EMS: Efficiency Measurement System User's Manual
Contents
1. SEIFORD 1994 Data Envelopment Analysis Theory Methodology and Application Kluwer Academic Publishers Dordrecht e W W Cooper L M SEIFORD and K TONE 2000 Data Envelopment Analysis A Comprehensive Text with Models Applications References and DEA Solver Software Kluwer Academic Publishers Norwell Massachusetts The latest news about EMS downloads and bugfixes you ll find on the EMS home page http www wiso uni dortmund de lsfg or scheel ems EMS uses the LP Solver DLL BPMPD 2 11 by Csaba M sz ros for the computation of the scores Sources http www netlib org It is an interior point solver If you have questions which are not answered in the following paragraphs or if you have suggestions for further developments send an email to H ScheelQwiso uni dortmund de 2 Preparing the input output data The first and probably most difficult step in an efficiency evaluation is to decide which input and output data should be included EMS accepts data in MS Excel or in text format Additionally to standard inputs and outputs EMS can also handle non discretionary inputs and outputs i e data which are not controlled by the DMUs The next sections describe how the data files should be prepared for EMS The size of your analysis is limited by the memory of your PC I e there is theoretically no limitation of the number of DMUs inputs and outputs in EMS Although the code is not optimized for large scale2. Journal of Econometrics 30 91 107 1A more detailed overview is given in German in H SCHEEL 2000 Effizienzmafe der Data Envel opment Analysis Gabler Wiesbaden 5 Running a DEA model If you want to compute a weighted objective function gt gt w s you can do this by preprocessing the data e g you may multiply each input output i by the corresponding wi maxAverage This measure a k a F re Lovell or Russell or SBM measure quantifies the maximal average of relative improvements input reduction output increase measured in percentages of the current level It has no straightforward price interpretation but it is both an indicator for Koopmans efficiency for positive data and units invariant The symbol denotes the componentwise product of two vectors i e 1 0 OX 14 OY 1401 XP 1 89m Xh 1 b1 VP Eda i rn 0 E YP gt 0 bj dixo 1 Livesol non or max 0 gt 0 1 Ho PEE Z gt input min SAE 00 YL Y erosi LE 0 Dyk output max d yS goret 621 D bn T See R FARE and C A K LOVELL 1978 Measuring the technical efficiency of production Journal of Economic Theory 19 150 162 minAverage This measure quantifies the minimal average of relative improvements which is necessary to become weakly efficient Weak efficiency means there does not exist a point in the technology set which is better in every input and output We denote the wea
3. damages resulting from the use of this software and makes no warranty either express or implied including but not limited to any implied warranty of fitness for a particular purpose The software is provided as it is and you its user assume all risks when using it 12
4. data we successfully solved problems with over 5000 DMUs and about 40 inputs and outputs Please let me know your experience with larger datasets 2 Preparing the input output data 2 1 Using MS Excel files EMS accepts Excel 97 and older files x1s The input output data should be collected in one worksheet Don t use formulas in this sheet it should only contain the pure data and nothing else EMS needs the following data format Data I 0 The name of the worksheet must be Data e The first line contains the input output names First inputs then outputs e Input names contain the string I e Output names contain the string O e The first column contains the DMU names Cf the example file EXAMPLE XLS 2 2 Using textfiles For those who prefer another spreadsheet software than MS Excel EMS accepts also plain textfiles txt For reading textfiles correctly EMS needs the file schema ini which contains some formatting information The following is necessary for using textfiles with EMS schema ini e Put schema ini in the same directory where your textfiles are e Modify schema ini by replacing Yourfile txt by the name of your file The textfile which contains the input output data should then satisfy the following e Columns are separated by Tabs Make sure that exactly one Tab appears between two columns and that you don t have Tabs at other places
