Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis E-Book

Toshiyuki Sueyoshi

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Series in Operations Research and Management Science
• Sprache: Englisch

Seitenzahl: 1210

Veröffentlichungsjahr: 2018

Beschreibung

Introduces a bold, new model for energy industry pollution prevention and sustainable growth Balancing industrial pollution prevention with economic growth is one of the knottiest problems faced by industry today. This book introduces a novel approach to using data envelopment analysis (DEA) as a powerful tool for achieving that balance in the energy industries--the world's largest producers of greenhouse gases. It describes a rigorous framework that integrates elements of the social sciences, corporate strategy, regional economics, energy economics, and environmental policy, and delivers a methodology and a set of strategies for promoting green innovation while solving key managerial challenges to greenhouse gas reduction and business growth. In writing this book the authors have drawn upon their pioneering work and considerable experience in the field to develop an unconventional, holistic approach to using DEA to assess key aspects of sustainability development. The book is divided into two sections, the first of which lays out a conventional framework of DEA as the basis for new research directions. In the second section, the authors delve into conceptual and methodological extensions of conventional DEA for solving problems of environmental assessment in all contemporary energy industry sectors. * Introduces a powerful new approach to using DEA to achieve pollution prevention, sustainability, and business growth * Covers the fundamentals of DEA, including theory, statistical models, and practical issues of conventional applications of DEA * Explores new statistical modeling strategies and explores their economic and business implications * Examines applications of DEA to environmental analysis across the complete range of energy industries, including coal, petroleum, shale gas, nuclear energy, renewables, and more * Summarizes important studies and nearly 800 peer reviewed articles on energy, the environment, and sustainability Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis is must-reading for researchers, academics, graduate students, and practitioners in the energy industries, as well as government officials and policymakers tasked with regulating the environmental impacts of industrial pollution.

Leseprobe

Table of Contents

COVER

TITLE PAGE

PREFACE

SECTION I: DATA ENVELOPMENT ANALYSIS (DEA)

