as usual that references to k are restricted to the domain of the set t A model that includes k will probably have several corresponding variables in the associated mathematical programming 68 Variables problem most likely one for each member of t In this way very large models can be constructed using a small number of variables It is quite unusual for a model to have as many as 50 distinct variables It is still unclear from the declaration whether utility is not domain checked or whether it is a scalar variable i e one without associated sets Later references will be used to settle the issue It is important that variable declarations include explanatory text and that this be as descriptive as possible since the text is used t
446. tes il NO Seattle i2 NO Portland i3 YES San Francisco i4 YES Los Angeles i5 YES The second columns represents whether the element belongs to set j or not 15 10 Global Item Formatting It is often important to be able to control the display format of output items In this section we describe how this is done For formatting purposes output items are classified into four categories These are labels numeric values set values and text For each global formatting of the field width and field justification is possible 15 10 1 Field Justification The possible global justifications are right value 1 left value 2 and center value 3 The field justification is represented by the following file suffixes lj label justification default 2 nj numeric justification default 1 Sj set value justification default 1 tj text justification default 2 148 The Put Writing Facility 15 10 2 Field Width This is done using the following file suffixes lw label field width default 12 DW numeric field width default 12 SW set value field width default 12 maximum 20 tw text field width default 0 The field width is specified with the number of spaces to be allocated to the field Variable length field widths are possible by using a suffix value of 0 This forces the field width to match the exact size of the item being displayed If a textual output item does not fit within the specified field truncation occurs to
447. that belong to t i Controlling indexing operations using the dollar condition can also be done as with any assignment Consider the following supply balance sb equation from GTM sb i sum j ij i j x i j l s i 11 6 2 Dollar Control over the Domain of Definition This is analogous to the dollar control on the left of assignments as discussed in Section 11 4 1 and if one thinks of on the left as meaning on the left of the then the analogy is even closer 118 Conditional Expressions Assignments and Equations ts The purpose of the dollar control over the domain of definition of equations is to restrict the number of constraints generated to less than that implied by the domain of the defining sets Consider the following example adapted from FERTS cc m i mpos m i sum p ppos p i b m p z p i 1 util k m i Cc is a capacity constraint defined for all units m and locations i Not all types of units exist at all locations however and the mapping set mpos m i is used to restrict the number of constraints actually generated The control of the summation over p with ppos p i is an additional one and is required because not all processes p are possible at all locations i 11 6 3 Filtering the Domain of Definition The same rules that apply to filtering assignments and controlling indices in indexed operations applies to equation domains as well Consider the following equation using
448. the GAMS program to the listing file 10 2 The Illustrative Model ALAN is a portfolio selection model whose object is to choose a portfolio of investments whose expected return meets a target while minimizing the variance We will discuss a simplified version of this model The input file is listed for reference Title A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a onsymlist onsymxref onuellist onuelxref Ontext This is a mini mean variance portfolio selection problem described in gt GAMS MINOS Three examples by Alan S Manne Department of Operations Research Stanford University May 1986 Offtext This model has been modified for use in the documentation Set i securities hardware software show biz t bills alias i j Scalar target target mean annual return on portfolio 10 lowyield yield of lowest yielding security highrisk variance of highest security risk Parameters mean i mean annual returns on individual securities hardware 8 software 9 show biz 12 t bills IA Table v i j variance covariance array squared annual return 92 GAMS Output hardware software show biz t bills hardware 4 3 1 0 software 3 6 1 0 show biz 1 1 10 0 t bills 0 0 0 0 lowyield smin i mean i highrisk smax i v i i display lowyield highrisk Variables x i fraction of portfolio invested in asset i variance variance of portfolio Positive Variable x Equations fs
449. the demands at several markets for a single commodity and we are given the unit costs of shipping the commodity from plants to markets The economic question is how much shipment should there be between each plant and each market so as to minimize total transport cost The algebraic representation of this problem is usually presented in a format similar to the following Indices i plants j markets Given Data a supply of commodity of plant i in cases bj demand for commodity at market j Cij cost per unit shipment between plant i and market j case Decision Variables zij amount of commodity to ship from plant to market j cases where x gt 0 for all i 7 Constraints Observe supply limit at plant i X jij lt a for alli cases Satisfy demand at market j X tij 2 bj for all j cases Objective Function Minimize 2 CijTij K Note that this simple example reveals some modeling practices that we regard as good habits in general and that are consistent with the design of GAMS First all the entities of the model are identified and grouped by type Second the ordering of entities is chosen so that no symbol is referred to before it is defined Third the lDantzig George B 1963 Linear Programming and Extensions Princeton University Press Princeton N J 6 A GAMS Tutorial by Richard E Rosenthal units of all entities are specified and fourth the units are chosen to a scale such that the
450. the exception that partial pages in the file are not padded with blank lines to fill out the page 3 ASCII page control characters inserted 15 6 Page Sections 143 4 Formatted output Non numeric output is quoted and each item is delimited with a blank space 5 Formatted output Non numeric output is quoted and each item is delimited with commas 6 Formatted output Non numeric output is quoted and each item is delimited with tabs 7 Fixed width Fills up line with trailing blanks 8 Formatted output Each item is delimited with a blank space page size ps Used to specify the number of rows lines which can be placed on a page of the document Can be reset by the user at any place in the program However an error will result if set to a value less than the number of rows which have already been written to the current page Maximum value is 130 The default value is 60 page width pw Used to specify the number of columns characters which can be placed on a single row of the page Can be reset by the user at any place in the program However an error will result if set to a value less than the number of rows or columns which have already been written to the current page The default value is 255 top margin tm Number of blank lines to be placed at the top margin of the page These lines are in addition to the number of lines specified in the ps file suffix Default value is 0 bottom margin bm Number of blank lines to be
451. the num ber of arguments is not limited returns the remainder of x divided by y function that computes a Chen Mangasarian smoothing equal ing e Z In l ez function that computes a Fisher smoothing equaling V 2 y2 2 Z ax y Z gt 0 default setting Z 0 NCP da smoothed min eu salt ife gt p ncp pow r s tya 24 A sl t PCa FR otherwise where t r s default setting MU 0 NCP Veelken Ulbrich smoothed min rt lil if ltl gt u nepVUsin 4 r4 s 2 sin 32 y 7 24 2 otherwise 2 where t r s default setting MU 0 generates a random number with normal distribution with mean MEAN and standard deviation STDDEV see Math World value of 7 3 141593 computes a polynomial over scalar x where result Ag A x2 Aou A3x this has a maximum of 20 arguments default setting A3 0 returns zY where Y must be an integer generates a random number with binomial distribution where n is the number of trials and p the probability of success for each trial see MathWorld generates a random number between LOW and HIGH with sns i 2 linear distribution SLOPE must be greater than HICH LOW generates a random number between LOW and HIGH with triangular distribution MID is the most probable number see MathWorld rounding x DECPL declares the number of decimal places default setting DECPL 0 60 Data Manipulations with Par
452. the right For numeric output items the decimal portion of a number is rounded or scientific notation used to fit the number within the given field If a number is still too large asterisks replace the value in the output file As an example to set the global numeric field width to four spaces from its default of 12 in the file out put we would use the following statement out nw 4 15 11 Local Item Formatting It is often useful to format only specific put items For this we use the local format feature which overrides global format settings The syntax of this feature is as follows item lt gt width decimals The item is followed by a justification symbol the field width and the number of decimals to be displayed The specification of the number of decimals is only valid for numeric output The following local justification symbols are applicable gt right justified lt left justified lt gt center justified Omitting any of the components causes their corresponding global format settings to be used As with global formatting when the field width is given a value of 0 the field width is variable in size The item width and decimals are delimited with colons as shown above The use of the local format feature as well as the inclusion any of the components for justification field width or the number of decimals is entirely optional The following example shows some examples of the local formatting feature d
