4y Spri ringer DATA ENVELOPMENT ANALYSIS. A Comprehensive Text with Models, Applications, References and DEA-Solver Software Second Edition

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1 DATA ENVELOPMENT ANALYSIS A Comprehensive Text with Models, Applications, References and DEA-Solver Software Second Edition WILLIAM W. COOPER University of Texas at Austin, U.S.A. LAWRENCE M. SEIFORD University of Michigan, U.S.A. KAORU TONE National Graduate Institute for Policy Studies, Japan 4y Spri ringer

2 Contents List of Tables List of Figures Preface xvii xxi xxv 1. GENERAL DISCUSSION Introduction Single Input and Single Output Two Inputs and One Output Case One Input and Two Outputs Case Fixed and Variable Weights Summary and Conclusion Problem Supplement for Chapter BASIC CCR MODEL Introduction Data The CCR Model From a Fractional to a Linear Program Meaning of Optimal Weights Explanatory Examples Example 2.1 (1 Input and 1 Output Case) Example 2.2 (2 Inputs and 1 Output Case) Illustration of Example Summary of Chapter Selected Bibliography Problem Supplement for Chapter CCR MODEL AND PRODUCTION CORRESPONDENCE Introduction Production Possibility Set The CCR Model and Dual Problem The Reference Set and Improvement in Efficiency 47

3 Vlll DATA ENVELOPMENT ANALYSIS 3.5 Theorems on CCR-Efficiency Computational Aspects of the CCR Model Computational Procedure for the CCR Model Data Envelopment Analysis and the Data Determination of Weights (=Multipliers) Reasons for Solving the CCR Model Using the Dual (DLP 0 ) Example The Output-Oriented Model An Extension of the Two Phase Process in the CCR Model Discretionary and Non-Discretionary Inputs Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter 3 71 ALTERNATIVE DEA MODELS Introduction The BCC Models The BCC Model The Output-oriented BCC Model The Additive Model The Basic Additive Model Translation Invariance of the Additive Model A Slacks-Based Measure of Efficiency (SBM) Definition of SBM Interpretation of SBM as a Product of Input and Output Inefficiencies Solving SBM SBM and the CCR Measure The Dual Program of the SBM Model Oriented SBM Models A Weighted SBM Model Decomposition of Inefficiency Numerical Example (SBM) A Hybrid Measure of Efficiency (Hybrid) A Hybrid Measure Decomposition of Inefficiency Comparisons with the CCR and SBM Models An Illustrative Example Russell Measure Models Summary of the Basic DEA Models Summary of Chapter Notes and Selected Bibliography Appendix: Free Disposal Hüll (FDH) Models Related DEA-Solver Models for Chapter Problem Supplement for Chapter 4 120

4 Contents IX RETURNS TO SCALE Introduction Geometrie Portrayais in DEA BCC Returns to Scale CCR Returns to Scale Most Productive Scale Size Further Considerations Relaxation of the Convexity Condition Decomposition of Technical Efficiency Scale Efficiency Mix Efficiency An Example of Decomposition of Technical Efficiency An Example of Returns to Scale Using a Bank Merger Simulation Background Efficiencies and Returns to Scale The Effects of a Merger Summary Additive Models Multiplicative Models and "Exact" Elasticity Summary of Chapter Appendix: FGL Treatment and Extensions Related DEA-Solver Models for Chapter Problem Supplement for Chapter MODELS WITH RESTRICTED MULTIPLIERS Introduction Assurance Region Method Formula for the Assurance Region Method General Hospital Example Change of Efficient Frontier by Assurance Region Method On Determining the Lower and Upper Bounds Another Assurance Region Model Cone-Ratio Method Polyhedral Convex Cone as an Admissible Region of Weights Formula for Cone-Ratio Method A Cone-Ratio Example How to Choose Admissible Directions An Application of the Cone-Ratio Model Negative Slack Values and Their Uses A Site Evaluation Study for Relocating Japanese Government Agencies out of Tokyo Background The Main Criteria and their Hierarchy Structure Scores of the 10 Sites with respect to the 18 Criteria Weights of the 18 Criteria by the 18 Council Members (Evaluators) Decision Analyses using Averages and Medians 201

5 x DATA ENVELOPMENT ANALYSIS Decision Analyses using the Assurance Region Model Evaluation of "Positive" of Each Site Evaluation of "Negative" of Each Site Uses of "Positive" and "Negative" Scores Decision by the Council Concluding Remarks Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter NON-DISCRETIONARY AND CATEGORICAL VARIABLES Introduction Examples Non-controllable, Non-discretionary and Bounded Variable Models Non-controllable Variable (NCN) Model An Example of a Non-Controllable Variable Non-discretionary Variable (NDSC) Model Bounded Variable (BND) Model An Example of the Bounded Variable Model DEA with Categorical DMUs An Example of a Hierarchical Category Solution to the Categorical Model Extension of the Categorical Model Comparisons of Efficiency between Different Systems Formulation Computation of Efficiency Illustration of a One Input and Two Output Scenario Rank-Sum Statistics and DEA Rank-Sum-Test (Wilcoxon-Mann-Whitney) Use of the Test for Comparing the DEA Scores of Two Groups Use of the Test for Comparing the Efficient Frontiers of Two Groups Bilateral Comparisons Using DEA An Example of Bilateral Comparisons in DEA Evaluating Efficiencies of Different Organization Forms Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter ALLOCATION MODELS Introduction Overall Efficiency with Common Prices and Costs Cost Efficiency Revenue Efficiency Profit Efficiency An Example 261