1 GENERAL DESCRIPTION

1.1 INTRODUCTION

1.2 STRUCTURE

1.3 CONTRIBUTIONS IN SECTIONS I AND II

1.4 ABBREVIATIONS AND NOMENCLATURE

1.5 SUMMARY

2 OVERVIEW

2.1 INTRODUCTION

2.2 WHAT IS DEA?

2.3 REMARKS

2.4 REFORMULATION FROM FRACTIONAL PROGRAMMING TO LINEAR PROGRAMMING

2.5 REFERENCE SET

2.6 EXAMPLE FOR COMPUTATIONAL DESCRIPTION

2.7 SUMMARY

3 HISTORY

3.1 INTRODUCTION

3.2 ORIGIN OF L1 REGRESSION

3.3 ORIGIN OF GOAL PROGRAMMING

3.4 ANALYTICAL PROPERTIES OF L1 REGRESSION

3.5 FROM L1 REGRESSION TO L2 REGRESSION AND FRONTIER ANALYSIS

3.6 ORIGIN OF DEA

3.7 RELATIONSHIPS BETWEEN GP AND DEA

3.8 HISTORICAL PROGRESS FROM L1 REGRESSION TO DEA

3.9 SUMMARY

4 RADIAL MEASUREMENT

4.1 INTRODUCTION

4.2 RADIAL MODELS: INPUT‐ORIENTED

4.3 RADIAL MODELS: DESIRABLE OUTPUT‐ORIENTED

4.4 COMPARISON BETWEEN RADIAL MODELS

4.5 MULTIPLIER RESTRICTION AND CROSS‐REFERENCE APPROACHES

4.6 COST ANALYSIS

4.7 SUMMARY

5 NON‐RADIAL MEASUREMENT

5.1 INTRODUCTION

5.2 CHARACTERIZATION AND CLASSIFICATION ON DMUs

5.3 RUSSELL MEASURE

5.4 ADDITIVE MODEL

5.5 RANGE‐ADJUSTED MEASURE

5.6 SLACK‐ADJUSTED RADIAL MEASURE

5.7 SLACK‐BASED MEASURE

5.8 METHODOLOGICAL COMPARISON: AN ILLUSTRATIVE EXAMPLE

5.9 SUMMARY

6 DESIRABLE PROPERTIES

6.1 INTRODUCTION

6.2 CRITERIA FOR OE

6.3 SUPPLEMENTARY DISCUSSION

6.4 PREVIOUS STUDIES ON DESIRABLE PROPERTIES

6.5 STANDARD FORMULATION FOR RADIAL AND NON‐RADIAL MODELS

6.6 DESIRABLE PROPERTIES FOR DEA MODELS

6.7 SUMMARY

APPENDIX

7 STRONG COMPLEMENTARY SLACKNESS CONDITIONS

7.1 INTRODUCTION

7.2 COMBINATION BETWEEN PRIMAL AND DUAL MODELS FOR SCSCs

7.3 THREE ILLUSTRATIVE EXAMPLES

7.4 THEORETICAL IMPLICATIONS OF SCSCs

7.5 GUIDELINE FOR NON‐RADIAL MODELS

7.6 SUMMARY

APPENDIX

8 RETURNS TO SCALE

8.1 INTRODUCTION

8.2 UNDERLYING CONCEPTS

8.3 PRODUCTION‐BASED RTS MEASUREMENT

8.4 COST‐BASED RTS MEASUREMENT

8.5 SCALE EFFICIENCIES AND SCALE ECONOMIES

8.6 SUMMARY

9 CONGESTION

9.1 INTRODUCTION

9.2 AN ILLUSTRATIVE EXAMPLE

9.3 FUNDAMENTAL DISCUSSIONS

9.4 SUPPORTING HYPERPLANE

9.5 CONGESTION IDENTIFICATION

9.6 THEORETICAL LINKAGE BETWEEN CONGESTION AND RTS

9.7 DEGREE OF CONGESTION

9.8 ECONOMIC IMPLICATIONS

9.9 SUMMARY

10 NETWORK COMPUTING

10.1 INTRODUCTION

10.2 NETWORK COMPUTING ARCHITECTURE

10.3 NETWORK COMPUTING FOR MULTI‐STAGE PARALLEL PROCESSES

10.4 SIMULATION STUDY

10.5 SUMMARY

11 DEA‐DISCRIMINANT ANALYSIS

11.1 INTRODUCTION

11.2 TWO MIP APPROACHES FOR DEA‐DA

11.3 CLASSIFYING MULTIPLE GROUPS

11.4 ILLUSTRATIVE EXAMPLES

11.5 FRONTIER ANALYSIS

11.6 SUMMARY

12 LITERATURE STUDY FOR SECTION I

12.1 INTRODUCTION

12.2 COMPUTER CODES

12.3 PEDAGOGICAL LINKAGE FROM CONVENTIONAL USE TO ENVIRONMENTAL ASSESSMENT

REFERENCES FOR SECTION I

SECTION II: DEA ENVIRONMENTAL ASSESSMENT

13 WORLD ENERGY

13.1 INTRODUCTION

13.2 GENERAL TREND

13.3 PRIMARY ENERGY

13.4 SECONDARY ENERGY (ELECTRICITY)

13.5 PETROLEUM PRICE AND WORLD TRADE

13.6 ENERGY ECONOMICS

13.7 SUMMARY

14 ENVIRONMENTAL PROTECTION

14.1 INTRODUCTION

14.2 EUROPEAN UNION

14.3 JAPAN

14.4 CHINA

14.5 THE UNITED STATES OF AMERICA

14.6 SUMMARY

15 CONCEPTS

15.1 INTRODUCTION

15.2 ROLE OF DEA IN MEASURING UNIFIED PERFORMANCE

15.3 SOCIAL SUSTAINABILITY VERSUS CORPORATE SUSTAINABILITY

15.4 STRATEGIC ADAPTATION

15.5 TWO DISPOSABILITY CONCEPTS

15.6 UNIFIED EFFICIENCY UNDER NATURAL AND MANAGERIAL DISPOSABILITY

15.7 DIFFICULTY IN DEA ENVIRONMENTAL ASSESSMENT

15.8 UNDESIRABLE CONGESTION AND DESIRABLE CONGESTION

15.9 COMPARISON WITH PREVIOUS DISPOSABILITY CONCEPTS

15.10 SUMMARY

16 NON‐RADIAL APPROACH FOR UNIFIED EFFICIENCY MEASURES

16.1 INTRODUCTION

16.2 UNIFIED EFFICIENCY

16.3 UNIFIED EFFICIENCY UNDER NATURAL DISPOSABILITY

16.4 UNIFIED EFFICIENCY UNDER MANAGERIAL DISPOSABILITY

16.5 PROPERTIES OF NON‐RADIAL APPROACH

16.6 NATIONAL AND INTERNATIONAL FIRMS IN PETROLEUM INDUSTRY

16.7 SUMMARY

17 RADIAL APPROACH FOR UNIFIED EFFICIENCY MEASURES

17.1 INTRODUCTION

17.2 UNIFIED EFFICIENCY

17.3 RADIAL UNIFICATION BETWEEN DESIRABLE AND UNDESIRABLE OUTPUTS