453. thinks is a good unit and what constitutes a well scaled model 17 3 1 The Scale Option To facilitate the translation between a natural model and a well scaled model GAMS has introduced the concept of a scale factor both for variables and equations The notations and definitions are quite simple Scaling is turned off by default Setting the model suffix scaleopt to 1 turns on the scaling feature For example model mymodel all mymodel scaleopt 1 solve mymodel using nlp maximizing dollars The statement should be inserted somewhere after the model statement and before the solve statement In order to turn scaling off again set the model scaleopt parameter to 0 before the next solve The scale factor of a variable or an equation is referenced with the suffix scale i e the scale factor of variable x i is referenced as x scale i Note that there is one scale value for each individual component of a multi dimensional variable or equation Scale factors can be defined using assignment statements The default scale factor is always 1 GAMS scaling is in most respects hidden from the user The solution values reported back from a solution algorithm are always reported in the user s notation The algorithm s versions of the equations and variables are 17 3 Model Scaling The Scale Option 165 only reflected in the derivatives in the equation and column listings in the GAMS output if the options limrow and limcol are positiv
454. tiation Numerical Operators Multiplication Division Unary operators Plus Minus Binary operators addition subtraction t Numerical Relationship operators lt lt lt gt gt gt Logical Operators not not and and or XOT or xor Table 11 2 Operator precedence Note that in the case of operators with the same precedence the order in which the operator appears in the expression is used as the precedence criterion with the order reducing from left to right ts It is always advisable to use parentheses rather than relying on the precedence order of operators It prevents errors and makes the intention clear Consider the following example for illustration 112 Conditional Expressions Assignments and Equations x 5 y and z 5 is treated equivalent to x 5 y and z 5 However note that the use of parenthesis does make the expression clearer to understand 11 2 8 Mixed Logical Conditions Examples Some simple examples of logical conditions containing the building blocks described in the previous sub sections are shown in table 11 3 to illustrate the generation and use of more complex logical conditions Logical Condition Numerical Value Logical Value 1 lt 2 3 lt 4 2 True 2 lt 1 and 3 lt 4 0 False 4 5 3 10 8 17 125 True 4 5 3 or 10 8 1 True 4 and 5 2 3 lt 6 2 True 4 and 0 2 3 lt 6 0 False Table 11 3
455. ting file putfile put contains Line 1 of text Line 2 of text Line 3 of text Line 4 of text There is also a variant onPutS that permits parameter substitution and another variant onPutV that forbids parameter substitution as onPut also does Consider the following example set it TEST file putfile put putfile onPutS Line 1 of text it Line 2 of text hit offPut The created putfile contains Line 1 of text TEST Line 2 of text TEST while the putfile created by 232 Dollar Control Options set it TEST file putfile put putfile onPutV Line 1 of text it Line 2 of text it offPu contains Line 1 of text Zit Line 2 of text hit In contrast to the second case in the first case 1t is substituded by TEST on off Recurse offRecurse Allows a file to include itself For example a file called file1 gms can contain onrecurse include filel Note that the maximum include nesting level is 40 and if it is exceeded an error is triggered on off StrictSingleton onStrictSingleton With offStrictSingleton GAMS does not complain about a data statement for a singleton set with more than one element but takes the first one With onStrictSingleton such a data statement creates an error on off SymList offSymList Controls the complete listing of all symbols that have been defined and their text including pre defined functions and symbols in alphabetical order grouped by symbol type
456. tion 0 a e a a we es 288 J82 Multivariate Normal Distributions e sa soe ce eR aa ss 288 K Installation and System Notes 291 EL nettles oa cs et woe eh ww A eek ee ee ae ee ee Oe A ee KB Oe a 291 K2 Command Line Use of GAMS 2 ee es 292 K3 Tistallai n 6 466 44 bd a eek Be od bk de we ee ee ae be Be Es 292 Ra Acree ie GAMS scared A ee eo ee ee A eG See ka bw a PA AA a 293 Es Tsai IEA a ae a 294 ke Aws tO GAMS cc ha di a a ee AS 295 Kok EXSAMplE 0 ru eee ee eee eae ORR eR EG ER Dh eG eae eR ea eS 295 Index 299 List of Tables 2 1 2 2 2 3 al de 3 4 4 1 6 1 6 2 6 3 el 8 1 8 2 g1 9 2 11 1 11 2 11 3 14 1 14 2 C 1 DA E 1 Jl J 2 J 4 J5 J 6 3 8 Data for the transportation problem adapted from Dantzig 1963 6 The basic components of a GAMS model e 8 Permissible variable types scout a a ra 12 Organization of GAMS programs ocios aaa a a A Rae 29 Legal characters coords a AR AA 30 Reserved words and symbols ooo e a e es 30 Rules for constructing identifiers and labels oo es cc wag o o e e e 31 Examples of the compact representation of sets o e e 41 GAMS TORS dardos ss a e a ee eel eda 63 Special symbols for extended arithmetic ee 65 Expenentintion and Division oa ce s saoe aama eae Ree Rade a A ee 66 Variable types and default Bounds lt e coos s se s s wii oa oea a 68
457. tion 208 card operator on sets 127 case GAMS call parameter 180 cauchy distribution 281 283 cdfBVN function 288 cdf TVN function 288 cdfUVN function 288 ceil function 58 76 centropy function 58 300 INDEX cerr GAMS call parameter 180 character set valid 35 charset GAMS call parameter 180 CHENERY example from GAMSLIB 70 76 117 chiSquare distribution 281 283 clear dollar control option 208 clearError s dollar control option 208 cns GAMS call parameter 180 GAMS option 247 CNS model type 16 80 column 169 listing 98 comma in data lists 32 in put statements 140 comment dollar control option 209 using eolcom 33 using inlinecom 33 compilation 169 actions during 179 errors 105 errors at time 106 output 92 complement a set operation 123 compress 265 dollar control option 209 Compressed and Encrypted Input Files 265 conditional expressions numerical values 111 operator precedence 111 using set membership 110 with logical operators 110 with numerical relationship operators 109 constant set 169 constraint 169 continuous 169 control reference type 94 controlling index 54 set 49 155 controlling sets 169 cos function 58 cosh function 58 cosine function 286 CRAZY example from GAMSLIB 65 107 curdir GAMS call parameter 180 cvPower function 58 data entered as parameters 46 entered as tables 48 entry 45 handling aspects
458. tion about the library itself and the extrinsic functions it implements to the GAMS execution system For example the information that the cosine function has an endogenous required first argument and an exogenous optional second argument is avail able from the querylibrary callback The q1 py file that generated the file tricclibql c and also the Delphi and Fortran90 equivalents tridclibql inc and triifortlibql f90 does so by processing the specification file tri spec See the comments in this file for info on how to write such a specification The ql py script is invoked by executing ql py tri spec from the shell When implementing a function in a library this function needs to return the function value of the input point Furthermore the solver might need derivative information at the input point Therefore the implementation of the function needs to be able to return gradient and Hessian values This can sometimes be inconvenient GAMS can use the function values at points close to the input point to estimate the gradient and Hessian values using finite differences However this is not as accurate as analytic derivatives and requires a number of function evaluations so the convenience comes at a price The attribute MaxDerivative in the specification of a function signals GAMS the highest derivatives this function will provide For higher order derivatives GAMS will use finite differences to approximate the derivative values J 7 Build Your O
459. tioned above standard syntax as eolcomment set i 1 3 scalar cond 0 parameter a i 1 1 23 2 2 65 3 1 34 maxcol 40 onend loop i do loop i display a display a endloop J3 if cond then if cond display a display a else else a i a i 2 a i a i 2 display a display a endif for cond 1 to 5 do for cond 1 to 5 a i 2 a i a i 2 a i endfor while cond lt 2 do while cond lt 2 a i a i 2 a i a i 2 endwhile ve Note that the alternate syntax is more in line with syntax used in some of the popular programming languages t Both forms of the syntax will never be valid simultaneously Setting the onend option will make the alternate syntax valid but makes the standard syntax invalid on off EolCom offEo1Com Switch to control the use of end of line comments By default the end of line comment symbol is set to 11 but the processing is disabled Consider running the following slice of code oneolcom set i 1 2 1 set declaration parameter a i parameter declaration 228 Dollar Control Options Note that comments can now be entered on the same line as GAMS code t feolcom automatically sets oneolcom Consider the following example eolcom gt set i 1 2 gt set declaration parameter a i gt parameter declaration The character set gt serves as the end of line comment indicator onjoff Eps offEps This option is used to