6 Contents xi 8.3 New Cost Efficiency under Different Unit Prices A New Scheme for Evaluating Cost Efficiency Differences Between the Two Models An Empirical Example Extensions Decomposition of Cost Efficiency Loss due to Technical Inefficiency Loss due to Input Price Inefficiency Loss due to Allocative Inefficiency Decomposition of the Actual Cost An Example of Decomposition of Actual Cost Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter DATA VARIATIONS Introduction Sensitivity Analysis Degrees of Freedom Algorithmic Approaches Metrie Approaches Multiplier Model Approaches Statistical Approaches Chance-Constrained Programming and Satisficing in DEA Introduction Satisficing in DEA Deterministic Equivalents Stochastic Efficiency Summary of Chapter SUPER-EFFICIENCY MODELS Introduction Radial Super-efficiency Models Non-radial Super-efficiency Models Definition of Non-radial Super-efficiency Measure Solving Super-efficiency Input/Output-Oriented Super-efficiency An Example of Non-radial Super-efficiency Extensions to Variable Returns-to-Scale Radial Super-efficiency Case Non-radial Super-efficiency Case Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter

7 XÜ DATA ENVELOPMENT ANALYSIS 11. EFFICIENCY CHANGE OVER TIME Introduction Window Analysis An Example Application Analysis Malmquist Index Dealing with Panel Data Catch-up Effect Frontier-shift Effect Malmquist Index The Radial MI The Non-radial and Slacks-based MI The Non-radial and Non-oriented MI Scale Efficiency Change Illustrative Examples for Model Comparisons Concluding Remarks Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter SCALE ELASTICITY AND CONGESTION Introduction Scale Elasticity in Production Congestion Strong Congestion Weak Congestion Summary of Degree of Scale Economies and Congestion Illustrative Examples Degree of Scale Economies and Strong Congestion Weak vs. Strong Congestion Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter UNDESIRABLE OUTPUTS MODELS Introduction An SBM with Undesirable Outputs An Undesirable Output Model Dual Interpretations Returns-to-scale (RTS) Issues Imposing Weights to Inputs and/or Outputs Non-separable 'Good' and 'Bad' Output Model Illustrative Examples Separable Bad Outputs Models An Example with Both Separable and Non-separable Inputs/Outputs 375

8 Contents XÜi 13.5 Comparisons with Other Methods Summary of Chapter Related DEA-Solver Models for Chapter ECONOMIES OF SCOPE AND CAPACITY UTILIZATION Introduction Economies of Scope Definition Checking for Economies of Scope Checking a Virtual Merger Comparisons of Business Models Illustrative Examples Capacity Utilization Fixed vs. Variable Input Resources Technical Capacity Utilization Price-Based Capacity Utilization Measure Long-Run and Short-Run Capacity Utilization Illustrative Examples Summary of Chapter Notes and Selected Bibliography Related DEA-Solver Models for Chapter Problem Supplement for Chapter A DEA GAME Introduction Formulation Coalition and Characteristic Function Solution Coalition and Individual Contribution The Shapley Value DEA min Game Summary of Chapter Notes and Selected Bibliography Problem Supplement for Chapter MULTI-STAGE USE OF PARAMETRIC AND NON-PARAMETRIC MODELS Introduction OLS Regressions Modification and Extensions Stochastic Frontier Analysis and Composed Error Models DEA and Regression Combinations Multi-stage DEA-Regression Combinations and its Application to Japanese Banking Introduction The Multistage Framework An Application to Japanese Banking 433

9 xiv DATA ENVELOPMENT ANALYSIS Discussion Summary of This Case Study Summary of Chapter Notes and Selected Bibliography 439 Appendices 443 A-Linear Programming and Duality 443 AI Linear Programming and Optimal Solutions 443 A.2 Basis and Basic Solutions 443 A.3 Optimal Basic Solutions 444 A4 Dual Problem 445 A.5 Symmetrie Dual Problems 446 A.6 Complementarity Theorem 447 A.7 Farkas' Lemma and Theorem of the Alternative 448 A.8 Strong Theorem of Complementarity 449 A.9 Linear Programming and Duality in General Form 451 B-Introduction to DEA-Solver 454 B.l Platform 454 B.2 Installation of DEA-Solver 454 B.3 Notation of DEA Models 454 B.4 Included DEA Models 456 B.5 Preparation of the Data File 456 B.5.1 The CCR, BCC, IRS, DRS, GRS, SBM, Super-Efficiency, Scale Elasticity, Congestion and FDH Models 456 B.5.2 The AR Model 457 B.5.3 The ARG Model 458 B.5.4 The NCN and NDSC Models 459 B.5.5 The BND Model 460 B.5.6 The CAT, SYS and Bilateral Models 460 B.5.7 The Cost and New-Cost Models 461 B.5.8 The Revenue and New-Revenue Models 462 B.5.9 The Profit, New-Profit and Ratio Models 462 B.5.10 The Window and Malmquist Models 462 B.5.11 The Hybrid Model 463 B.5.12 Weighted SBM Model 464 B.5.13 The Bad Outputs Model 465 B.5.14 The Non-separable Outputs Model 465 B.6 Starting DEA-Solver 466 B.7 Results 466 B.8 Data Limitations 473 B.8.1 Problem Size 473 B.8.2 Inappropriate Data for Each Model 474 B.9 Sample Problems and Results 475 BIO Summary 475 B.10.1 Models that Require Numbers to be Supplied through Keyboard 475

10 Contents XV B.10.2 Summary of Headings to Inputs/Outputs 475 C-Bibliography 477 Index 479 Index 483