Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References

✍ Scribed by William W. Cooper, Lawrence M. Seiford, Kaoru Tone

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 379
• Edition: 1
• Category: Library

✦ Synopsis

Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References has been carefully designed by the authors to provide a systematic introduction to DEA and its uses as a multifaceted tool for evaluating problems in a variety of contexts. The authors have been involved in DEA's development from the beginning. William Cooper (with Abraham Charnes and Edwardo Rhodes) is a founder of DEA. Lawrence Seiford and Kaoru Tone have been actively involved as researchers and practitioners from its earliest beginnings. All have been deeply involved in uses of DEA in practical applications as well as in the development of its basic theory and methodologies. The result is a textbook grounded in authority, experience and substance.

✦ Table of Contents

Contents......Page 6
List of Tables......Page 12
List of Figures......Page 15
Preface......Page 17
1.1 Introduction......Page 33
1.2 Single Input and Single Output......Page 34
1.3 Two Inputs and One Output Case......Page 38
1.4 One Input and Two Outputs Case......Page 40
1.5 Fixed and Variable Weights......Page 44
1.6 Summary and Conclusion......Page 45
1.7 Problem Supplement for Chapter 1......Page 47
2.1 Introduction......Page 53
2.2 Data......Page 54
2.4 From a Fractional to a Linear Program......Page 55
2.6 Explanatory Examples......Page 57
2.6.1 Example 2.1 (1 Input and 1 Output Case)......Page 58
2.6.2 Example 2.2 (2 Inputs and 1 Output Case)......Page 59
2.7 Illustration of Example 2.2......Page 62
2.8 Summary of Chapter 2......Page 64
2.9 Selected Bibliography......Page 65
2.10 Problem Supplement for Chapter 2......Page 66
3.1 Introduction......Page 72
3.2 Production Possibility Set......Page 73
3.3 The CCR Model and Dual Problem......Page 74
3.4 The Reference Set and Improvement in Efficiency......Page 78
3.5 Theorems on CCR-Efficiency......Page 79
3.6.1 Computational Procedure for the CCR Model......Page 81
3.6.4 Reasons for Solving the CCR Model Using the Envelopment Form......Page 83
3.7 Example......Page 84
3.8 The Output-Oriented Model......Page 89
3.9 Discretionary and Non-Discretionary Inputs......Page 91
3.10 Summary of Chapter 3......Page 95
3.11 Notes and Selected Bibliography......Page 96
3.12 Related DEA-Solver Models for Chapter 3......Page 98
3.13 Problem Supplement for Chapter 3......Page 99
4.1 Introduction......Page 114
4.2 The BCC Models......Page 116
4.2.1 The BCC Model......Page 118
4.2.2 The Output-oriented BCC Model......Page 120
4.3.1 The Basic Additive Model......Page 121
4.3.2 Translation Invariance of the Additive Model......Page 124
4.4 A Slacks-Based Measure of Efficiency (SBM)......Page 126
4.4.1 Definition of SBM......Page 127
4.4.3 Solving SBM......Page 128
4.4.4 SBM and the CCR Measure......Page 130
4.4.5 The Dual Program of the SBM Model......Page 131
4.4.7 A Weighted SBM Model......Page 132
4.5 Russell Measure Models......Page 133
4.6 Summary of the Basic DEA Models......Page 135
4.7 Summary of Chapter 4......Page 137
4.9 Appendix: Free Disposal Hull (FDH) Models......Page 138
4.10 Related DEA-Solver Models for Chapter 4......Page 140
4.11 Problem Supplement for Chapter 4......Page 141
5.1 Introduction......Page 149
5.2 Geometric Portrayals in DEA......Page 152
5.3 BCC Returns to Scale......Page 154
5.4 CCR Returns to Scale......Page 156
5.5 Most Productive Scale Size......Page 161
5.6 Further Considerations......Page 165
5.7 Relaxation of the Convexity Condition......Page 168
5.8.1 Scale Efficiency......Page 170
5.8.2 Mix Efficiency......Page 172
5.8.3 An Example of Decomposition of Technical Efficiency......Page 173
5.9.2 Efficiencies and Returns to Scale......Page 174
5.9.3 The Effects of a Merger......Page 177
5.11 Additive Models......Page 180
5.12 Multiplicative Models and "Exact" Elasticity......Page 183
5.13 Summary of Chapter 5......Page 188
5.14 Appendix: FGL Treatment and Extensions......Page 189
5.16 Problem Supplement for Chapter 5......Page 191
6.1 Introduction......Page 195
6.2.1 Formula for the Assurance Region Method......Page 196
6.2.2 General Hospital Example......Page 199
6.2.3 Change of Efficient Frontier by Assurance Region Method......Page 201
6.2.4 On Determining the Lower and Upper Bounds......Page 202
6.3 Another Assurance Region Model......Page 203
