Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis (Wiley Series in Operations Research and Management Science)

PREFACE xv SECTION I DATA ENVELOPMENT ANALYSIS (DEA) 1 1 General Description 3 1.1 Introduction 3 1.2 Structure 4 1.3 Contributions in Sections I and II 10 1.4 Abbreviations and Nomenclature 13 1.4.1 Abbreviations Used in This Book 13 1.4.2 Nomenclature Used in This Book 18 1.4.3 Mathematical Concerns 23 1.5 Summary 24 2 Overview 25 2.1 Introduction 25 2.2 What is DEA? 26 2.3 Remarks 33 2.4 Reformulation from Fractional Programming to Linear Programming 35 2.5 Reference Set 38 2.6 Example for Computational Description 39 2.7 Summary 44 3 History 45 3.1 Introduction 45 3.2 O rigin of L1 Regression 46 3.3 O rigin of Goal Programming 50 3.4 Analytical Properties of L1 Regression 53 3.5 From L1 Regression to L2 Regression and Frontier Analysis 55 3.5.1 L2 Regression 55 3.5.2 L1?-based Frontier Analyses 55 3.6 O rigin of DEA 59 3.7 Relationships between GP and DEA 61 3.8 Historical Progress From L1 Regression to DEA 64 3.9 Summary 64 4 Radial Measurement 67 4.1 Introduction 67 4.2 Radial Models: Input?-Oriented 70 4.2.1 Input?-Oriented RM(v) under Variable RTS 70 4.2.2 Underlying Concept 72 4.2.3 Input?-Oriented RM(c) under Constant RTS 74 4.3 Radial Models: Desirable Output?-Oriented 75 4.3.1 Desirable Output?-oriented RM(v) under Variable RTS 75 4.3.2 Desirable Output?-oriented RM(c) under Constant RTS 77 4.4 Comparison Between Radial Models 79 4.4.1 Comparison Between Input?-Oriented and Desirable Output-Oriented Radial Models 79 4.4.2 Hybrid Radial Model: Modification 81 4.5 Multiplier Restriction and Cross?-Reference Approaches 82 4.5.1 Multiplier Restriction Methods 82 4.5.2 Cone Ratio Method 84 4.5.3 Cross?-reference Method 86 4.6 Cost Analysis 88 4.6.1 Cost Efficiency Measures 88 4.6.2 Type of Efficiency Measures in Production and Cost Analyses 89 4.6.3 Illustrative Example 91 4.7 Summary 94 5 Non?-Radial Measurement 95 5.1 Introduction 95 5.2 Characterization and Classification on DMUs 97 5.3 Russell Measure 99 5.4 Additive Model 103 5.5 Range?-Adjusted Measure 105 5.6 Slack?-Adjusted Radial Measure 106 5.7 Slack?-Based Measure 108 5.8 Methodological Comparison: An Illustrative Example 111 5.9 Summary 113 6 Desirable Properties 115 6.1 Introduction 115 6.2 Criteria For OE 117 6.3 Supplementary Discussion 119 6.4 Previous Studies on Desirable Properties 120 6.5 Standard Formulation for Radial and Non?-Radial Models 122 6.6 Desirable Properties for DEA Models 126 6.6.1 Aggregation 126 6.6.2 Frontier Shift Measurability 128 6.6.3 Invariance to Alternate Optima 131 6.6.4 Formal Definitions on Other Desirable Properties 132 6.6.5 Efficiency Requirement 133 6.6.6 Homogeneity 134 6.6.7 Strict Monotonicity 136 6.6.8 Unique Projection for Efficiency Comparison 137 6.6.9 Unit Invariance 138 6.6.10 Translation Invariance 139 6.7 Summary 140 6.A Appendix 142 6.A.1 Proof of Proposition 6.1 142 6.A.2 Proof of Proposition 6.6 143 6.A.3 Proof of Proposition 6.7 145 6.A.4 Proof of Proposition 6.8 146 6.A.5 Proof of Proposition 6.10 147 6.A.6 Proof of Proposition 6.11 147 7 Strong Complementary Slackness Conditions 149 7.1 Introduction 149 7.2 Combination Between Primal and Dual Models for SCSCs 150 7.3 Three Illustrative Examples 154 7.3.1 First Example 155 7.3.2 Second Example 158 7.3.3 Third Example 161 7.4 Theoretical Implications of SCSCs 162 7.5 Guideline for Non-Radial Models 167 7.6 Summary 167 7.A Appendix 168 7.A.1 Proof of Proposition 7.1 168 7.A.2 Proof of Proposition 7.4 169 7.A.3 Proof of Proposition 7.6 170 8 Returns to Scale 173 8.1 Introduction 173 8.2 Underlying Concepts 174 8.3 Production?