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Contents
List of Tables List of Figures Preface
1.
GENERAL DISCUSSION 1.1Introduction 1.2Single Input and Single Output 1.3Two Inputs and One Output Case 1.4One Input and Two Outputs Case 1.5Fixed and Variable Weights 1.6Summary and Conclusion 1.7Problem Supplement for Chapter 1
2.THE BASIC CCR MODEL 2.1Introduction 2.2Data 2.3The CCR Model 2.4From a Fractional to a Linear Program 2.5Meaning of Optimal Weights 2.6Explanatory Examples 2.6.1 Example 2.1 (1 Input and 1 Output Case) 2.6.2Example 2.2 (2 Inputs and 1 Output Case) 2.7Illustration of Example 2.2 2.8Summary 2.9Selected Bibliography 2.10Problem Supplement for Chapter 2
3.
THE CCR MODEL AND PRODUCTION CORRESPONDENCE 3.1Introduction 3.2Production Possibility Set 3.3The CCR Model and Dual Problem 3.4The Reference Set and Improvement in Efficiency
xiii xvii xix
1 1 2 6 8 12 13 15
21 21 22 23 23 25 25 26 27 30 32 33 34
41 41 42 43 47
viii
DATA ENVELOPMENT ANALYSIS
3.5Theorems on CCREfficiency 3.6the CCR ModelComputational Aspects of 3.6.1 Computational Procedure for the CCR Model 3.6.2Data Envelopment Analysis and the Data 3.6.3Determination of Weights (=Multipliers) 3.6.4Reasons for solving the CCR model using the dual 3.7Example 3.8ModelThe OutputOriented 3.9the Two Phase Process in the CCR ModelAn Extension of 3.10Discretionary and NonDiscretionary Inputs 3.11Summary of Chapter 3 3.12Notes and Selected Bibliography 3.13Related DEASolver Models for Chapter 3 3.14Problem Supplement for Chapter 3
48 50 50 52 52 52 53 58 60 63 67 68 70 71
4.ALTERNATIVE DEA MODELS85 4.1Introduction85 4.2The BCC Models87 4.2.1 The BCC Model88 4.2.2The Outputoriented BCC Model90 4.3The Additive Model91 4.3.1 The Basic Additive Model91 4.3.2Modelof the Additive Translation Invariance 94 4.4A SlacksBased Measure of Efficiency (SBM)96 4.4.1Definition of SBM97 4.4.2Interpretation of SBM as a Product of Input and Output Inefficiencies98 4.4.3Solving SBM98 4.4.4SBM and the CCR Measure100 4.4.5Numerical Example101 4.5Summary of the Basic DEA Models101 4.6Summary of Chapter 4104 4.7Notes and Selected Bibliography104 4.8Appendix: Free Disposal Hull (FDH) Models105 4.9for Chapter 4Related DEASolver Models 106 4.10Problem Supplement for Chapter 4107
5.RETURNS TO SCALE 5.1Introduction 5.2Geometric Portrayals in DEA 5.3BCC Returns to Scale 5.4CCR Returns to Scale 5.5Most Productive Scale Size 5.6Further Considerations 5.7Relaxation of the Convexity Condition 5.8EfficiencyDecomposition of Technical
115 115 118 120 122 127 131 134 136
5.8.1 Scale Efficiency 5.8.2 Mix Efficiency 5.8.3 An Example of Decomposition of Technical Efficiency 5.9Returns to Scale Using a Bank Merger SimulationAn Example of 5.9.1 Background 5.9.2 Efficiencies and Returns to Scale 5.9.3 The Effects of a Merger 5.10Summary of Chapter 5 5.11Related DEASolver Models for Chapter 5 5.12Problem Supplement for Chapter 5
Contents
6.MODELS WITH RESTRICTED MULTIPLIERS 6.1Introduction 6.2Assurance Region Method 6.2.1 Formula for the Assurance Region Method 6.2.2General Hospital Example 6.2.3 Change of Efficient Frontier by Assurance Region Method 6.2.4 On Determining the Lower and Upper Bounds 6.3ConeRatio Method 6.3.1 Polyhedral Convex Cone as an Admissible Region of Weights 6.3.2Formula for ConeRatio Method 6.3.3 A ConeRatio Example 6.3.4 How to Choose Admissible Directions 6.4the ConeRatio ModelAn Application of 6.5Negative Slack Values and Their Uses 6.6A DecisionMaking Method Using Assurance Region Models 6.6.1 Background 6.6.2 Evaluation of Candidate Sites 6.6.3 Group Decision 6.6.4 Use of the Assurance Region Model 6.6.5Merits of the Method 6.6.6Remarks 6.7Summary of Chapter 6 6.8Notes and Selected Bibliography 6.9Related DEASolver Models for Chapter 6 6.10Problem Supplement for Chapter 6
7.