460. tions are listed and described in Table J 9 Function Endogenous Description Classifica tion pdfUVN x NLP PDF of uni variate normal see MathWorld or R cdfUVN x NLP CDF of uni variate normal see MathWorld or R pdfBVN x y r NLP PDF of bivariate normal see MathWorld or R cdfBVN x y r NLP CDF of bivariate normal see MathWorld or R pdf TVN x y z r21 r31 r32 NLP PDF of trivariate normal see MathWorld or R cdf TVN x y z r21 r31 r32 NLP CDF of trivariate normal see MathWorld or R Table J 9 CPP Library functions J 8 1 Automatic differentiation Often extrinsic functions are created so that they can be used with endogenous arguments In such cases it is necessary that we provide first and second derivatives w r t these arguments in addition to the function values themselves One way to compute these derivatives is via automatic differentiation techniques see the Wikipedia article for details With C it is possible to overload the usual arithmetic operators assignment addition multiplication etc so that this automatic differentiation occurs with little or no change to the function only source code This is the technique used to compute the derivatives in the CPP Library Test Library model cpp1ib00 includes all the source code for the CPP Library and illustrates exercises the steps to build the library from this source The source is a working self documentation of how the process of automatic differentiation wo
461. to add power and flexibility of expression calculations They are indexed operations functions and extended range arithmetic 6 3 2 Indexed Operations In addition to the simple operations explained before GAMS also provides the following four indexed operations sum Summation over controlling index prod Product over controlling index smin Minimum value over controlling index smax Maximum value over controlling index These four operations are performed over one or more controlling indices The syntax in GAMS for these operations is indexed_op controlling_indices expression If there is only one controlling index the parentheses around it can be removed The most common of these is sum which is used to calculate totals over the domain of a set Consider the following simple example adapted from ANDEAN for illustration 6 3 Expressions 57 sets i plants cartagena callao moron m product nitr acid sulf acid amm sulf parameter capacity i m capacity in tons per day totcap m total capacity by process totcap m sum i capacity i m This would be written using normal mathematical representation as totCm gt Cim The index over which the summation is done i is separated from the reserved word sum by a left parenthesis and from the data term capacity i m by a comma i is again called the controlling index for this operation The scope of the control is the pair of parentheses that starts immedi
462. to configure GAMS It prompts the user for default solvers to be used for each model type If possible choose solvers you have licensed since unlicensed solvers will only run in demonstration mode The solver defaults can be changed by a rerunning gamsinst and resetting the default values b setting a command line default e g gams trnsport lp bdmlp c by an option statement in the GAMS model e g option 1p bdmlp The system wide solver defaults are shared by the command line and the GAMS IDE so you can also choose to set these defaults using the GAMS IDE Unix K 3 Installation To install GAMS please follow the steps below as closely as possible We advise you to read this entire document before beginning the installation procedure Additionally a video on how to install GAMS on Linux is available at https www youtube com watch v Mx_tYI3wyP4 1 Obtain the GAMS distribution file which is available from http www gams com download in one large self extracting zip archive with a _sfx exe file extension e g linux_x64 64 sfx exe on a Linux 64bit system Check that it has the execute permission set If you are not sure how to do this just type in the command e g chmod 755 linux_x64_64_sfx exe Choose a location where you want to create the GAMS system directory the GAMS system directory is the directory where the GAMS system files should reside At this location the GAMS installer will create a subdirectory with a name
463. to save and restart the state of a GAMS program Depending on the context we refer to those files as work files save files or restart files 258 Secure Work Files G 2 A First Example The model TRNSPORT from the GAMS model library will be used to illustrate the creation and deployment of a secure work file Assume we want to distribute this model but have concerns about proprietary formulations and data In addition we would like to protect the user from making unintentional modifications to the model We assume that the objective function and the supply constraints are to be hidden from other users and only the demand figures can be changed Data that is not needed any more will be purged as well This will be demonstrated below using the command line interface to GAMS First we will copy the model from the GAMS model library run the model and save a normal work file gt gamslib trnsport gt gams trnsport s t1 We continue to enter access control commands in a file called t2 gms and create a secure work file with the name t2 g00 gt type t2 gms eolcom protect all make all symbol read only purge df remove items d and f hide cost supply a make objective invisible expose transport b allow changes to b gt gams t2 r t1 s t2 plicense target GAMS Rev 124 Copyright C 1987 2001 GAMS Development Licensee Source User Name Source Company Name Creating a Secure Restart File for RK Target User Name eK
464. treat a zero as an EPS in a parameter or table data statement This can be useful if one overloads the value zero with existence interpolation Consider running the following slice of code set i one two three four parameter a i oneps one 0 offeps two 0 three EPS ye display a The result of the display statement in the listing file is as follows 8 PARAMETER A one EPS three EPS Note that only those entries specifically entered as 0 are treated as EPS onjoff Expand offExpand Changes the processing of macros appearing in the arguments of a macro call The default operation is not to expand macros in the arguments The switch onExpand enables the recognition and expansion of macros in the macro argument list and 0ffexpand will restore the default behavior on off Global offGlobal When an include file is inserted it inherits the dollar control options from the higher level file However the dollar control option settings specified in the include file do not affect the higher level file This convention is common among most scripting languages or command processing shells In some cases it may be desirable to break this convention This option allows an include file to change options of the parent file as well Consider running the following slice of code include inc inc hidden after first call to include file onglobal include inc inc hidden after second call to include file where th
465. trol option 221 loadDCM dollar control option 221 loadDCR dollar control option 221 loadM dollar control option 221 loadR dollar control option 221 locally infeasible 100 optimal 100 log dollar control option 222 function 76 log function 58 log10 function 58 log2 function 58 logarithmic distribution 282 284 logBeta function 58 logfile GAMS call parameter 190 logGamma function 58 logistic distribution 281 283 logline GAMS call parameter 190 logNormal distribution 281 283 logoption GAMS call parameter 191 LogOption function 287 loop example 156 statement 155 syntax 155 lower bound 69 lo 69 lower case 30 Ip GAMS call parameter 191 GAMS option 248 LP model type 15 80 It relational operator 30 109 Mac OS X Installation Notes 294 macro dollar control option 222 mapping sets 39 maps symbol listing 95 symbol reference 93 mapVal function 58 MARCO example from GAMSLIB 87 marginal 71 104 171 value m 69 matrix element 171 max function 58 76 maxcol dollar control option 224 maxExecError function 61 maxGoto dollar control option 224 maximizing 86 maxprocdir GAMS call parameter 191 mcp GAMS call parameter 192 GAMS option 248 MCP model type 16 80 MEXSS example from GAMSLIB 153 min function 58 76 mincol dollar control option 224 minimizing 85 86 minlp GAMS call parameter 192 GAMS option 248 MINLP model type
466. trols the time limit for a GAMS job The system will terminate with a compilation or execution error if the limit is reached execerr execerr 0 execution time error limit Entering or processing a solve statement with more than execerr errors will abort Values O no errors allowed n n errors allowed C 3 Detailed Description of Command Line Parameters 185 execmode execmode 0 limits on call execute put and echo commands Values O everything allowed 1 interactive shells in call and execute commands are prohibited 2 all call and execute commands are prohibited 3 echo or put commands can only write below the working or scratch directory 4 echo and put commands are not allowed expand ef tezt expand file name The expand parameter generates a file that contains information about all the input files processed during a particular compilation The names of the input files are composed by completing the name with the current directory The following example illustrates the use of the expand parameter Consider the following slice of code parameter a a 0 include file2 inc include file2 inc The content of the include file file2 inc is shown below a ati display a Running the model with the command line flag expand myfile fil results in the creation of the file myfile fil The content of this file is provided below 1 INPUT 0 0 0 1 7 E TEMP FILE1 GMS 2 INCLUDE 1 1 2 2 4 E XTEMPAFILE2 INC 3 INCLUDE 1 1 3 5 7 E