-Based RTS Measurement 178 8.4 Cost?-Based RTS Measurement 182 8.5 Scale Efficiencies and Scale Economies 185 8.6 Summary 188 9 Congestion 189 9.1 Introduction 189 9.2 An Illustrative Example 191 9.3 Fundamental Discussions 195 9.4 Supporting Hyperplane 200 9.4.1 Location of Supporting Hyperplane 200 9.4.2 Visual Description of Congestion and RTS 201 9.5 Congestion Identification 204 9.5.1 Slack Adjustment for Projection 204 9.5.2 Congestion Identification on Projected Point 206 9.6 Theoretical Linkage Between Congestion and RTS 207 9.7 Degree of Congestion 209 9.8 Economic Implications 211 9.9 Summary 212 10 Network Computing 215 10.1 Introduction 215 10.2 Network Computing Architecture 216 10.3 Network Computing for Multi?-Stage Parallel Processes 218 10.3.1 Theoretical Preliminary 218 10.3.2 Computational Strategy for Network Computing 221 10.3.3 Network Computing in Multi?-Stage Parallel Processes 221 10.4 Simulation Study 229 10.5 Summary 241 11 DEA?-Discriminant Analysis 243 11.1 Introduction 243 11.2 Two MIP Approaches for DEA?-DA 245 11.2.1 Standard MIP Approach 245 11.2.2 Two?-stage MIP Approach 248 11.2.3 Differences between Two MIP Approaches 254 11.2.4 Differences between DEA and DEA?-DA 255 11.3 Classifying Multiple Groups 255 11.4 Illustrative Examples 259 11.4.1 First Example 259 11.4.2 Second Example 259 11.5 Frontier Analysis 261 11.6 Summary 263 12 Literature Study for Section I 265 12.1 Introduction 265 12.2 Computer Codes 265 12.3 Pedagogical Linkage From Conventional Use to Environmental Assessment 268 References for Section I 270 SECTION II DEA ENVIRONMENTAL ASSESSMENT 281 13 World Energy 283 13.1 Introduction 283 13.2 General Trend 284 13.3 Primary Energy 286 13.3.1 Fossil Fuel Energy 286 13.3.2 Non?-fossil Energy 293 13.4 Secondary Energy (Electricity) 297 13.5 Petroleum Price and World Trade 299 13.6 Energy Economics 300 13.7 Summary 303 14 Environmental Protection 305 14.1 Introduction 305 14.2 European Union 306 14.2.1 General Description 306 14.2.2 Environmental Action Program 308 14.3 Japan 310 14.4 China 311 14.5 The United States of America 315 14.5.1 General Description 315 14.5.2 Regional Comparison between PJM and California ISO 317 14.5.3 Federal Regulation of PJM and California ISO 318 14.5.4 Local Regulation on PJM 319 14.5.5 Local Regulation on California ISO 320 14.6 Summary 322 15 Concepts 325 15.1 Introduction 325 15.2 Role of DEA in Measuring Unified Performance 327 15.3 Social Sustainability Versus Corporate Sustainability 331 15.3.1 Why Is Social Sustainability Important? 332 15.3.2 Why Is Corporate Sustainability Important? 333 15.4 Strategic Adaptation 336 15.5 Two Disposability Concepts 339 15.6 Unified Efficiency under Natural and Managerial Disposability 341 15.7 Difficulty in DEA Environmental Assessment 343 15.8 Undesirable Congestion and Desirable Congestion 345 15.9 Comparison With Previous Disposability Concepts 346 15.9.1 Weak and Strong Disposability 347 15.9.2 Null?