17.4 UNIFIED EFFICIENCY UNDER NATURAL DISPOSABILITY

17.5 UNIFIED EFFICIENCY UNDER MANAGERIAL DISPOSABILITY

17.6 COAL‐FIRED POWER PLANTS IN THE UNITED STATES

17.7 SUMMARY

APPENDIX

18 SCALE EFFICIENCY

18.1 INTRODUCTION

18.2 SCALE EFFICIENCY UNDER NATURAL DISPOSABILITY: NON‐RADIAL APPROACH

18.3 SCALE EFFICIENCY UNDER MANAGERIAL DISPOSABILITY: NON‐RADIAL APPROACH

18.4 SCALE EFFICIENCY UNDER NATURAL DISPOSABILITY: RADIAL APPROACH

18.5 SCALE EFFICIENCY UNDER MANAGERIAL DISPOSABILITY: RADIAL APPROACH

18.6 UNITED STATES COAL‐FIRED POWER PLANTS

18.7 SUMMARY

19 MEASUREMENT IN TIME HORIZON

19.1 INTRODUCTION

19.2 MALMQUIST INDEX

19.3 FRONTIER SHIFT IN TIME HORIZON

19.4 FORMULATIONS FOR NATURAL DISPOSABILITY

19.5 FORMULATIONS UNDER MANAGERIAL DISPOSABILITY

19.6 ENERGY MIX OF INDUSTRIAL NATIONS

19.7 SUMMARY

APPENDIX

20 RETURNS TO SCALE AND DAMAGES TO SCALE

20.1 INTRODUCTION

20.2 UNDERLYING CONCEPTS

20.3 NON‐RADIAL APPROACH

20.4 RADIAL APPROACH

20.5 JAPANESE CHEMICAL AND PHARMACEUTICAL FIRMS

20.6 SUMMARY

21 DESIRABLE AND UNDESIRABLE CONGESTIONS

21.1 INTRODUCTION

21.2 UC AND DC

21.3 UNIFIED EFFICIENCY AND UC UNDER NATURAL DISPOSABILITY

21.4 UNIFIED EFFICIENCY AND DC UNDER MANAGERIAL DISPOSABILITY

21.5 COAL‐FIRED POWER PLANTS IN UNITED STATES

21.6 SUMMARY

22 MARGINAL RATE OF TRANSFORMATION AND RATE OF SUBSTITUTION

22.1 INTRODUCTION

22.2 CONCEPTS

22.3 A POSSIBLE OCCURRENCE OF DESIRABLE COnGESTION (DC)

22.4 MEASUREMENT OF MRT AND RSU UNDER DC

22.5 MULTIPLIER RESTRICTION

22.6 EXPLORATIVE ANALYSIS

22.7 INTERNATIONAL COMPARISON

22.8 SUMMARY

23 RETURNS TO DAMAGE AND DAMAGES TO RETURN

23.1 INTRODUCTION

23.2 CONGESTION, RETURNS TO DAMAGE AND DAMAGES TO RETURN

23.3 CONGESTION IDENTIFICATION UNDER NATURAL DISPOSABILITY

23.4 CONGESTION IDENTIFICATION UNDER MANAGERIAL DISPOSABILITY

23.5 ENERGY AND SOCIAL SUSTAINABILITY IN CHINA

23.6 SUMMARY

24 DISPOSABILITY UNIFICATION

24.1 INTRODUCTION

24.2 UNIFICATION BETWEEN DISPOSABILITY CONCEPTS

24.3 NON‐RADIAL APPROACH FOR DISPOSABILITY UNIFICATION

24.4 RADIAL APPROACH FOR DISPOSABILITY UNIFICATION

24.5 COMPUTATIONAL FLOW FOR DISPOSABILITY UNIFICATION

24.6 US PETROLEUM INDUSTRY

24.7 SUMMARY

25 COMMON MULTIPLIERS

25.1 INTRODUCTION

25.2 COMPUTATIONAL FRAMEWORK

25.3 COMPUTATIONAL PROCESS

25.4 RANK SUM TEST

25.5 JAPANESE ELECTRIC POWER INDUSTRY

25.6 SUMMARY

26 PROPERTY OF TRANSLATION INVARIANCE TO HANDLE ZERO AND NEGATIVE VALUES

26.1 INTRODUCTION

26.2 TRANSLATION INVARIANCE

26.3 ASSESSMENT IN TIME HORIZON

26.4 EFFICIENCY MEASUREMENT FOR FUEL MIX STRATEGY

26.5 SUMMARY

27 HANDLING ZERO AND NEGATIVE VALUES IN RADIAL MEASUREMENT

27.1 INTRODUCTION

27.2 DISAGGREGATION

27.3 UNIFIED EFFICIENCY MEASUREMENT

27.4 POSSIBLE OCCURRENCE OF DESIRABLE CONGESTION

27.5 US INDUSTRIAL SECTORS

27.6 SUMMARY

28 LITERATURE STUDY FOR DEA ENVIRONMENTAL ASSESSMENT

28.1 INTRODUCTION

28.2 APPLICATIONS IN ENERGY AND ENVIRONMENT

28.3 ENERGY

28.4 ENERGY EFFICIENCY

28.5 ENVIRONMENT

28.6 OTHER APPLICATIONS

28.7 SUMMARY

REFERENCES IN SECTION II

INDEX

END USER LICENSE AGREEMENT

List of Tables

Chapter 02

TABLE 2.1 Performance assessment: one input and one desirable output

TABLE 2.2 Performance assessment: two inputs and a desirable output

TABLE 2.3 Performance assessment: one input and two desirable outputs

TABLE 2.4 Illustrative example for computation

TABLE 2.5 Computational summary

Chapter 03

TABLE 3.1 An illustrative example

TABLE 3.2 An illustrative example for L1 frontier analyses

TABLE 3.3 Efficiency measures by L1‐based Frontier analyses

Chapter 04

TABLE 4.1 An illustrative example

TABLE 4.2 Production‐based efficiency measures

TABLE 4.3 An illustrative example

TABLE 4.4 Production and cost‐based efficiency measures

Chapter 05

TABLE 5.1 An illustrative example

TABLE 5.2 Comparison among radial and non‐radial approaches

Chapter 06

TABLE 6.1 Relationship between seven models and nine desirable properties.