6.4.1 Polyhedral Convex Cone as an Admissible Region of Weights......Page 204
6.4.2 Formula for Cone-Ratio Method......Page 205
6.4.3 A Cone-Ratio Example......Page 206
6.5 An Application of the Cone-Ratio Model......Page 207
6.6 Negative Slack Values and Their Uses......Page 212
6.7.1 Background......Page 214
6.7.2 The Main Criteria and their Hierarchy Structure......Page 215
6.7.3 Scores of the 10 Sites with respect to the 18 Criteria......Page 216
6.7.4 Weights of the 18 Criteria by the 18 Council Members (Evaluators)......Page 217
6.7.6 Decision Analyses using the Assurance Region Model......Page 219
6.7.8 Evaluation of "Negative" of Each Site......Page 220
6.7.10 Decision by the Council......Page 221
6.7.11 Concluding Remarks......Page 222
6.8 Summary of Chapter 6......Page 223
6.10 Related DEA-Solver Models for Chapter 6......Page 224
6.11 Problem Supplement for Chapter 6......Page 225
7.1 Introduction......Page 232
7.2 Examples......Page 234
7.3.1 Non-controllable Variable (NCN) Model......Page 236
7.3.2 An Example of a Non-Controllable Variable......Page 237
7.3.3 Non-discretionary Variable (NDSC) Model......Page 239
7.3.5 An Example of the Bounded Variable Model......Page 241
7.4.1 An Example of a Hierarchical Category......Page 244
7.4.2 Solution to the Categorical Model......Page 245
7.4.3 Extension of the Categorical Model......Page 246
7.5.1 Formulation......Page 248
7.5.3 Illustration of a One Input and Two Output Scenario......Page 249
7.6 Rank-Sum Statistics and DEA......Page 250
7.6.1 Rank-Sum-Test (Wilcoxon-Mann-Whitney)......Page 251
7.6.2 Use of the Test for Comparing the DEA Scores of Two Groups......Page 252
7.6.4 Bilateral Comparisons Using DEA......Page 253
7.6.5 An Example of Bilateral Comparisons in DEA......Page 254
7.6.6 Evaluating Efficiencies of Different Organization Forms......Page 255
7.9 Related DEA-Solver Models for Chapter 7......Page 257
7.10 Problem Supplement for Chapter 7......Page 259
8.1 Introduction......Page 273
8.2.1 Cost Efficiency......Page 274
8.2.3 Profit Efficiency......Page 276
8.2.4 An Example......Page 277
8.3.1 A New Scheme for Evaluating Cost Efficiency......Page 278
8.3.2 Differences Between the Two Models......Page 280
8.3.3 An Empirical Example......Page 281
8.3.4 Extensions......Page 283
8.4.1 Loss due to Technical Inefficiency......Page 285
8.4.2 Loss due to Input Price Inefficiency......Page 286
8.4.4 Decomposition of the Actual Cost......Page 287
8.5 Summary of Chapter 8......Page 288
8.6 Notes and Selected Bibliography......Page 289
8.7 Related DEA-Solver Models for Chapter 8......Page 290
8.8 Problem Supplement for Chapter 8......Page 292
9.2.1 Degrees of Freedom......Page 298
9.2.3 Metric Approaches......Page 299
9.2.4 Multiplier Model Approaches......Page 302
9.3 Statistical Approaches......Page 306
9.4.2 Satisficing in DEA......Page 313
9.4.3 Deterministic Equivalents......Page 314
9.4.4 Stochastic Efficiency......Page 317
9.5.1 An Example......Page 319
9.5.2 Application......Page 320
9.5.3 Analysis......Page 322
9.6 Summary of Chapter 9......Page 323
9.7 Related DEA-Solver Models for Chapter 9......Page 324
10.1 Introduction......Page 328
10.2 Radial Super-efficiency Models......Page 329
10.3 Non-radial Super-efficiency Models......Page 332
10.3.1 Definition of Non-radial Super-efficiency Measure......Page 333
10.3.2 Solving Super-efficiency......Page 334
10.3.4 An Example of Non-radial Super-efficiency......Page 335
10.4.1 Radial Super-efficiency Case......Page 336
10.4.2 Non-radial Super-efficiency Case......Page 337
10.7 Related DEA-Solver Models for Chapter 10......Page 338
10.8 Problem Supplement for Chapter 10......Page 339
A.2 Basis and Basic Solutions......Page 341
A.3 Optimal Basic Solutions......Page 342
A.4 Dual Problem......Page 343
A.5 Symmetric Dual Problems......Page 344
A.6 Complementarity Theorem......Page 345
A.7 Farkas' Lemma and Theorem of the Alternative......Page 346
A.8 Strong Theorem of Complementarity......Page 347
A.9 Linear Programming and Duality in General Form......Page 349
B.3 Notation of DEA Models......Page 352
B.5 Preparation of the Data File......Page 353
B.7 Results......Page 362
B.8 Data Limitations......Page 366
B.10 Summary of Headings to Inputs/Outputs......Page 368
C–Bibliography......Page 369
K......Page 370
Z......Page 371
B......Page 372
D......Page 373
F......Page 374
M......Page 375
P......Page 376
S......Page 377
U......Page 378
Z......Page 379

✦ Subjects

Финансово-экономические дисциплины;Математические методы и моделирование в экономике;