5. in the file e g at the end You can check this in a texteditor by making the Tabs visible e Input names contain the string I 3 Preparing weights restrictions e Output names contain the string O e The first column contains the DMU names Cf the example file EXAMPLE TXT 2 3 Non discretionary inputs and outputs EMS accepts non discretionary data if in the data file the corresponding input name contains IN instead of I or the corresponding output name contains ON instead of O IN ON When EMS computes an efficiency score which is a distance to the efficient frontier it doesn t alter the values of non discretionary data I e the distance will only be computed in the directions of the normal descretionary inputs and outputs while the non discretionary are fixed Literature EMS uses the idea of R D BANKER and R C Morey 1986 Efficiency Analysis for Exogenously Fixed Inputs and Outputs Operations Research 34 513 521 See also for an overview M STAAT 1999 Treating non discretionary variables one way or the other Implications for efficiency scores and their interpre tation In G Westermann ed Data Envelopment Analysis in the Service Sector pp 23 50 Gabler Wiesbaden 3 Preparing weights restrictions You can specify weights restrictions of the form W p q gt 0 where p is the vector of input weights and q is the vect
6. EMS Efficiency Measurement System User s Manual Holger Scheel Version 1 3 2000 08 15 Contents 1 Introduction 2 Preparing the input output data 2 1 Using MS Excel files ets soca p i anie parik a a a a ee ee h o ge USE DEBATES a a a R TR ek HY Ae e e a TE ad 2 3 Non discretionary inputs and outputs e a Preparing weights restrictions 31 Using MS Excel T s soste a a eg ee a pei a ae ee a ga Usimpe dele ea aa aTe o a a baa b aa a ee a i a Starting EMS and loading data Running a DEA model 5 1 Preparing the results format n sooo a a 5 2 Choosing a technology structure o ooa a 5 3 Choosing an efficiency measure 0 e eee ee ee 5 4 Advanced modeling options lt lt e ccc aoe mote pa t ega e Results Acknowledgements Disclaimer 11 12 12 1 Introduction 1 Introduction Efficiency Measurement System EMS is a software for Windows 9x NT which computes Data Envelopment Analysis DEA efficiency measures This manual is intended to be an introduction to the usage of the software It is not an introduction to DEA which you can found e g in the following books e H O FRIED C A K LOVELL and S SCHMIDT 1993 The measurement of productive efficiency Techniques and applications Oxford University Press New York e R FARE S GROSSKOPF and C A K LOVELL 1994 Production Frontiers Cambridge University Press Cambridge e A CHARNES W W COOPER A Y LEWIN and L M
7. a sorted by periods T 0 t i e the first column of the data file looks like DMU 1 TO DMU 2 TO DMU n TO DMU 1 T1 DMU n T1 DMU 1 Tt DMU n Tt then EMS supports computation of Window Analysis and Malmquist indices For Window Analysis you have to specify the number of periods and the window width For Malmquist indices you have to specify the number of periods EMS computes then scores E t T t 1 i e the DMUs of period t are evaluated with respect to the technology built by the DMUs in period t 1 The scores E t T t can be computed by running a Window Analysis with window width 1 Dividing these scores is left to your spreadsheet See the Malmquist sheet in example xls for details 6 Results If computations are finished EMS will display the results in a table The window caption tells which model was computed e g example xls_CRS_RAD_IN_WR example contains the results of a DEA model based on the input output data file example xl1s with constant returns to scale radial distance input orientation weights restrictions with restriction matrix stored in example xls The result table contains recall that the number of decimals to display can be modified in Menu DEA Format DMU name An additional X indicates that this DMU was excluded from building the technology as specified in Technology A DMU name without score indicates that this DMU built the technology but was not evaluated as specified in Evalu
8. ation 11 7 Acknowledgements The efficiency score as defined above the weights shadow prices W or virtual inputs outputs V as selected in Menu DEA Format benchmarks e for inefficient DMU the reference DMUs with corresponding intensities the lambdas in brackets e for efficient DMU the number of inefficient DMUs which have chosen the DMU as Benchmark slacks S or factors F Depending of the chosen distance for radial and additive measures the slacks are displayed For the minAverage and maxAverage measures the factors i e the 6 6 as defined above are displayed In addition for the minAverage measure slacks are displayed for those inputs and outputs with factors 1 or 0 for non oriented measure For Nonconvex FDH models instead of the weights for each DMU the number of dominated and dominating DMUs and lists of these DMUs are displayed Copy Save The result table can be copied to your spreadsheet via the Windows clipboard Use Menu Edit Copy Ctrl C for copying your current selection or Copy All Ctr1 A for the whole results table The result table can be saved as an ASCII file Menu File Save or Save As 7 Acknowledgements Thanks to BPMPD s author Csaba M sz ros for the kind support during the develop ment of EMS Thanks to Laurens Cherchye for valuable discussions 8 Disclaimer The author of the program described here accepts no responsibility for