TABLE 6.2 Reformulation as a standard model (expression by λ): Model (6.1)

EXAMPLE 6.1

EXAMPLE 6.2

EXAMPLE 6.3

EXAMPLE 6.4

EXAMPLE 6.5

EXAMPLE 6.6

EXAMPLE 6.7

EXAMPLE 6.8

EXAMPLE 6.9

EXAMPLE 6.10

EXAMPLE 6.11

EXAMPLE 6.12

EXAMPLE 6.13

Chapter 07

TABLE 7.1 Computational Summary for DMUs {A} and {D} by Model (7.9)

TABLE 7.2 RM(c) without SCSCs

TABLE 7.3 RM(v) without SCSCs

TABLE 7.4 RM(c) with SCSCs

TABLE 7.5 RM(v): with SCSCs

TABLE 7.6 Third illustrative data

TABLE 7.7 Computational result of input‐oriented

RM

(

v

): Model (7.1)

TABLE 7.8 Computational result of input‐oriented RM(v) with SCSCs: Model (7.9)

Chapter 10

TABLE 10.1 Comparison between CPU time and network computing

TABLE 10.2 Comparison between CPU time and network computing

TABLE 10.3 Comparison between CPU time and network computing

TABLE 10.4 Comparison between CPU time and network computing

Chapter 11

TABLE 11.1 Differences between DEA and DEA‐DA

TABLE 11.2 Illustrative data set and hit rates

TABLE 11.3 Weight estimates and hit rates (multiple classifications)

Chapter 12

TABLE 12.1 Available Computer Codes for DEA

Chapter 14

TABLE 14.1 PJM and California ISO on air quality requirements

Chapter 15

TABLE 15.1 Structural differences between two disposability combinations

Chapter 16

TABLE 16.1 Unified efficiency (2005–2009)

TABLE 16.2 Unified efficiency under natural disposability (2005–2009)

TABLE 16.3 Unified efficiency under managerial disposability (2005–2009)

Chapter 17

TABLE 17.1 Number of coal‐fired power plants

TABLE 17.2 Unified efficiency (1995–2007)

TABLE 17.3 Unified efficiency under natural disposability (1995–2007)

TABLE 17.4 Unified efficiency under managerial disposability (1995–2007)

Chapter 18

TABLE 18.1 Plant primary fuel and capacity factor

TABLE 18.2 Unified efficiencies on power plants: non‐radial approach

TABLE 18.3 Mean tests on unified efficiencies: non‐radial approach

Chapter 19

TABLE 19.1 Malmquist index under natural disposability: no frontier crossover

TABLE 19.2 Malmquist index under natural disposability: frontier crossover

TABLE 19.3 Malmquist index under managerial disposability: no frontier crossover

TABLE 19.4 Malmquist index under managerial disposability: frontier crossover

TABLE 19.A1 Popular indexes for productivity measurement

Chapter 20

TABLE 20.1 Strategies measured by RTS and DTS

TABLE 20.2 Returns to scale

TABLE 20.3 Damages to scale

Chapter 21

TABLE 21.1 Unified efficiency measures, dual variables and type of undesirable congestion (UC)

TABLE 21.2 Unified efficiency, dual variables and type of desirable congestion (DC)

Chapter 22

TABLE 22.1 Computational results for 2012: Model (21.9).

TABLE 22.2 UEM(DC) comparison among three regional blocks.

TABLE 22.3 Marginal rate of transformation (

).

TABLE 22.4 Marginal rate of transformation (

).

TABLE 22.5 Marginal rate of transformation (

).

TABLE 22.6 Rate of substitution (

ug/w

1

b

1

).

TABLE 22.7 Rate of substitution (

ug/w

2

b

2

).

Chapter 23

TABLE 23.1 UEN(UC) and type of UC: Model (23.4)

TABLE 23.2 UEM(DC) and type of DC: Model (23.14)

TABLE 23.3 UEN(UC) and type of UC: Model (23.9)

TABLE 23.4 UEM(DC) and type of DC: Model (23.16)

TABLE 23.5 Classification of RTD and DTR of 30 municipalities and provinces

Chapter 24

TABLE 24.1 Unified efficiency measures: non‐radial approach

TABLE 24.2 Scale efficiency measures: non‐radial approach

Chapter 25

TABLE 25.1 Differences between DEA and DEA/SCSCs

TABLE 25.2 Efficiency and multipliers measured by Model (7.1) or (7.2)

TABLE 25.3 Efficiency and multipliers measured by Model (25.1)

TABLE 25.4 Efficiency (DEA) and adjusted efficiency (proposed approach)