-joint Relationship (Assumption on “Byproducts”) 347 15.10 Summary 350 16 Non?-Radial Approach for Unified Efficiency Measures 351 16.1 Introduction 351 16.2 Unified Efficiency 352 16.2.1 Formulation 352 16.2.2 Visual Implications of UE 357 16.3 Unified Efficiency under Natural Disposability 359 16.4 Unified Efficiency under Managerial Disposability 362 16.5 Properties of Non?-Radial Approach 364 16.6 National and International Firms in the Petroleum Industry 366 16.6.1 Business Structure 366 16.6.2 National and International Oil Companies 367 16.6.3 UE Measures 367 16.6.4 UE Measures under Natural Disposability 369 16.6.5 UE Measures under Managerial Disposability 369 16.7 Summary 373 17 Radial Approach for Unified Efficiency Measures 375 17.1 Introduction 375 17.2 Unified Efficiency 376 17.3 Radial Unification between Desirable and Undesirable Outputs 378 17.4 Unified Efficiency under Natural Disposability 381 17.5 Unified Efficiency under Managerial Disposability 383 17.6 Coal?-Fired Power Plants in the United States 385 17.6.1 ISO and RTO 385 17.6.2 Data 387 17.6.3 Unified Efficiency 388 17.6.4 Unified Efficiency under Natural Disposability 390 17.6.5 Unified Efficiency under Managerial Disposability 391 17.7 Summary 392 17.A Appendix 393 18 Scale Efficiency 395 18.1 Introduction 395 18.2 Scale Efficiency under Natural Disposability: Non?-Radial Approach 396 18.3 Scale Efficiency under Managerial Disposability: Non?-Radial Approach 399 18.4 Scale Efficiency under Natural Disposability: Radial Approach 401 18.5 Scale Efficiency under Managerial Disposability: Radial Approach 403 18.6 United States Coal?-Fired Power Plants 404 18.6.1 The Clean Air Act 404 18.6.2 Production Factors 406 18.6.3 Research Concerns 407 18.6.4 Unified Efficiency Measures of Power Plants 410 18.6.5 Mean Tests 410 18.7 Summary 414 19 Measurement in a Time Horizon 417 19.1 Introduction 417 19.2 Malmquist Index 418 19.3 Frontier Shift in Time Horizon 419 19.3.1 No Occurrence of Frontier Crossover 419 19.3.2 Occurrence of Frontier Crossover 422 19.4 Formulations for Natural Disposability 424 19.4.1 No Occurrence of Frontier Crossover 425 19.4.2 Occurrence of Frontier Crossover 428 19.5 Formulations under Managerial Disposability 430 19.5.1 No Occurrence of Frontier Crossover 430 19.5.2 Occurrence of Frontier Crossover 432 19.6 Energy Mix of Industrial Nations 435 19.7 Summary 437 19.A Appendix 440 20 Returns to Scale and Damages to Scale 443 20.1 Introduction 443 20.2 Underlying Concepts 444 20.2.1 Scale Elasticity 444 20.2.2 Differences Between RTS and DTS 445 20.3 Non?-Radial Approach 447 20.3.1 Scale Economies and RTS under Natural Disposability 447 20.3.2 Scale Damages and DTS under Managerial Disposability 450 20.4 Radial Approach 451 20.4.1 Scale Economies and RTS under Natural Disposability 451 20.4.2 Scale Damages and DTS under Managerial Disposability 454 20.5 Japanese Chemical and Pharmaceutical Firms 455 20.6 Summary 461 21 Desirable and Undesirable Congestions 463 21.1 Introduction 463 21.2 UC and DC 464 21.3 Unified Efficiency and UC under Natural Disposability 469 21.4 Unified Efficiency and DC under Managerial Disposability 473 21.5 Coal?