ems

EMS: Efficiency Measurement System User’s Manual Holger Scheel Version 1.3 2000-08-15 Contents 1 Introduction 2 2 Preparing the input output data 2 2.1 Using MS Excel files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Using textfiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Non-discretionary inputs and outputs . . . . . . . . . . . . . . . . . . . . 4 3 Preparing weights restrictions 4 3.1 Using MS Excel files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Using textfiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 Starting EMS and loading data 6 5 Running a DEA model 6 5.1 Preparing the results format . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.2 Choosing a technology structure . . . . . . . . . . . . . . . . . . . . . . . 7 5.3 Choosing an efficiency measure . . . . . . . . . . . . . . . . . . . . . . . . 7 5.4 Advanced modeling options . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6 Results 11 7 Acknowledgements 12 8 Disclaimer 12 1 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: • H. O. Fried, C. A. K. Lovell, and S. Schmidt (1993), The measurement of productive efficiency: Techniques and applications, Oxford University Press, New York • R. Fa¨re, S. Grosskopf, and C. A. K. Lovell (1994), Production Frontiers, Cambridge University Press, Cambridge • A. Charnes, W. W. Cooper, A. Y. Lewin, and L. M. Seiford (1994), Data Envelopment Analysis: Theory, Methodology, and Application, Kluwer Academic Publishers, Dordrecht • 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 Me´sza´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.Scheel@wiso.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 scale 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 2 Preparing the input output data 2.1 Using MS Excel files EMS accepts Excel 97 (and older) files (*.xls). 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} {O} • The name of the worksheet must be “Data”. • The first line contains the input/output names. First inputs, then outputs. • Input names contain the string “{I}”. • Output names contain the string “{O}”. • 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 • Put schema.ini in the same directory where your textfiles are. • 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: • 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 in the file (e. g. at the end). You can check this in a texteditor by making the Tabs “visible”. • Input names contain the string “{I}”. 3 3 Preparing weights restrictions • Output names contain the string “{O}”. • 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) ≥ 0, where p is the vector of input weights and q is the vector 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 p1 ≥ 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 ≤ q1q2 ≤ 3, then you transform them into two constraints q1−0.3q2 ≥ 0 and−q1 + 3q2 ≥ 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 W =  1 −1 0 0 00 0 0 1 −0.3 0 0 0 −1 3  4 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 (*.xls). 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 • 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.) • The first row (the input/output names) should be identical to the corresponding Data sheet. • 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 textfile, 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.txt]” by the name of your file. The textfile which contains W should then satisfy the following: • Columns are separated by Tabs. • The first row (the input/output names) should be identical to the corresponding input output data file. • 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. 5 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 (Ctrl+O) Now you should connect EMS to the data: Your input output data can be loaded by pressing Ctrl+O (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 • if the filename appears in the statusbar (at the bottom of the EMS window) and • the sand clock vanishes. EMS 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 (Ctrl+O) in EMS again. EMS always loads the file version from the harddisk. Menu File Load Weight Restr (Ctrl+W) The file which contains the matrix W can be loaded by pressing Ctrl+W (Menu File → 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 → 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. 6 5 Running a DEA model Moreover, you can decide whether • the pure input and ouput weights (shadow prices) pi and qj should be displayed (Option pure weights) or • the “virtual inputs and outputs”, i.e. the weights multiplied by the input and output values pi · xi0, qj · yj0 (Option virtual inputs/outputs) should be displayed in the results table. 5.2 Choosing a technology structure Ctrl+M (Menu DEA → Run model) will display a dialog where you can specify the model you want to compute. Under Models you may choose between various technology struc- tures: Menu DEA Run model (Ctrl+M) Structure Returns to Scale • convex and nonconvex envelopment, • 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. Orientation 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: • The “primal” interpretation, i. e. the meaning of the efficiency score with respect to input and output quantities, 7 5 Running a DEA model • 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). Most of the measures are similar with respect to these criteria, whence in this manual only essential differences are mentioned roughly1 when the measures are defined below. T denotes the technology and (Xk, Y k) 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{θ | ((1− θ)Xk, (1 + θ)Y k) ∈ T } input: min{θ | (θXk, Y k) ∈ T } output: max{φ | (Xk, φY k) ∈ 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. non-oriented: max {∑ i si + ∑ j tj | (Xk − s, Y k + t) ∈ T , (s, t) = 0 } input: max {∑ i si | (Xk − s, Y k) ∈ T , s = 0 } output: max {∑ j tj | (Xk, Y k + t) ∈ T , t = 0 } 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, Journal of Econometrics, 30, 91–107. 1A more detailed overview is given (in German) in H. Scheel (2000), Effizienzmaße der Data Envel- opment Analysis, Gabler, Wiesbaden. 8 5 Running a DEA model If you want to compute a weighted objective function ∑ iwi · si 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. Fa¨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−θ)�Xk, (1+φ)�Y k) := ((1+θ1)Xk1 , . . . , (1+θm)Xkm; (1+φ1)Y k1 , . . . , (1+φn)Y kn ) . non-or.: max {∑ i:Xki >0 θi + ∑ j:Y kj >0 φj∑ i:Xki >0 1 + ∑ j:Y kj >0 1 ∣∣∣∣ (θ, φ) ≥ 0,((1− θ)�Xk, (1 + φ)� Y k) ∈ T } input: min {∑ i:Xk i >0 θi∑ i:Xk i >0 1 | (θ �Xk, Y k) ∈ T , θ 5 ~1 } output: max {∑ j:Y k j >0 φj∑ j:Y k j >0 1 | (Xk, φ� Y k) ∈ T , φ = ~1 } See R. Fa¨re 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 weakly efficient subset of T by ∂T .) 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. non-or.: min {∑ i:Xki >0 θi + ∑ j:Y kj >0 φj∑ i:Xki >0 1 + ∑ j:Y kj >0 1 ∣∣∣∣ (θ, φ) ≥ 0,((1− θ)�Xk, (1 + φ)� Y k) ∈ ∂T } input: max {∑ i:Xk i >0 θi∑ i:Xk i >0 1 | (θ �Xk, Y k) ∈ ∂T , θ 5 ~1 } output: min {∑ j:Y k j >0 φj∑ j:Y k j >0 1 | (Xk, φ� Y k) ∈ ∂T , φ = ~1 } 9 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), Ho¨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 score 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 (Ctrl+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 data sorted by periods T = 0, ..., t i.e. the first column of the data file looks like DMU 1 T0 DMU 2 T0 .. . DMU n T0 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.xls 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 Evaluation. 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: • for inefficient DMU: the reference DMUs with corresponding intensities (the “lambdas”) in brackets • 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 θi, φj 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