Chapter 26

TABLE 26.1 Unified efficiency under natural disposability: window analysis

TABLE 26.2 Unified efficiency under managerial disposability: window analysis

TABLE 26.3 Efficiency growth under natural disposability: window analysis

TABLE 26.4 Efficiency growth under managerial disposability: window analysis

TABLE 26.5 Fuel mix strategy under managerial disposability: window analysis

TABLE 26.6 Fuel mix strategies measured by eight approaches

Chapter 27

TABLE 27.1 Unified efficiency measures of US industrial sectors

TABLE 27.2 Unified efficiency measures of US industrial sectors: natural and managerial disposability

TABLE 27.3 Unified efficiency measures of US industrial sectors under desirable congestion

TABLE 27.4 Investment strategy on industrial sector

Chapter 28

TABLE 28.1 Previous research efforts: application areas and periods

TABLE 28.2 Articles applied to the electricity industry

TABLE 28.3 Articles applied to oil, coal, gas and heat

TABLE 28.4 Articles applied to renewable energies

TABLE 28.5 Articles applied to energy efficiency

TABLE 28.6 Articles applied to environment

TABLE 28.7 Articles applied to other applications

List of Illustrations

Chapter 01

FIGURE 1.1 Developments and contributions.

Chapter 02

FIGURE 2.1 Efficiency frontier and performance assessment (a) An efficiency frontier under constant RTS (returns to scale) passes from the origin to {C}. The constant RTS implies that a unit increase in an input propositionally increases a desirable output, as depicted in the straight line for the efficiency frontier. See Chapter 8 for a description on RTS. (b) The {C} is efficient and the remaining others have some level of inefficiency under such a production condition.

FIGURE 2.2 Efficiency frontier and regression line (a) An efficiency frontier passes from the origin to {C}. This DMU is efficient and the remaining others have some level of inefficiency. (b) The regression line locates on the center of all observations (i.e., DMUs). (c) The regression analysis is used for future prediction and the efficiency frontier is used for performance assessment.

FIGURE 2.3 Efficiency frontier and performance assessment: two inputs and one desirable output (a) An efficiency frontier consists of piece‐wise linear contour line segments by connecting {C–B–H}. The other DMUs are inefficient. They need to improve their performance levels so that they can attain the efficiency frontier. (b) The production possibility set locates in the north‐east area of the figure where all efficient and inefficient DMUs can exist under their production technology.

FIGURE 2.4 Efficiency measurement for DMU {A} (a) DMU {A} needs to reduce an amount of the two inputs. For example, {A} can shift to any projected points between A

1

and {B}. The point A

2

is one of such possible projected points in the case where the two inputs are reduced. (b) An efficiency frontier for {A} consists of part of a line segment between the two DMUs {B and C}. (c) The efficiency measure of {A} is determined by the ratio of the two distances (i.e., OA

2

/OA) measured on the L2 norm for our visual description. See Chapter 3 about the L2 norm distance measurement. Such a treatment is for our visual convenience. This chapter understands that the reality of DEA efficiency measurement should be discussed by the L1 norm distance.

FIGURE 2.5 Efficiency frontier and performance assessment in one input and two desirable outputs (a) DMU {E} needs to increase the amount of the two desirable outputs. For example, the DMU can shift to any projected points between {F} and {G}. The point E

1

is one such possible projected point in the case where the two desirable outputs are increased. (b) An efficiency frontier consists of line segments between the DMUs {B–C–F–G}. (c) The level of efficiency of {E} is determined by the ratio of the two distances (i.e., OE/OE

1

) in the L2 norm distance measurement. Such is just for our visual convenience, as mentioned previously. This chapter understands that DEA belongs to the L1 norm measurement. See Chapter 3 on the L1 and L2 distance measurements.

FIGURE 2.6 Efficiency measurement of DMU {A} (a) The example is for the input‐oriented measurement under variable RTS. (b) An efficiency frontier consists of {E}‐{D}‐{C}. They are efficient on the frontier, but the other DMUs exhibit some level of inefficiency. (c) DMU{A} needs to reduce the amount of two inputs to attain the status of efficiency, specified by A

1

, while maintaining the same level of an output. (d) DMU{F} is on the frontier so that the efficiency score is unity. However, the DMU contains a slack related to the first input on optimality. Therefore, the DMU is inefficient.

Chapter 03

FIGURE 3.1 Three regression lines: L1 regression and two frontier analyses (a) Each dot (•) indicates an observation. (b) The L1 regression, locating in the middle of observations, is measured by Model (3.8). The L1‐based lower frontier line is measured by Model (3.13) and the L1‐based upper frontier line is measured by Model (3.14).

FIGURE 3.2 Progress from L1 regression to DEA.

Chapter 04

FIGURE 4.1 Efficiency frontiers under constant and variable RTS

FIGURE 4.2 Multiplier restriction (a) The figure is prepared for our visual convenience. The number of efficient DMUs decreases from five {D1‐D2‐D3‐D4‐D5} on the efficiency frontier to one, {D3}. It is necessary for us to understand that strong multiplier restriction often produces an infeasible solution on optimality. The two directional vectors (A1 and A2) are used to restrict the direction of input multipliers. (b) It is assumed that all DMUs produce the same amount of a desirable output.

