Network Data Envelopment Analysis : Foundations and Extensions

Annotation This book presents the underlying theory, model development, and applications of network Data Envelopment Analysis (DEA) in a systematic way. The field of network DEA extends and complements conventional DEA by considering not only inputs and outputs when measuring system efficiency, but also the internal structure of the system being analyzed. By analyzing the efficiency of individual internal components, and more particularly by studying the effects of relationships among components which are modeled and implemented by means of various network structures, the network DEA approach is able to help identify and manage the specific components that contribute inefficiencies into the overall systems. This relatively new approach comprises an important analytical tool based on mathematical programming techniques, with valuable implications to production and operations management. The existing models for measuring the efficiency of systems of specific network structures are also discussed, and the relationships between the system and component efficiencies are explored. This book should be able to inspire new research and new applications based on the current state of the art. Performance evaluation is an important task in management, and is needed to (i) better understand the past accomplishments of an organization and (ii) plan for its future development. However, this task becomes rather challenging when multiple performance metrics are involved. DEA is a powerful tool to cope with such issues. For systems or operations composed of interrelated processes, managers need to know how the performances of the various processes evaluated and how they are aggregated to form the overall performance of the system. This book provides an advanced exposition on performance evaluation of systems with network structures. It explores the network nature of most production and operation systems, and explains why network analyses are necessary." Preface 6 Contents 10 About the Author 16 Chapter 1: Introduction 17 1.1 History of Network DEA 18 1.2 Basic Ideas of Efficiency Measurement 19 1.3 Multi-input Case 23 1.4 Multi-output Case 25 1.5 Whole-Unit Analysis 27 1.6 Network Analysis 29 1.7 Supplementary Literature 31 References 32 Chapter 2: Output-Input Ratio Efficiency Measures 34 2.1 CCR Model 35 2.1.1 Input Model 35 2.1.2 Output Model 39 2.2 BCC Model 41 2.2.1 Input Model 42 2.2.2 Output Model 45 2.3 Restrictions on Multipliers 48 2.4 Ranking 50 2.5 Supplementary Literature 54 References 54 Chapter 3: Distance Function Efficiency Measures 57 3.1 Production Possibility Set 58 3.2 Input Distance Function 61 3.3 Output Distance Function 67 3.4 Directional Distance Function 72 3.5 Supplementary Literature 75 References 76 Chapter 4: Slacks-Based Efficiency Measures 78 4.1 Additive Model 79 4.2 Russell Measures 82 4.2.1 Input Model 82 4.2.2 Output Model 85 4.2.3 Input-Output Average Model 87 4.3 Russell Ratio Model 90 4.4 A Classification of Efficiency Measures 94 4.5 Supplementary Literature 98 References 98 Chapter 5: Efficiency Measurement in Special Production Stages 101 5.1 Multiplicative Model 102 5.1.1 Variable Returns to Scale 103 5.1.2 Constant Returns to Scale 107 5.2 Free Disposal Hull 110 5.2.1 General Case 110 5.2.2 Constant Returns to Scale 113 5.3 Congestion 115 5.3.1 Weak Disposability Model 116 5.3.2 Slack-Measure Model 117 5.3.3 Input-Fixing Model 119 5.3.4 Comparison 