467. ts s Sector manuf agri services government r regions north eastcoast midwest sunbelt Fo 4 3 The Alias Statement Multiple Names for a Set It is sometimes necessary to have more than one name for the same set In input output models for example each commodity may be used in the production of all other commodities and it is necessary to have two names for the set of commodities to specify the problem without ambiguity In the general equilibrium model ORANI the set of commodities is written set c commodities food clothing and a second name for the set c is established with either of the following statements alias c cp alias cp c where cp is the new set that can be used instead of the original set c t The newly introduced set can be used as an alternative name for the original set and will always contain only the same elements as the original set The alias statement can be used to introduce more than one new name for the original set alias c cp cpp cppp where the new sets cp cpp cppp are all new names for the original set c t The order of the sets in the alias statement does not matter The only restriction set by GAMS is that exactly one of the sets in the statement be defined earlier All the other sets are introduced by the alias statement We will not demonstrate the use of set aliases until later Just remember they are used for cases when a set has to be referred to by mor
468. ts functions or other control variables with numerical values No whitespace is allowed in the expression For differences to eval and evalLocal check the example in the description of eval Note that GAMS allows one to define scoped local and global variables with the same name and has to prioritize under some cases Consider the following slice of code evalglobal notunique 11 evallocal notunique 22 eval notunique 33 log notunique log will echo 22 the current value of notunique to the log file evalLocal evalLocal evaluates a numerical expression at compile time and places it into a local control variable In turn one can use if and ife to do numeric testing on the value of this variable The format is evalLocal varname expression where the expression must consist of constants functions or other control variables with numerical values No whitespace is allowed in the expression For differences to eval and evalGlobal check the example in the description of eval Note that GAMS allows one to define scoped local and global variables with the same name and has to prioritize under some cases Consider the following slice of code 214 Dollar Control Options exit evalglobal notunique 11 evallocal notunique 22 eval notunique 33 log notunique log will echo 22 the current value of notunique to the log file This option will cause the compiler to exit stop reading from the current file This is equival
469. ts encapsulating all include files into one GAMS file If activated a file will be written containing GAMS source code for the entire problem The file name is the input file name plus the extension dmp Values O no dumpfile 1 extract referenced data from the restart file using original set element names 2 extract referenced data from the restart file using new set element names 3 extract referenced data from the restart file using new set element names and drop symbol text 4 extract referenced symbol declarations from the restart file 11 write processed input file without comments 21 write processed input file with all comments To illustrate the use of the dumpopt option TRNSPORT has been split into two files The first file say trans1 gms contains most of the original file except for the solve statement and looks as follows sets i canning plants seattle san diego j markets new york chicago topeka parameters a i capacity of plant i in cases seattle 350 san diego 600 b j demand at market j in cases new york 325 chicago 300 topeka 275 table d i j distance in thousands of miles new york chicago topeka seattle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 scalar f freight in dollars per case per thousand miles 90 parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 variables 182 The GAMS Call x i j shipment quantities in cases z total transportation
470. ts to individual rows and columns in the problem generated The NON ZERO ELEMENTS entry refers to the number of non zero coefficients in the problem matrix There are four entries that provide additional information about nonlinear models The NON LINEAR N Z entry refers to the number of nonlinear matrix entries in the model All forms of nonlinearity do not have the same level of complexity For example x y is a simpler form of nonlinearity than exp x y So even though both these terms count as 1 nonlinear entry in the matrix additional information is required to provide the user with a feel for the complexity of the nonlinearity GAMS provides the CODE LENGTH entry as a good yardstick for this purpose There are two other entries DERIVATIVE POOL and CONSTANT POOL that provide some more information about the nonlinearity In general the more nonlinear a problem is the more difficult it is to solve The times that follow statistics are also useful The GENERATION TIME is the time used since the syntax check finished This includes the time spent in generating the model The measurement units are given and represent ordinary clock time on personal computers or central processor usage CPU time on other machines 10 5 4 The Solve Summary This is the point chronologically speaking where the model is solved and the next piece of output contains details about the solution process It is divided into two parts the first being common to all
471. tten to During file declaration the external file name and explanatory text are optional When the external file name is omitted GAMS will provide a system specific default external file name often fname put Note that multiple files can be defined using a single file statement Consider the following example file classi class2 this defines a specific external file report txt con this defines access to the console screen for PC systems The first output file is recognized in the model by the name class1 and corresponds to the default file class1 put for a PC system The second output file is recognized in the model by the name class2 and it corresponds to the defined external file report txt Lastly the special internal file name con is defined to write output to the console screen for a PC systems Writing to the screen can be useful to advise the user of various aspects of the model during the model s execution 15 4 2 Assigning Files The put statement is used both to assign the current file and to write output items to that file The complete syntax for using the put statement is put fname item s fname item s As indicated by this syntax multiple files can be sequentially written using a single put statement Note that only one file is current at a time After the output items following an internal file name are written the current file is reassigned based on the next internal file name in the statement The last inte
472. ttle 2 5 1 7 1 8 san diego 2 5 1 8 1 4 The effect of this statement is to declare the parameter d and to specify its domain as the set of ordered pairs in the Cartesian product of i and j The values of d are also given in this statement under the appropriate heading If there are blank entries in the table they are interpreted as zeroes As in the list format GAMS will perform domain checking to make sure that the row and column names of the table are members of the appropriate sets Formats for entering tables with more columns than you can fit on one line and for entering tables with more than two dimensions are given in Chapter 5 page 45 2 4 3 Data Entry by Direct Assignment The direct assignment method of data entry differs from the list and table methods in that it divides the tasks of parameter declaration and parameter assignment between separate statements The transportation model contains the following example of this method Parameter c i j transport cost in thousands of dollars per case c i j f d i j 1000 It is important to emphasize the presence of the semicolon at the end of the first line Without it the GAMS compiler would attempt to interpret both lines as parts of the same statement GAMS would fail to discern a valid interpretation so it would send you a terse but helpful error message The effects of the first statement above are to declare the parameter c to specify the domain i j and to provide
473. ubtypes A dynamic set is most often used as a controlling index in an assignment or an equation definition or as the controlling entity in a dollar controlled indexed operation 12 2 1 The Syntax In general the syntax in GAMS for assigning membership to dynamic sets is set_name domain_name domain_label yes no Set_name is the internal name of the set also called an identifier in GAMS Yes and no are keywords used in GAMS to denote membership or absence respectively from the assigned set ts The most important principle to follow is that a dynamic set should always be domain checked at declaration time to be a subset of a static set or sets ts It is of course possible to use dynamic sets that are not domain checked and this provides additional power flexibility lack of intelligibility and danger Any label is legal as long as the dimensionally once established is preserved 12 2 2 Illustrative Example The following example adapted from ZLOOF is used to illustrate the assignment of membership to dynamic sets 120 Dynamic Sets set item all items dish ink lipstick pen pencil perfume subitemi item first subset of item pen pencil subitem2 item second subset of item subitem1 ink yes subitem1 lipstick subitem2 item yes subitem2 perfume display subitem1 subitem2 yes no Note that the sets subitem1 and subitem2 are declared like any other set The two sets bec