9. does not display your data If you want to edit your data you should open the datafile in Excel or in your texteditor and edit it there You should save the changes it s not necessary to close the file and then Load data Ctr1 0 in EMS again EMS always loads the file version from the harddisk Menu File Load Weight Restr Ctr1 w The file which contains the matrix W can be loaded by pressing Ctr1 wW Menu File gt Load Weight Restr When the file is successfully loaded its name is displayed in the statusbar like the input output data file 5 Running a DEA model bpmpd par Before running a DEA model make sure that the file bpmpd par is in the same folder as your data file 5 1 Preparing the results format Menu DEA Format Ctrl F Ctrl F Menu DEA gt Format will display the Format dialog Here you may specify the number of decimals to display in the results table wich will be produced by EMS 5 Running a DEA model Moreover you can decide whether e the pure input and ouput weights shadow prices p and q should be displayed Option pure weights or e the virtual inputs and outputs i e the weights multiplied by the input and output values p Ta qj Yjo Option virtual inputs outputs should be displayed in the results table 5 2 Choosing a technology structure Ctrl M Menu DEA gt Run model will display a dialog where you can specify the model you want t
10. e but the DMU under evaluation is excluded from the constraints i e the definition of the technology set See P AN DERSEN and N C PETERSEN 1993 A Procedure for Ranking Efficient Units in Data Envelopment Analysis Management Science 39 1261 1264 big If you have chosen the superefficiency model then in the results table a score big may appear This means that the DMU remains efficient under arbitrary large increased inputs input oriented or decreased outputs output oriented respectively Restrict weights If you have loaded weights restrictions data you can check this box to incorporate the weights restrictions in the model If the box is not checked then the weights restrictions will be ignored 5 4 Advanced modeling options When you have opened the Run model dialog Ctr1 M or Menu DEA Run model then you may specify some advanced models in Options which are described in the following paragraphs Evaluation Technology You may specify selections of DMUs which should be computed Evaluation and which should be used for building the envelopment Technology This allows you to compute program efficiency I e for each DMU selected in Evaluation a score is computed 10 6 Results constrained by the DMUs selected in Technology The lists allow selections of multiple entries via Ctrl click and Shift click Window Analysis Malmquist If you have panel dat
11. ile you ll have to do the same like for the input output data First put the file schema ini in the directory of your textfiles and modify it i e replace Yourweightfile txtl by the name of your file The textfile which contains W should then satisfy the following e Columns are separated by Tabs e The first row the input output names should be identical to the corresponding input output data file e The first column contains a name for each restriction Cf the example file WEIGHTS TXT Literature See for an overview R ALLEN A ATHANASSOPOULOS R DYSON and E THANASSOULIS 1997 Weights restrictions and value judgements in Data Envelopment Analysis Evolution development and future directions Annals of Operations Research 73 13 34 4 Starting EMS and loading data 4 Starting EMS and loading data When you ve prepared the data in Excel and or textfiles as described above you can start EMS by clicking on it in the program folder Menu File Load data Ctr1 0 Now you should connect EMS to the data Your input output data can be loaded by pressing Ctr1 0 Menu File Load data If you select an appropriate filename then EMS tries to connect to this file For large scale DEA evaluations with thousands of DMUs this connection may need a few seconds The connection was successful e if the filename appears in the statusbar at the bottom of the EMS window and e the sand clock vanishes EMS