DISCRETIONARY, NONDISCRETIONARY AND CATEGORICAL VARIABLES 7.1Introduction 7.2Examples 7.3An Application 7.3.1 An Example of a NonControllable Variable 7.3.2 Extensions of the NonDiscretionary Model 7.3.3 An Example of the Bounded Variable Model 7.4DEA with Categorical DMUs 7.4.1 An Example of a Hierarchical Category 7.4.2 Solution to the Categorical Model
ix
136 138 139 139 140 140 143 145 146 146
151 151 152 152 155 157 158 159 159 160 161 162 162 167 169 169 170 170 171 172 173 174 174 175 176
183 183 185 187 188 189 190 193 193 194
x
DATA ENVELOPMENT ANALYSIS
7.5
7.6
7.7 7.8 7.9 7.10
7.4.3Extension of the Categorical Model194 Comparisons of Efficiency between Different Systems197 7.5.1 Formulation197 7.5.2Computation of Efficiency198 7.5.3Illustration of a One Input and Two Output Scenario198 RankSum Statistics and DEA200 7.6.1 RankSumTest (WilcoxonMannWhitney)200 7.6.2Use of the Test for Comparing the DEA Scores of Two Groups201 7.6.3 Use of the Test for Comparing the Efficient Frontiers of Two Groups201 7.6.4Bilateral Comparisons using DEA201 7.6.5An Example of Bilateral Comparisons in DEA203 7.6.6Evaluating Efficiencies of Different Organization Forms204 Summary of Chapter 7205 Notes and Selected Bibliography205 Related DEASolver Models for Chapter 7206 Problem Supplement for Chapter 7207
8.ALLOCATION MODELS 8.1Introduction 8.2Profit Objectives 8.3Radial Efficiency Components 8.4Additive Model Alternatives 8.5Examples 8.6Profit Ratios 8.6.1 Actual to Maximum Profit Ratio 8.6.2Maximization of Revenue vs. Cost Ratio 8.7Summary of Chapter 8 8.8Related DEASolver Models for Chapter 8 8.9Problem Supplement for Chapter 8
9.DATA VARIATIONS 9.1Introduction 9.2Sensitivity Analysis 9.2.1 Degrees of Freedom 9.2.2Algorithmic Approaches 9.2.3Metric Approaches 9.2.4 Multiplier Model Approaches 9.3Statistical Approaches 9.4ChanceConstrained Programming and Satisficing in DEA 9.4.1Introduction 9.4.2Satisficing in DEA 9.4.3 Deterministic Equivalents 9.4.4 Stochastic Efficiency 9.5Window Analysis 9.5.1Introduction 9.5.2 An Example
221 221 221 223 225 229 233 233 234 235 236 238
251 251 252 252 252 252 255 259 266 266 266 267 269 272 272 272
9.6 9.7
9.5.3Application 9.5.4Analysis Summary of Chapter 9 Related DEASolver Models for Chapter 9
Appendices A–Linear Programming and Duality A.1Linear Programming and Optimal Solutions A.2Basis and Basic Solutions A.3Optimal Basic Solutions A.4Dual Problem A.5Symmetric Dual Problem A.6Complementarity Theorem A.7Farkas' Lemma and Theorem of the Alternative A.8Strong Theorem of Complementarity A.9Linear Programming and Duality in General Form B–Introduction to DEASolver B.1Platform B.2Installation of DEASolver B.3Notation of DEA Models B.4Included DEA Models B.5Preparation of the Data File B.5.1 The CCR, BCC, IRS, DRS, GRS, SBM and FDH Models B.5.2The AR Model B.5.3The NCN Model B.5.4The BND Model B.5.5The CAT, SYS and Bilateral Models B.5.6The Cost Model B.5.7The Revenue Model B.5.8The Profit and Ratio Models B.5.9The Window Model B.6Starting DEASolver B.7Results B.8Data Limitations B.8.1 Problem Size B.8.2 Inappropriate Data for Each Model B.9Sample Problems and Results C–Bibliography
Index
Contents
xi
273 275 276 277
281 281 281 281 282 283 284 285 286 287 289 292 292 292 292 293 294 294 295 296 297 297 298 299 299 299 300 301 304 304 304 306 307
309
xii
Index
DATA ENVELOPMENT ANALYSIS
311
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