474. ue fx 69 lower bound lo 69 marginal or dual value m 69 scale value scale 69 upper bound up 69 variable bounds activity level 70 fixing 69 variable type 173 vcPower function 58 vector 173 version dollar control option 242 warning dollar control option 243 warnings GAMS call parameter 201 weibull distribution 281 283 while example 158 statement 158 syntax 158 Windows 291 workdir GAMS call parameter 201 workfactor GAMS call parameter 202 workspace GAMS call parameter 202 xor relational operator 121 xsave GAMS call parameter 202 zero default 173 Zerores GAMS call parameter 202 zeroresrep GAMS call parameter 202 ZLOOF example from GAMSLIB 119
475. ue Then we can use execute_loadhandle to load the solution for model minvar back into the GAMS data base Using handlestatus and loadhandle instead of the simpler handlecollect adds one more layer of control to the final collection loop We now need one additional if statement inside the above collection loop Repeat loop pp h pp if handlestatus h pp 2 minvar handle h pp execute_loadhandle minvar xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i display handledelete h pp trouble deleting handles h pp 0 272 The GAMS Grid Computing Facility display sleep card h 0 2 sleep some time until card h O or timeelapsed gt 100 xres i pp h pp na Now we are ready to run the modified model The execution log will contain some new information that may be useful on more advanced applications LOOPS pp pl Soa 46 rows 37 columns 119 non zeroes 311 nl code 7 nl non zeroes a 14 discrete columns Submitting model minvar with handle grid137000002 Executing after solve GDXin C answerv5 gams_srcdev 225j grid137000003 gmsgrid gdx Removing handle grid137000003 The log will now contain some additional information about the submission retrieval and removal of the solution instance In the following sections we will make use of this additional information You can find a complete example of a grid enabled transport model in the GAM
476. ues known before a solve statement is processed and not changed by the solve In GAMS most often parameters explanatory text See text exponent A scale factor used to conveniently represent very large or small numbers extended arithmetic The usual computer arithmetic is extended to include plus and minus infinity inf and inf and a special value for an arbitrarily a small number i e one which is close to zero known as epsilon eps Also not available na can be used to indicate missing data and undefined undf is the result of illegal operation GAMS allows extended arithmetic for all operations and functions The library problem CRAZY demonstrates extended arithmetic by showing the results for all operations and functions e format The representation of numbers when an exponent is used explicitly For example 1 1E 07 feasible Often used to describe a model that has at least one feasible solution see below 171 feasible solution A solution to a model in which all column activity levels are within the bounds and all the constraints are satisfied GAMS coordinator The person who looks after the administration of a GAMS system and who will know what solvers are available and can tell you who to approach for help with GAMS problems Unlikely to apply to personal computer versions identifiers Names given to data entities Also called symbols index position s Another way of describing the set s that must be used when
477. uld be used Newton s method is the assertion that if x is an approximation to the square root of v then x v x 2 is a better one set i set to drive iterations i 1 i 100 parameter value i used to hold successive approximations scalars target number whose square root is needed 23 456 sqrtval final approximation to sqrt target curacc accuracy of current approximation reltol required relative accuracy 1 0e 06 abort target lt 0 argument to newton must be positive target value i 1 target 2 curacc 1 loop i curacc gt reltol value i 1 0 5 value i target value i sqrtval value i 1 curacc abs value i 1 value i 1 abs value i 1 3 abort curacc gt reltol square root not found option decimals 8 display square root found within tolerance sqrtval value The output is e 18 square root found within tolerance 18 PARAMETER SQRTVAL 4 84313948 final approximation to sqrt target nae 18 PARAMETER VALUE used to hold successive approximations i 1 11 72800000 i 2 6 86400000 i 3 5 14062471 i 4 4 85174713 i 5 4 84314711 i 6 4 84313948 i 7 4 84313948 16 3 The If Elseif Else Statement The if else statement is useful to branch conditionally around a group of statements In some cases this can also be written as a set of dollar conditions but the if statement may be used to make the GAMS code more readable An optional else part allows you to formul
478. ults of the optimization The results are first presented in as standard mathematical programming output format with the added feature that rows and columns are grouped and labeled according to names that are appropriate for the specific model just solved In this format there is a line of printout for each row and column giving the lower limit level upper limit and marginal Generic equation block and the column output group the row output by generic variable block Set element names are embedded in the output for easy reading In the transportation example the solver outputs for supply i demand j and x i j are as follows EQU SUPPLY observe supply limit at plant i LOWER LEVEL UPPER MARGINAL seattle INF 350 000 350 000 EPS san diego INF 550 000 600 000 EQU DEMAND satisfy demand at market j LOWER LEVEL UPPER MARGINAL new york 325 000 325 000 INF 0 225 chicago 300 000 300 000 INF 0 153 topeka 275 000 275 000 INF 0 126 VAR X shipment quantities in cases LOWER LEVEL UPPER MARGINAL seattle new york a 50 000 INF seattle chicago k 300 000 INF seattle topeka s INF 0 036 san diego new york E 275 000 INF san diego chicago A INF 0 009 san diego topeka 275 000 INF The single dots in the output represent zeroes The entry EPS which stands for epsilon mean very small but nonzero In this case EPS indicates degeneracy The slack variable for the Seattle supply constraint is in the basis at ze
479. um fractions must add to 1 0 dmean definition of mean return on portfolio dvar definition of variance fsum sum i x i e 1 0 dmean sum i mean i x i e target dvar sum i x i sum j v i j x j e variance Model portfolio fsum dmean dvar Solve portfolio using nlp minimizing variance 10 3 Compilation Output This is the output produced during the initial check of the program often referred to as compilation It contains two or three parts the echo print of the program an explanation of any errors detected and the maps The next four sub sections will discuss each of these in detail 10 3 1 Echo Print of the Input File The Echo Print of the program is always the first part of the output file It is just a listing of the input with the lines numbers added The offlisting directive would turn off the listing of the input file A Quadratic Programming Model for Portfolio Analysis ALAN SEQ 124a This is a mini mean variance portfolio selection problem described in gt GAMS MINOS Three examples by Alan S Manne Department of Operations Research Stanford University May 1986 9 This model has been modified for use in the documentation Note that the first line number shown is 9 If the lines on the input are counted it can be seen that this comment line shown above appears after 8 lines of dollar directives and comments The line starting title has caused text of the users choice to be put on the pa
480. umber where the string replacement was requested Also note that Asystem incname has been substituted by the name of the file completed with the absolute path Also note that the leading blanks on the second line of the example are ignored Macro GAMS includes the ability to define macros as of version 22 9 The definition takes the form macro name arg1 arg2 arg3 body where name is the name of the macro which has to be unique argl arg2 arg3 are the arguments and body defines what the macro should do Consider the following example scalar x1 2 x2 3 y macro oneoverit y 1 y y oneoverit x1 display y macro ratio a b a b y ratio x2 x1 display y The resulting listing file contains Sas 5 PARAMETER y 0 500 1 500 Sar 9 PARAMETER y Macros can also be included within macros macro product a b a b macro addup i x z sum i product x i z when called with z addup j al x1 will expand into D 3 Detailed Description of Dollar Control Options 223 z sum j al j x1 The recognition of macros and expansion of arguments can be more carefully controlled by the use of ampersands 8 in the macro body Ordinarily the macro will only substitute for full words thus the macro group macro f i sum j x i j macro equh q equation equ_q i equ_q i q e 0 equh f i which would expand to become equation equ_q i equ_q i sum j x i j e 0 Note this contains q in a number