FIGURE 4.3 Efficiency measures (a).

FIGURE 4.4 Input‐oriented projections and two efficiency frontiers

Chapter 06

FIGURE 6.1 Sensitivity relationship between seven models

Chapter 07

FIGURE 7.1 Occurrence of multiple projections.

Chapter 08

FIGURE 8.1 Three types of RTS and supporting hyperplanes

FIGURE 8.2 Type of cost‐based RTS and supporting hyperplane

FIGURE 8.3 Occurrence of multiple supporting hyperplanes

Chapter 09

FIGURE 9.1 Congestion among three zones.

FIGURE 9.2 Occurrence of congestion. (b) This chapter updates their work. The market which has two zones where A and B are generators in a remote zone and C and D are generators in a city zone.

FIGURE 9.3 Market clearing price: no line limit. This chapter updates their work.

FIGURE 9.4 Market clearing price (line limit). (a) Source: Sueyoshi and Goto (2016) This chapter updates their work.

FIGURE 9.5 Occurrence of congestion (a) A possible occurrence of congestion is measured by allocating equality to an input vector (

X

) as found in Models (9.2) and (9.7). The analytical feature will be further explored and changed in Chapter 21. (b) RM(c) cannot measure an occurrence of congestion because

under constant RTS. Thus, it is necessary for us to use RM(v) for the identification.

FIGURE 9.6 Five types of returns to scale. (a) Source: Sueyoshi and Goto (2016b). This chapter reorganizes their work. (b) RTS: Returns to scale; IRTS: increasing RTS; CRTS: constant RTS; DRTS: decreasing RTS. (c) Positive RTS under no congestion is further separated into IRTS, CRTS and DRTS. (d) Negative RTS and No RTS correspond to strong congestion and weak congestion if two production factors have only a single component. If they have multiple components, then these concepts do not link to each other. (e) RM(c) cannot measure an occurrence of congestion because

under constant RTS. Thus, it is necessary for us to use only RM(v) for this type of identification.

FIGURE 9.7 Classification of returns to scale under congestion

FIGURE 9.8 Implications of congestion

Chapter 10

FIGURE 10.1 Client–server environment (star configuration)

FIGURE 10.2 Computational strategy for network computing. (b) This chapter reorganizes it for our description. ECD stands for efficiency candidates, which are a group of DMUs that may belong to

.

FIGURE 10.3 Stage I (parallel computing for

J

n

(a) Source: Sueyoshi and Honma (2003)). This chapter reorganizes it for our description. (b)

NY

: a group of DMUs which are “not yet” examined at the current stage.

FIGURE 10.4 Stage II (network computing for

J

n

(a) Source: Sueyoshi and Honma (2003)). This chapter reorganizes it for our description.

FIGURE 10.5 Network computing at the

c

‐th client. This chapter reorganizes it for our description.

FIGURE 10.6 Stage III (parallel computing for

J

d

at the

c

‐th client. This chapter reorganizes it for our description.

Chapter 11

FIGURE 11.1 Classification and overlap identification at Stage 1

FIGURE 11.2 Overlap identification at Stage 1

FIGURE 11.3 Classification at Stage 1

FIGURE 11.4 Final classification at Stage 2

FIGURE 11.5 Classification of multiple groups(b) This type of multiple group classification by DEA‐DA has a limited classification capability because it produces same cutting off hyperplanes except an intercept. There is a possibility that DEA‐DA produces an infeasible solution when such hyperplanes cannot separate multiple groups

FIGURE 11.6 Structure of performance measurement

Chapter 13

FIGURE 13.1 Trend of world primary energy consumption(b) We prepared the figure based upon the numbers listed in the data source. (c) A large increase in energy consumption can be found in the Asia Pacific region during the observed decades. An increase can be found in Europe and Eurasia, as well. A rapid economic development has been accomplished in the two regions.

FIGURE 13.2 World energy consumption by energy sources in the annual periods(b) We prepared the figure based upon the numbers listed in the source data. (c) The figure indicates that fossil fuel components (i.e., oil, natural gas and coal) are the major energy resources in the world, all of which are used not only for modern business (e.g., transport and industry sectors) and the household sector but also for military purposes. (d) Fluctuations in the oil price may influence the market condition of business because oil is the most important primary energy resource.

FIGURE 13.3 World oil proved reserves as of 2012(b) We prepared the figure based upon the numbers listed in the data source. (c) The figure excludes an amount of Canadian oil sands and Venezuela’s Orinoco Belt. The shale oil reserve is also excluded from the figure. The largest shale oil reserve exists in China and the second is the United States.

FIGURE 13.4 Trend of world oil production: regional classification(b) We prepared the figure based upon the numbers listed in the source data.

FIGURE 13.5 Trend of world oil production by OPEC and non‐OPEC nations(b) We prepared the figure based upon the numbers listed in the source data.

FIGURE 13.6 Trend of world oil consumption by OECD and non‐OECD nations(b) We prepared the figure based upon the numbers listed in the data source. (c) There was no major increase in OECD nations, but there was an increasing trend in the non‐OECD nations. The result indicates that industrial nations in the OECD attained the almost maximum limit on oil consumption. In contrast, non‐OECD nations increased consumption for their industrial developments along with their population increase.