12. kly efficient subset of 7 by OT Notice that for a weakly effi cient point an arbitrary small improvement suffices to become Koopmans efficient whence the minAverage measure also quantifies the infimum average of improve ments which is necessary to become Koopmans efficient It has neither a straightforward price interpretation nor is it an indicator for Koop mans efficiency but it is units invariant FT 0 2 YE gt 0 j min Die i input max pt 00X Y e aT 0 2 xk gt o 0 20 1 0 non or Lixtsol Li vesol KI LAO YE E07 HA X Do kG O output min Soon ILY YK caT 621 2 jyk gt o 5 Running a DEA model This measure is based on ideas in A CHARNES J J ROUSSEAU and J H SEM PLE 1996 Sensitivity and Stability of Efficiency Classifications in Data Envelop ment Analysis The Journal of Productivity Analysis 7 5 18 See also W BRIEC 1999 H lder distance function and measurement of technical efficiency Journal of Productivity Analysis 11 111 132 Superefficiency If you choose a radial distance then EMS allows you to compute so called superef ficiency scores by checking the box For inefficient DMUs the superefficiency score coincides with the standard score defined above For efficient DMUs a score is computed which indicates the maximal radial change which is feasible such that the DMU remains efficient Formally it is defined like the standard scor
13. l only essential differences are mentioned roughly when the measures are defined below T denotes the technology and X Y denotes the input output data of the DMU under evaluation Distance Radial This measure a k a Debreu Farrell measure or radial part of the CCR BCC measure indicates the necessary improvements when all relevant factors are im proved by the same factor equiproportionally Its oriented versions have nice price interpretations cost reduction revenue increase but it doesn t indicate Koop mans efficiency non oriented max 9 1 0 X 1 0 Y T input minf0 0X Y T output max X Y T See M J FARRELL 1957 The measurement of productive efficiency Journal of the Royal Statistical Society Series A 120 3 253 290 Additive This measure quantifies the maximal sum of absolute improvements input reduction output increase measured in slacks It has a price interpretation as difference between actual and maximal profit and indicates Koopmans efficiency but it isn t invariant with respect to units of measurement f k k non oriented max Y sa jti A 3 0 7 5 1 2 o input max 9 s X s Y ET s20 output max Y ty XE YK t eT t20 See A CHARNES W W COOPER B GOLANY L SEIFORD and J STUTZ 1985 Foundations of Data Envelopment Analysis for Pareto Koopmans efficient empirical production functions
14. o compute Under Models you may choose between various technology struc tures Menu DEA Run model Ctr1 M Structure Returns to Scale e convex and nonconvex envelopment e constant variable nonincreasing or nondecreasing returns to scale 5 3 Choosing an efficiency measure An efficiency measure quantifies in one way or another a distance to the efficient fron tier of the technology EMS allows computation of various distances in input output and non oriented versions Drientation An input oriented measure quantifies the input reduction which is necessary to become efficient holding the outputs constant Symmetrically an output oriented measure quan tifies the necessary output expansion holding the inputs constant A non oriented mea sure quantifies necessary improvements when both inputs and outputs can be improved simultaneously It seems that in applications the choose of a certain measure mostly depends on three criteria e The primal interpretation i e the meaning of the efficiency score with respect to input and output quantities 5 Running a DEA model Most the dual interpretation i e the meaning of the efficiency score with respect to input and output prices the axiomatic properties of the efficiency measure e g monotonicity units invari ance indication of efficiency continuity of the measures are similar with respect to these criteria whence in this manua
15. or of output weights or shadow prices Hence you can incorporate both Cone Ratio constraints and Assurance Region constraints Example Suppose you have 3 inputs and 2 outputs and you want to have the re striction p gt p2 then corresponding row in the weights restriction matrix W is 1 1 0 0 0 If you have in addition bounds on the marginal rates of substitutions like 0 3 lt A lt 3 then you transform them into two constraints q 0 3q2 gt 0 and q 3q2 gt 0 yielding the rows 0 0 0 1 0 3 and 0 0 0 1 3 in the matrix W Thus in this example one has Lol 0 0 0 W 0 00 1 0 3 0 0 0 1 3 3 Preparing weights restrictions Like the input output data EMS accepts weights restriction data W in MS Excel and textfiles 3 1 Using MS Excel files EMS accepts Excel 97 and older files x1s The weights restriction data should be collected in one worksheet Don t use formulas in this sheet it should only contain the pure data and nothing else EMS needs the following data format Weights e The name of the worksheet must be Weights It can be contained in the same file as the Data sheet but you may also choose another file e The first row the input output names should be identical to the corresponding Data sheet e The first column contains a name for each restriction Cf the example file EXAMPLE XLS 3 2 Using textfiles If you have W in a textf
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