481. ured framework for developing general data organization and transformation capabilities Math ematical programming provides a way of describing a problem and a variety of methods for solving it The following principles were used in designing the system 1 All existing algorithmic methods should be available without changing the user s model representation Introduction of new methods or of new implementations of existing methods should be possible without requiring changes in existing models Linear nonlinear mixed integer mixed integer nonlinear optimizations and mixed complementarity problems can currently be accommodated 2 The optimization problem should be expressible independently of the data it uses This separation of logic and data allows a problem to be increased in size without causing an increase in the complexity of the representation 2 Introduction 3 The use of the relational data model requires that the allocation of computer resources be automated This means that large and complex models can be constructed without the user having to worry about details such as array sizes and scratch storage 1 2 2 Documentation The GAMS model representation is in a form that can be easily read by people and by computers This means that the GAMS program itself is the documentation of the model and that the separate description required in the past which was a burden to maintain and which was seldom up to date is no longer needed
482. urn 13 3 1 The Ord Operator Ord returns the relative position of a member in a set amp Ord can be used only with a one dimensional static ordered set Some examples show the usage set t time periods 1985 1995 parameter val t val t ord t As a result of the statements above the value of val 1985 will be 1 va1 1986 will be 2 and so on A common use of ord is in setting up vectors that represent quantities growing in some analytically specified way For example suppose a country has 56 million people in the base period and population is growing at the rate of 1 5 percent per year Then the population in succeeding years can be calculated by using population t 56 1 015 ord t 1 It is often useful to simulate general matrix operations in GAMS The first index on a two dimensional parameter can conveniently represent the rows and the second the columns and order is necessary The example below shows how to set the upper triangle of a matrix equal to the row index plus the column index and the diagonal and lower triangle to zero set i row and column labels x1 x10 alias i j parameter a i j a general square matrix a i j ord i 1t ord j ord i ord j 13 4 Lag and Lead Operators 127 13 3 2 The Card Operator Card returns the number of elements in a set Card can be used with any set even dynamic or unordered ones The following example illustrates its use set t ti
483. use The solution report from the solver is automatically reformatted so that related equations and variables are grouped together and appropriately labeled Also the display command allows you to modify and tabulate results very easily gt If you are teaching or learning modeling you can benefit from the insistence of the GAMS compiler that every equation be mathematically consistent Even if you are an experienced modeler the hundreds of ways in which errors are detected should greatly reduce development time gt By using the dollar operator and other advanced features not covered in this tutorial one can efficiently implement large scale models Specific applications of the dollar operator include the following 1 It can enforce logical restrictions on the allowable combinations of indices for the variables and equations to be included in the model You can thereby screen out unnecessary rows and columns and keep the size of the problem within the range of solvability 2 It can be used to build complex summations and products which can then be used in equations or customized reports 3 It can be used for issuing warning messages or for terminating prematurely conditioned upon context specific data edits 26 A GAMS Tutorial by Richard E Rosenthal 3 GAMS Programs 3 1 Introduction This chapter provides a look at the structure of the GAMS language and its components It should be emphasized again that GAMS is a programmi
484. use one or more individual equations to be suppressed and this may not be desirable in every case Consider the following modified set of constraints to the one discussed in the previous example It is expressed with the lag and lead operators being used to control the domain of the equation definition kk t 1 k t 1 e k t i t kfirst tfirst k tfirst e k0 Here the important boundary is the one at the beginning of the set rather than at the end This can be expressed more compactly as kk t k t e k t 1 kO tfirst t i t 1 In general the choice between using lag and lead operators as reference or in domain control is often a matter of taste 13 7 Summary 131 13 6 3 Circular Lag and Lead Operators In the case of circular lag and lead operators the difference between its use in domain control and as reference is not important because it does not lead to any equations or terms being suppressed Consider the following artificial example set s seasons spring summer autumn winter variable prod s amount of goods produced in each season avail s amount of goods available in each season sold s amount of goods sold in each season equation matbal s matbal s avail s 1 e prod s sold s In this example four individual examples are generated They are listed below avail summer e prodn spring sold spring avail autumn e prodn summer sold summer avail winter e pro
485. used to set various global system parameters that control output detail solution process and the layout of displays They are processed at execution time unlike the dollar control options discussed in Appendix D They are provided to give flexibility to the user who would like to change the way GAMS would normally do things GAMS does provide default values that are adequate for the most purposes but there are always cases when the user would like to maintain control of aspects of the run E 1 1 The Syntax The general form of an option statement is option keyword1 valuel EOL keyword2 value2 where the keyword1 and keyword2 are recognized option names but not reserved words and the value1 and value2 are valid values for each of the respective options Note that commas or end of line characters are both legal separators between options t Option names are not reserved words and therefore do not conflict with other uses of their name There are five possible formats 1 a display specifier 2 a recognized name number following sign or value a recognized name number following an sign then an unsigned integer value a recognized name number following an sign then an unsigned real number Cu a ee a recognized name number following an sign then either of two recognized words t An option statement is executed by GAMS in sequence with other instructions Ther
486. ut data format dollar set the dollar character offDelim delimited data statement syntax off offDigit off number precision check offEmbedded no embedded text or data allowed offEmpty disallow empty data initialization statements offEnd disallow alternate program control syntax offEps disallow interpretation of EPS as 0 offGlobal disallow inheritance of parent file settings of fUNDF do not allow UNDF as input of fWarning do not convert domain errors into warnings onDelim delimited data statement syntax on onDigit on number precision check Options affecting output format double double spaced listing follows echo echo text echoN echo a string to a file without ending the line eject advance to next page hidden ignore text and do not list lines next number of lines have to fit on page log send message to the log offDollar turn the listing of DCO lines off offEcho end of block echo offInclude turn off listing of include file names offListing turn off echoing input lines to listing file offLog turn off line logging of fPut end of block put offVerbatim stop verbatim copy onDollar turn the listing of DCO lines on Options affecting listing of reference maps of fSymList off symbol list of fSymXRef off symbol cross reference listing of fUE1List off unique element listing of fUE1XRef off unique element cross reference Options affecting program control abort issue an error message and abort compilation ba
487. vailable by the following directive FuncLibIn lt InternalLibName gt stodclib Function Description SetSeed SEED defines the seed for random number generator Continous distributions beta SHAPE 1 SHAPE_2 cauchy LOCATION SCALE ChiSquare DF exponential LAMBDA f DF_1 DF_2 gamma SHAPE SCALE gumbel LOCATION SCALE invGaussian MEAN SHAPE laplace MEAN SCALE logistic LOCATION SCALE logNormal LOCATION SCALE normal MEAN STDDEV pareto SCALE SHAPE rayleigh SIGMA studentT DF triangular LOW MID HIGH uniform LOW HIGH weibull SHAPE SCALE Beta distribution with shape parameters SHAPE_1 and SHAPE_2 see MathWorld Cauchy distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Chi squared distribution with degrees of freedom DF see MathWorld Exponential distribution with rate of changes LAMBDA see MathWorld F distribution with degrees of freedom DF_1 and DF_2 see MathWorld Gamma distribution with shape parameter SHAPE and scale parameter SCALE see MathWorld Gumbel distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Inverse Gaussian distribution with mean MEAN and scaling parameter SHAPE see MathWorld Laplace distribution with mean MEAN and scale parameter SCALE see MathWorld Logistic distribution with location parameter LOCATION and scale param eter SCALE see MathWorld Log Normal