FIGURE 13.7 World natural gas: proved reserves as of 2013(b) We prepared the figure based upon the numbers listed in the source data.

FIGURE 13.8 Nuclear generation capacity in three groups of OECD nations(b) We prepared the figure based upon the numbers listed in the source data. (c) GWe stands for Gigawatt‐electrical.

FIGURE 13.9 Amount of nuclear power generation in three groups of OECD nations(b) We prepared the figure based upon the numbers listed in the data source. (c) TWh stands for Terawatt hour.

FIGURE 13.10 Cumulative installed photovoltaic power from 1999 to 2013(b) We prepared the figure based upon the numbers listed in the data source. (c) MW stands for Megawatt.

FIGURE 13.11 Global cumulative installed wind power generation capacity from 1997 to 2014(b) We prepared the figure based upon the numbers listed in the data source. (c) MW stands for Megawatt.

FIGURE 13.12 Trend in world electricity consumption(b) We prepared the figure based upon the numbers listed in the data source. (c) TWh stands for Terawatt hour.

FIGURE 13.13 An equilibrium point in power trading market(b) The market clearing price (MCP) is found on the equilibrium point (EP).

Chapter 15

FIGURE 15.1 Position of DEA in environmental assessment (a) This figure was first proposed by Sueyoshi and Goto (2015a). This chapter reorganizes it by incorporating a consensus building capability into the original figure.

FIGURE 15.2 Triangular relationship between three production factors (a) Undesirable outputs are byproducts of desirable outputs, both of which are produced by inputs. The more desirable outputs and less undesirable outputs produce the better performance in a DEA environmental assessment.

FIGURE 15.3 Influence of regulation and eco‐technology innovation(b) The amount of an input is not listed in the figure for our descriptive convenience. The figure implicitly considers an input increase or decrease. (c) An important feature of this figure is that an input change causes shifts in a desirable output and an undesirable output as depicted in the figure. The first shift is due to a change from non‐regulation to regulation. The second shift is due to eco‐technology innovation. Such a change implies “desirable congestion” due to a regulation change and an occurrence of eco‐technology innovation. See Chapter 21 for a description on desirable congestion. (d) This type of strategy is referred to as “managerial disposability”, later in this chapter.

FIGURE 15.4 Computational flow for unified efficiency

FIGURE 15.5 Gradual improvement for performance unification (a) For our visual convenience, this chapter depicts the relationship between a unification level and a time horizon by a straight line. The reality is much different from the figure. Therefore, it may be characterized by a nonlinear relationship between them.

FIGURE 15.6 Unification process between desirable and undesirable outputs (a) EF stands for efficiency frontier. (b) PrPS, PoPS and Pr&PoPS indicate production possibility set, pollution possibility set, and production and pollution possibility set, respectively. (c) Stage (III) is the final unification process which incorporates an assumption that an undesirable output is a byproduct of a desirable output. The figure incorporates an occurrence of desirable congestion.

FIGURE 15.7 Undesirable congestion and desirable congestion

FIGURE 15.8 Natural and managerial disposability and strong and weak disposability (a) An existence of “slack” means that constraints are considered as “inequality” so that corresponding dual variables are positive or zero in their signs. In contrast, “no slack” implies that they are considered as “equality”. The corresponding dual variables are unrestricted so that they may take positive, zero or negative in their signs. Thus, we can identify a possible occurrence of capacity limit under natural disposability or a possible occurrence of eco‐technology innovation under managerial disposability. (b) The conventional framework of DEA incorporates only the left‐hand side of the above four flows. Meanwhile DEA environmental assessment incorporates all of the four methodological flows. Thus, there are analytical differences between DEA and its environmental assessment.

Chapter 16

FIGURE 16.1 Two efficiency frontiers for measuring unified efficiency (a) The direction of NW (north‐west) indicates a projection of {K} toward an efficiency frontier ({A}–{B}–{C}) that is incorporated into the conventional framework of DEA. (b) DEA environmental assessment incorporates the projection of SW (south‐west) from {K} toward an efficiency frontier ({G}–{H}–{D}) under natural disposability and the projection of SE (south‐east) from {K} toward an efficiency frontier ({D}–{E}–{F}) under managerial disposability. The projection of NW serves a basis for the performance assessment of conventional DEA. The projection of NE (north‐east) toward an efficient frontier ({C}–{I}) has been excluded from the conventional use. The proposed environmental assessment incorporates the projection toward NE along with an increase in components of an input vector. (c) The figure corresponds to Stages I (A) and (B) of Figure 15.6. As depicted in Figure 15.6, the proposed DEA environmental assessment is much more completed than the one described in this figure. (d) NW + SW: natural disposability and NE + SE: managerial disposability. Both are incorporated in the proposed DEA environmental assessment.