120 5.4 Supplementary Literature 122 References 123 Chapter 6: Special Types of Input and Output Factors 125 6.1 Non-discretionary Factors 126 6.1.1 Input Model 126 6.1.2 Output Model 128 6.1.3 Dual Model Interpretation 130 6.1.4 Constant Returns to Scale 131 6.2 Undesirable Factors 133 6.2.1 Input-Output Exchange Approach 133 6.2.2 Data Transformation 134 6.2.2.1 Inverse Transformation 134 6.2.2.2 Negative Transformation 135 6.2.2.3 Shifted Negative Transformation 136 6.2.3 Weak Disposability Approach 136 6.2.3.1 Hyperbolic Model 138 6.2.3.2 Directional Distance Model 138 6.2.4 Slacks-Based Approach 139 6.3 Supplementary Literature 140 References 141 Chapter 7: Special Types of Data 144 7.1 Negative Data 145 7.2 Ordinal Data 147 7.3 Qualitative Data 148 7.4 Stochastic Data 152 7.5 Interval Data 157 7.6 Fuzzy Data 159 7.7 Supplementary Literature 163 References 164 Chapter 8: Changes of Efficiency Over Time 167 8.1 Theoretic Foundation of MPI 168 8.1.1 Input Index 168 8.1.2 Output Index 169 8.1.3 Productivity Index 169 8.2 DEA Measurement of MPI 171 8.3 Global Malmquist Productivity Index 176 8.4 Luenberger Productivity Index 179 8.5 Supplementary Literature 183 References 183 Chapter 9: Basic Ideas in Efficiency Measurement for Network Systems 186 9.1 The Black-Box Model 188 9.2 Independent Model 190 9.2.1 Multiplier Form 190 9.2.2 Envelopment Form 191 9.2.3 Slacks-Based Form 192 9.3 Connected Model 194 9.3.1 Envelopment Form 194 9.3.2 Multiplier Form 196 9.3.3 Slacks-Based Form 198 9.4 Relational Model 199 9.4.1 Multiplier Form 199 9.4.2 Envelopment Form 201 9.4.3 Slacks-Based Form 202 9.5 An Example 203 9.5.1 Independent Model 204 9.5.2 Connected Model 207 9.5.3 Relational Model 211 9.6 Supplementary Literature 214 References 214 Chapter 10: Basic Two-Stage Systems 216 10.1 Independent Model 217 10.2 Ratio-Form Efficiency Measures 220 10.2.1 Efficiency Decomposition 220 10.2.1.1 Constant Returns to Scale 220 10.2.1.2 Variable Returns to Scale 223 10.2.1.3 Game-Theoretic Approach 227 10.2.2 Efficiency Aggregation 228 10.3 Distance Function Efficiency Measures 232 10.3.1 System Parameter 232 10.3.2 Division Parameters 236 10.4 Slacks-Based Efficiency Measures 238 10.5 Supplementary Literature 240 References 242 Chapter 11: General Two-Stage Systems 246 11.1 Feedback System 247 11.2 Independent Efficiency Measures 252 11.3 Ratio-Form Efficiency Measures 255 11.3.1 Game Approach 255 11.3.2 Efficiency Aggregation 257 11.3.3 Efficiency Decomposition 259 11.4 Distance Function Efficiency Measures 264 11.4.1 System Parameter 264 11.4.2 Division Parameters 267 11.4.3 Directional Distance Parameter 269 11.5 Slacks-Based Efficiency Measures 270 11.6 Shared Input 273 11.7 Supplementary Literature 277 References 280 Chapter 12: General Multi-Stage Systems 283 12.1 Basic Series Structure 284 12.1.1 Efficiency Decomposition 284 12.1.2 Efficiency Aggregation 288 12.2 Independent Efficiency Measures 290 12.3 Ratio-Form Efficiency Measures 291 12.3.1 Efficiency Aggregation 291 12.3.2 Efficiency Decomposition 293 12.4 Distance Function Efficiency Measures 297 12.4.1 System Parameter 297 12.4.2 Division Parameters 299 12.5 Slacks-Based Efficiency Measures 303 12.6 Reversal Links 306 12.6.1 Ratio-Form Efficiency Measures 307 12.6.2 Slacks-Based Efficiency Measures 309 12.7 Supplementary Literature 312 References 314 Chapter 13: Parallel Systems 316 13.1 Multi-Component Systems 317 13.2 Multi-Function Systems 321 13.3 Shared Input 325 13.3.1 Ratio-Form