-Fired Power Plants in United States 476 21.5.1 Data 476 21.5.2 Occurrence of Congestion 477 21.6 Summary 477 22 Marginal Rate of Transformation and Rate of Substitution 483 22.1 Introduction 483 22.2 Concepts 485 22.2.1 Desirable Congestion 485 22.2.2 MRT and RSU 485 22.3 A Possible Occurrence of DC 489 22.4 Measurement of MRT and RSU Under DC 491 22.5 Multiplier Restriction 492 22.6 Explorative Analysis 493 22.7 International Comparison 495 22.8 Summary 503 23 Returns to Damage and Damages to Return 505 23.1 Introduction 505 23.2 Congestion, RTD and DTR 506 23.2.1 UC and DC 506 23.2.2 RTD under UC 508 23.2.3 DTR under DC 510 23.2.4 Possible Occurrence of UC and DC 511 23.3 Congestion Identification under Natural Disposability 512 23.3.1 Possible Occurrence of UC 512 23.3.2 RTD Measurement under the Possible Occurrence of UC 516 23.4 Congestion Identification under Managerial Disposability 519 23.4.1 Possible Occurrence of DC 519 23.4.2 DTR Measurement under the Possible Occurrence of DC 522 23.5 Energy and Social Sustainability In China 524 23.5.1 Data and Empirical Results 524 23.6 Summary 534 24 Disposability Unification 537 24.1 Introduction 537 24.2 Unification between Disposability Concepts 538 24.3 Non?-Radial Approach for Disposability Unification 540 24.4 Radial Approach for Disposability Unification 545 24.5 Computational Flow for Disposability Unification 549 24.6 US Petroleum Industry 551 24.6.1 Data 551 24.6.2 Unified Efficiency Measures 554 24.6.3 Scale Efficiency 557 24.7 Summary 558 25 Common Multipliers 561 25.1 Introduction 561 25.2 Computational Framework 564 25.3 Data Envelopment Analysis-Discriminant Analysis 564 25.4 Rank Sum Test 571 25.5 Japanese Electric Power Industry 571 25.5.1 Underlying Concepts 571 25.5.2 Empirical Results 573 25.6 Summary 580 26 Property of Translation Invariance to Handle Zero and Negative Values 581 26.1 Introduction 581 26.2 Translation Invariance 582 26.3 Assessment in Time Horizon 585 26.3.1 Formulations under Natural Disposability 585 26.3.2 Formulations under Managerial Disposability 588 26.3.3 Efficiency Growth 588 26.4 Efficiency Measurement for Fuel Mix Strategy 590 26.4.1 Unified Efficiency Measures 591 26.4.2 Fuel Mix Strategy 595 26.5 Summary 598 27 Handling Zero and Negative Values in Radial Measurement 601 27.1 Introduction 601 27.2 Disaggregation 602 27.3 Unified Efficiency Measurement 603 27.3.1 Conceptual Review of Disposability Unification 603 27.3.2 Unified Efficiency under Natural Disposability with Disaggregation 606 27.3.3 Unified Efficiency under Managerial Disposability with Disaggregation 607 27.4 Possible Occurrence of Desirable Congestion 609 27.4.1 Unified Efficiency under Natural and Managerial Disposability 609 27.4.2 UENM with Desirable Congestion 610 27.4.3 Investment Rule 613 27.4.4 Computation Summary 614 27.5 United States Industrial Sectors 615 27.6 Summary 622 28 Literature Study for DEA Environmental Assessment 625 28.1 Introduction 625 28.2 Applications in Energy and Environment 626 28.3 Energy 628 28.3.1 Electricity 628 28.3.2 Oil, Coal, Gas and Heat 631 28.3.3 Renewable Energies 633 28.4 Energy Efficiency 634 28.5 Environment 637 28.6 Other Applications 639 28.7 Summary 640 References for Section II 641 INDEX 685