488. varcov R For the bivariate case there is one correlation coefficient r The CDF implementation is not quite accurate to machine precision having 14 or 15 digits of accuracy The trivariate case includes 3 correlation coefficients the 3 off diagonal elements from the lower triange of R above The accuracy of the CDF depends on the inputs it is higher when the correlation is nearly zero and poorer as the condition number of R increases Typically an accuracy of 1071 is all that can be achieved In both multivariate cases you should avoid evaluating at or near points where the correlation matrix is degenerate At nearly degenerate points the accuracy of the distribution and density functions suffers and when the correlation matrix becomes degenerate the distribution becomes so also 290 Extrinsic Functions K Installation and System Notes Windows K 1 Installation Run windows_x86_32 exe Windows 32bit or windows_x64_64 exe Windows 64bit Both files are avail able from http www gams com download The 32 bit version works both on a 32bit and on a 64bit operating system Please note that the installation may require administrative privileges on your machine You have two options to run the installer In default or advanced mode In the default mode the installer will prompt you for the name of the directory in which to install GAMS We call this directory the GAMS directory You may accept the default choice or pick anoth
489. variable which is free unconstrained in sign and scalar valued has no domain and which appears in an equation definition that equates it to the objective function 2 8 Model and Solve Statements The word model has a very precise meaning in GAMS It is simply a collection of equations Like other GAMS entities it must be given a name in a declaration The format of the declaration is the keyword model followed by the name of the model followed by a list of equation names enclosed in slashes If all previously defined equations are to be included you can enter a11 in place of the explicit list In our example there is one Model statement model transport all This statement may seem superfluous but it is useful to advanced users who may create several models in one GAMS run If we were to use the explicit list rather than the shortcut a11 the statement would be written as model transport cost supply demand The domains are omitted from the list since they are not part of the equation name The list option is used when only a subset of the existing equations comprises a specific model or sub model being generated Once a model has been declared and assigned equations we are ready to call the solver This is done with a solve statement which in our example is written as solve transport using lp minimizing z The format of the solve statement is as follows 1 The key word solve 2 The name of the model to be solved
490. variable that was defined with setGlobal The syntax is dropGlobal varname dropLocal Destroys a variable that was defined with setLocal The syntax is dropLocal varname echo The echo option allows to write text to a file echo text gt file echo text gt gt file These options send the message text to the file file Both the text and the file name can be quoted or unquoted The file name is expanded using the working directory The echo statement tries to minimize file operations by keeping the file open in anticipation of another echo to be appended to the same file The file will be closed at the end of the compilation or when a call or any kind of include statement is encountered The redirection symbols gt and gt gt have the usual meaning of starting at the beginning or appending to an existing file Consider the following example echo gt echo echo The message written goes from the first non blank gt gt echo echo to the first gt or gt gt symbol unless the text is gt gt echo echo is quoted The Listing File is gams input The gt gt echo echo file name echo will be completed with gt gt echo echo gams workdir gt gt echo echo gt gt echo The contents of the resulting file echo are as follows The message written goes from the first non blank to the first gt or gt gt symbol unless the text is is quoted The Listing File is C PROGRAM FILES GAMS
491. ve the instance from the system by calling the function handledelete which returns zero if successful see definition No harm is done if it fails but we want to be notified via the conditional display statement Before running the collection loop again we may want to wait a while to give the system time to complete more solution steps This is done with the sleep command that sleeps some time The final wrinkle is to terminate after 100 seconds elapsed time even if we did not get all solutions This is important because if one of the solution steps fails our program would never terminate The last statement sets the results of the missed solves to NA to signal the failed solve The parameter h will now contain the handles of the failed solvers for later analysis Alternatively we could have used the function handlestatus and collect the solution which is stored in a GDX file For example we could write loop pp handlestatus h pp 2 minvar handle h pp execute_loadhandle minvar xres i pp x 1 i report pp i inc xi 1 i report pp i dec xd 1 i The function handlestatus interrogates the solution process and returns 2 if the solution process has been completed and the results can be retrieved The solution is stored in a GDX file which can be loaded in a way similar to other gdx solution points First we need to tell GAMS what solution to retrieve by setting the minvar handle to the appropriate val
492. when circumstances change either naturally or by design This is often done by making many different changes to the base case and separately considering the effects it is sometimes called what if analysis The point is that the base can be saved using a work file and as many different scenarios as may be interesting can then be run separately by restarting Each scenario probably involves only making a change in data or in bounds solving the changed model the base solution is automatically used as a starting point and reporting This procedure is an example of how a work file is used in a tree structured way one work file is used with many different but probably very small input files to produce many different output files File handling is less likely to be a problem than in the sequential case above F 3 5 The GAMS Runtime License We assume the model and the data have been completely separated as shown above with file1 gms containing only the model and file2 gms containing only the data The developer of the model can run the first model with the following command gams filel s trans and then distribute the file trans g00 file that result along with the example file2 gms If the end user has a run time license for GAMS they will not be able to see the model nor change it by adding any new variables or equations The end user will only be able to change the data and run the model developed during the save process However th
493. wing equation variable shipped i j totcost equation costequ cost totcost e sum i j ij i j shipcost i j shipped i j where shipped is the amount of material shipped from i to j and totcost is the total cost of all shipment The equation above can be written as cost totcost e sum ij shipcost ij shipped ij However if the original equation is expressed as cost totcost e sum i j ij i j factor congestfac j distance i j shipped i j Index j appears separately from i in congestfac j The equation then needs to be simplified as cost totcost e sum ij i j factor congestfac j distance ij shipped ij Note that the presence of j separately in the indexed expression necessitated the use of ij i j rather than ij 11 4 Conditional Assignments 115 11 4 4 Filtering Sets in Assignments Consider the following statement u k s k a k where k and s k are sets while u and a are parameters This can be rewritten as u s a s Note that the assignment has been filtered through the conditionality without the use of the dollar operator This is a cleaner and more understable representation of the assignment This feature gets more useful when dealing with tuples sets with multiple indices Consider the following example for calculating the travel cost for a fictional parcel delivery service between collection sites i and regional transportation hubs j set i miami bo
494. without the extension GDX and the command opens the specified GDX file for reading The next use of gdxIn closes the specified GDX file The command must be used in conjunction with the command load gdxOut This dollar command is used in a sequence to unload specified items from a GDX file It is employed using the syntax gdxOut filename where filename gives the name of the GDX file with or without the extension GDX and the command opens the specified GDX file for writing The next use of gdx0ut closes the specified GDX file The command must be used in conjunction with the command unload goto id This option will cause GAMS to search for a line starting with label id and then continue reading from there This option can be used to skip over or repeat sections of the input files In batch include files the target labels or label arguments can be passed as parameters because of the manner in which parameter substitution occurs in such files In order to avoid infinite loops one can only jump a maximum of 100 times to the same label Consider the following example D 3 Detailed Description of Dollar Control Options 215 scalar a a 5 display a goto next a at5 display a label next a a 10 display a On reaching the goto next option GAMS continues from label next All lines in between are ignored On running the example a finally takes a value of 15 ts The goto and label have to be in th