Efficiency Measures 326 13.3.2 Distance Function Efficiency Measures 329 13.3.2.1 System Parameter 329 13.3.2.2 Division Parameters 330 13.3.2.3 Directional Distance Parameter 333 13.3.3 Slacks-Based Efficiency Measures 334 13.4 Supplementary Literature 337 References 339 Chapter 14: Hierarchical Systems 341 14.1 Multi-Component Systems 342 14.2 Multi-Function Systems 348 14.3 General Model 353 14.4 Slacks-based Efficiency Measures 357 14.5 Supplementary Literature 358 References 359 Chapter 15: Assembly and Disassembly Systems 360 15.1 Assembly Systems 361 15.1.1 The Basic Two-Division Series Structure 361 15.1.2 The Basic Two-Division Parallel Structure 362 15.1.3 The Basic Two-Division Series Structure with Exogenous Inputs 364 15.1.4 The Basic Three-Division (Assembly) Structure 367 15.1.5 The Basic Three-Division Structure with Exogenous Inputs 368 15.1.6 An Example 370 15.1.7 Non-Uniqueness of Decomposition 373 15.2 Disassembly Systems 375 15.2.1 The Basic Two-Division Series Structure 375 15.2.2 The Basic Two-Division Parallel Structure 375 15.2.3 The Basic Two-Division Series Structure with Exogenous Outputs 376 15.2.4 The Basic Three-Division (Disassembly) Structure 377 15.2.5 The Basic Three-Division Structure with Exogenous Outputs 379 15.2.6 An Example 380 15.2.7 Hierarchical Systems 383 15.3 Distance Function Efficiency Measures 386 15.4 Slacks-Based Efficiency Measures 388 15.5 Supplementary Literature 390 References 391 Chapter 16: Mixed Systems 392 16.1 Independent Efficiency Measures 393 16.2 Ratio-Form Efficiency Measures 396 16.3 Distance Function Efficiency Measures 399 16.4 Slacks-Based Efficiency Measures 401 16.4.1 The Environmental Protection Example 401 16.4.2 The Bank Profit Centers Example 404 16.4.3 The Corporate and Consumer Banking Example 406 16.4.4 The NBA Basketball Example 408 16.5 Supplementary Literature 411 References 412 Chapter 17: Dynamic Systems 414 17.1 Ratio-Form Efficiency Measures 415 17.1.1 The Whole-Unit Case 415 17.1.2 The Network Case 417 17.2 Distance Function Efficiency Measures 419 17.2.1 The Production Delays Example 420 17.2.2 The Period Distance Parameters Case 421 17.2.3 Directional Distance Function: Whole Unit 422 17.2.4 Directional Distance Function: Network 424 17.3 Slacks-Based Efficiency Measures 425 17.3.1 The Basic Dynamic Structure Case 426 17.3.2 The Aggregate Slack Case 427 17.3.3 The Network Case 429 17.4 Value-Based Efficiency Measures 431 17.5 Supplementary Literature 432 References 434 Chapter 18: Epilogue 437 18.1 Generality of Some Representative Models 437 18.2 Which Model to Use 441 18.3 Road Ahead 443 Index 445 Front Matter....Pages i-xv Introduction....Pages 1-17 Output–Input Ratio Efficiency Measures....Pages 19-41 Distance Function Efficiency Measures....Pages 43-63 Slacks-Based Efficiency Measures....Pages 65-87 Efficiency Measurement in Special Production Stages....Pages 89-112 Special Types of Input and Output Factors....Pages 113-131 Special Types of Data....Pages 133-155 Changes of Efficiency Over Time....Pages 157-175 Basic Ideas in Efficiency Measurement for Network Systems....Pages 177-206 Basic Two-Stage Systems....Pages 207-236 General Two-Stage Systems....Pages 237-273 General Multi-Stage Systems....Pages 275-307 Parallel Systems....Pages 309-333 Hierarchical Systems....Pages 335-353 Assembly and Disassembly Systems....Pages 355-386 Mixed Systems....Pages 387-408 Dynamic Systems....Pages 409-431 Epilogue....Pages 433-440 Back Matter....Pages 441-443