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Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis
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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

4.1 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

5.1 Introduction 95

5.2 Characterization and Classification on DMUs 97

5.3 Russell Measure 99

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

6.6 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

15.5 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

16.6.2 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

20.3.1 Scale Economies and RTS under Natural Disposability 447

20.3.2 Scale Damages and DTS under Managerial Disposability 450

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

Toshiyuki Sueyoshi, Ph.D. is a full professor at New Mexico Institute of Mining and Technology, Soccorro, New Mexico, USA. Dr. Sueyoshi has published more than 300 articles in well-known international (SCI/SSCI listed) journals. Mika Goto, Ph.D. is a full professor at Tokyo Institute of Technology, Tokyo, Japan. Dr. Goto has published more than 100 articles in well-known international (SCI/SSCI listed) journals.