495. wn Reading the GAMS Parameter File in your Library 287 J 7 Build Your Own Reading the GAMS Parameter File in your Library This library serves as an example of how to code and build an extrinsic function library that reads the information from the GAMS parameter file The library is included in the GAMS distribution in binary form and also as source code written in C that comes along with the GAMS Test Library model parlib01 Table J 8 lists the extrinsic functions that are implemented by the libraries Function Endogenous Description Classifica tion LogOption any Return the value for LogOption found in the parameter file Table J 8 GAMS Parameter File reading The C implementation of this extrinsic function library can be found in the files parcclib c and parcclibql c Together with the API specification file extrfunc h The reading of the GAMS Parameter file is done in the function LibInit 288 Extrinsic Functions J 8 CPP Library This library serves both as an example of how to use C to obtain gradients and Hessians for free and as a source of functions based on the multivariate normal distribution The library is available in compiled form and as C source Test Library model cpp1ib00 exercises the process of building a shared library from C source and doing some basic tests while models cpp1ib01 through cpp1ib05 are more thorough tests for the CPP library extrinsics shipped with the distribution These func
496. written with equivalent effect as subitemi item yes subitem2 item which is a terse form of the following statement subitemi item yes subitem2 item no not subitem2 item ts The value used in the implied else that goes with dollar on the right is no in a set assignment rather than zero which is used with normal data The second example from Section 12 2 4 can be rewritten as follows to illustrate the use of dynamic sets in defining parameters inventory item subitemi item 25 12 3 2 Indexed Operations Another important use of dollar controls with dynamic sets is to control the domain while performing indexed operations like sum and prod Consider the following adaptation of the second example from Section 12 3 1 parameter totinv total inventory totinv sum item subitem1 item inventory item This example has been shown only for illustration Note that the second statement above can also be rewritten tersely as totinv sum subitem1 inventory subitem1 This is not always possible Consider the following artificially created example sets item items sold pencil pen sup suppliers bic parker waterman dep department stationery household supply item sup supply pencil bic yes supply pen sup yes parameter totsales dep totsales dep sum item supply item bic sales dep item The assignment above is used to find the total sales of all
497. x positions It is initialized using parameter format and then displayed as shown below set i first index first second j second index one two three k third index Ja b 1 fourth index Icaro 3 parameter x i j k 1 a four dimensional structure second one a i inf first three b i 6 3161 first one b i 5 63559 second two b i 19 8350 second one b ii 17 29948 first two b ii 10 3457 first two a ii 0 02873 second one a ii 1 0037 second two a ii inf first two a i 2 9393 first one a ii 0 00000 FS display x This code fragment produces the following output a 12 PARAMETER X a four dimensional structure INDEX 1 first i ii one b 5 636 two a 2 939 0 029 two b 10 346 three b 6 316 INDEX 1 second i ii one a INF 1 004 one b 17 299 two a INF two b 19 835 Notice that there are two sub tables one for each label in the first index position Note that the zero in the list for x first one a ii has vanished since zero values are suppressed in each sub table separately The order of the labels is not the same as in the input data list 14 5 Display Controls GAMS allows the user to modify the number of row and column labels in the display listing as well as the accuracy of the data being displayed The global display controls allows the user to affect more than one display statement If specific data need to be listed in a particular format the local display controls can be us
498. y phi 1 v l v m The output looks similar except that of course the listing shows which of the values is being displayed Because zeroes and especially all zero rows or columns are suppressed the patterns seen in the level and marginal displays will be quite different since non zero marginal values are often associated with activity levels of zero Mexico Steel Small Static MEXSS SEQ 15 Execution aso 203 VARIABLE PHI L 538 811 total cost mill us a 203 VARIABLE V L imports mill tpy C ALL 0 000 Sane 203 VARIABLE V M imports mill tpy mexico df monterrey guadalaja steel 7 018 18 822 6 606 We should mention here a clarification of our previous discussion of displays It is actually the default values that are suppressed on display output For parameters and variable levels the default is zero and so zero entries are not shown For bounds however the defaults can be non zero The default value for the upper bound of a positive variable is INF and if above you also would display v up for example you will see A 203 VARIABLE V UP imports mill tpy C ALL INF If any of the bounds have been changed from the default value then only the entries for the changed elements will be shown This sounds confusing but since few users display bounds it has not proved troublesome in practice 7 5 Summary Remember that wherever a parameter can appear in a display or an assignment statement a variable can also appear
499. ymbolic relationships Examples are table parameter variable model assignment and display statements static set See constant set superbasic In nonlinear programming a variable that it is not in the basis but whose value is between the bounds Nonlinear algorithms often search in the space defined by the superbasic variables symbol An identifier table One of the ways of initializing parameters Used for two and higher dimensional data structures text A description associated with an identifier or label 173 type See data type problem type or variable type unique element A label used to define set membership variable type The classification of variables The default bounds are implicit in the type and also whether continuous or discrete The types are free positive binary integer semicont semiint and negative vector A one dimensional array corresponding to a symbol having one index position zero default Parameter values are initially set to zero Other values can be initialized using parameter or table statements Assignment statements have to be used thereafter to change parameter values 174 Glossary B The GAMS Model Library Professor Paul Samuelson is fond of saying that he hopes each generation economists will be able to stand on the shoulders of the previous generation The library of models included with the GAMS system is a reflection of this desire We believe that the quality of modeling w
500. yntax of the loop statement is loop controlling_domain condition statement 4 statement 3 If the controlling domain consists of more than one set then parentheses are required around it The loop statement causes GAMS to execute the statements within the scope of the loop for each member of the driving set s in turn The order of evaluation is the entry order of the labels A loop is thus another more general type of indexed operation The loop set may be dollar controlled and does not need to be static or nested Loops may be controlled by more than one set t One cannot make declarations or define equations inside a loop statement t It is illegal to modify any controlling set inside the body of the loop 156 Programming Flow Control Features 16 2 2 Examples Consider a hypothetical case when a growth rate is empirical set t 1985 1990 parameter pop t 1985 3456 growth t 1985 25 3 1986 27 3 1987 26 2 1988 27 1 1989 26 6 1990 26 6 The loop statement is then used to calculate the cumulative sums loop t pop t 1 pop t growth t in an iterative rather than a parallel way In this example there is one statement in the scope of the loop and one driving or controlling set A loop is often used to perform iterative calculations Consider the following example which uses finds square roots by Newton s method This example is purely for illustration in practice the function sqrt sho
501. your program In the example below we show ordered and unordered sets and the map showing the order The input is 126 Sets as Sequences Ordered Sets onuellist set ti 1987 1988 1989 1990 1991 t2 1983 1984 1985 1986 1987 t3 1987 1989 1991 1983 1985 The map below shows the entry order the important one and the sorted order obtained by sorting the labels into dictionary order The single digits on the left are the sequence numbers of the first label on that line General Algebraic Modeling System Unique Element Listing Unique Elements in Entry Order 1 1987 1988 1989 1990 1991 1983 7 1984 1985 1986 Unique Elements in Sorted Order 1 1983 1984 1985 1986 1987 1988 7 1989 1990 1991 A set can always be made ordered by moving its declaration closer to the beginning of the program With these restrictions in mind we move on the operations that are used in dealing with sets as sequences 13 3 Ord and Card In Chapter 4 it was explained that labels do not have a numerical value The examples used were that the label 1986 does not have a numerical value of 1986 and the label 01 is different from the label 1 This section introduces two operators ord and card that return integer values when applied to sets While the integer values returned do not represent the numerical value of the label they can be used for the same purpose The next two subsections describe each of these two functions in t

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