FIGURE 16.2 Sustainability development (a) Energy firms under public ownership can more easily access capital (so attaining a large amount of capital accumulation) than those under private ownership. As the result of such easy capital accessibility, public firms cannot make corporate efforts toward their growth processes. Public ownership often invites serious corruption between governments and energy firms, as found in many developing countries. Privatization will be necessary for most energy firms under public ownership.

Chapter 17

FIGURE 17.1 Projection onto efficiency frontier for desirable outputs.

FIGURE 17.2 Projection onto efficiency frontier for undesirable outputs.

Chapter 18

FIGURE 18.1 Two efficiency frontiers under different RTS . (b) See Figure 15.6. This figure corresponds to Stage I (A) of Figure 15.6. (c) This figure is prepared for a desirable output‐oriented case. (d) RTS stands for returns to scale.

FIGURE 18.2 Two efficiency frontiers under different DTS (b) See Figure 15.6. This figure corresponds to Stage I (B) of Figure 15.6. (c) This figure is prepared for an undesirable output‐oriented case. (d) DTS stands for damages to scale.

FIGURE 18.3 Power plant management under different regulation environments. (b) The “liberalization” is a process of market reforms to introduce competition and a less restrictive regulation framework for companies in the electricity industry. (c) The “deregulation” is the modification or repeal of existing regulation or the removal of state control and the introduction of a more formal regulatory framework.

Chapter 19

FIGURE 19.1 Frontier shift under natural disposability. (b) The efficiency frontier shifts toward an increase in desirable outputs without any frontier crossover between the two periods. The natural disposability implies that the first priority is operational performance and the second priority is environmental performance. The figure assumes that an undesirable output (

b

) is same for all DMUs, so reducing the influence on a frontier shift. (c) The figure assumes that DEA does not suffer from an occurrence of multiple projections and multiple reference sets. (d) A unique projection onto the two efficiency frontiers is for our visual convenience. This chapter fully understands that a real projection in DEA is more complicated than the one depicted in the figure. (e) As discussed in Chapter 3, this chapter clearly understands that the projection should be measured by the L1‐metric distance, not the L2‐metric distance, as depicted in the figure. Such a metric change is for our visual convenience.

FIGURE 19.2 Frontier shift under managerial disposability. (b) The efficiency frontier shifts toward a decrease in undesirable outputs without any frontier crossover between the two periods. The managerial disposability implies that the first priority is environmental performance and the second priority is operational performance. The figure assumes that desirable outputs are same on all DMUs, so dropping an influence on the frontier shift. (c) See the notes for Figure 19.1.

FIGURE 19.3 Frontier crossover between two periods under natural disposability. (b) See the notes for Figure 19.1. (c) The dotted line of the upper curve indicates the frontier for the

t

–1 th and

t

th periods.

FIGURE 19.4 Frontier crossover between two periods under managerial disposability. (b) See the notes for Figure 19.2. (c) The dotted line of the bottom curve indicates the frontier for the

t

–1 th and

t

th periods.

Chapter 21

FIGURE 21.1 Undesirable congestion (UC) and desirable congestion (DC) (a) Each occurrence of congestion is classified into three categories: strong, weak and no. (b) The top of the figure indicates the possible occurrence of UC within a conventional DEA framework on

x

and

g

. This type of congestion has been long discussed in the DEA community. See Chapter 9. (c) The bottom left‐hand side indicates the possible occurrence of UC in which an enhanced component(s) of an input vector increases some component(s) of the undesirable output vector, but decreases some component(s) of the desirable output vector. The equality constraints without slacks should be assigned to undesirable outputs (

B

) in the proposed formulations. (d) The bottom right‐hand side indicates the possible occurrence of DC, or eco‐technology innovation for pollution mitigation. In DEA environmental assessment, this type of occurrence indicates that an enhanced component(s) of an input vector increases some component(s) of a desirable output vector, but decreases some component(s) of an undesirable output vector. This study thinks that eco‐technology innovation can solve various pollution issues, so that the occurrence of DC is important in DEA environmental assessment. For identifying the possible occurrence of DC, equality constraints without slacks are assigned to desirable outputs (

G

) in the proposed formulations. (e) The convex function at the bottom right‐hand side depends upon the assumption that undesirable outputs (

B

) are “byproducts” of desirable outputs (

G

). It should be a concave function without such an assumption. The assumption is acceptable and realistic as long as DC occurs on

B

. See Chapter 15 on the assumption.

FIGURE 21.2 Undesirable congestion (UC) and unsustainability. (b) See Figure 9.5 in which

x

and

g

indicate the horizontal and vertical coordinates, respectively. Many previous studies extend Figure 9.5 to Figure 21.2 in discussing the occurrence of UC. The identification of UC is important in energy economics because it indicates a capacity limit.

FIGURE 21.3 Desirable congestion (DC) and sustainability.

Chapter 22

FIGURE 22.1 Damages to return under managerial disposability (a) The middle of the figure assumes that an undesirable output (

b

) is a byproduct of a desirable output (

g

). (b) The type of DTR is classified into decreasing, constant and increasing under no DC. See Chapter 23 for a description of DTR.

FIGURE 22.2 Marginal rate of transformation and rate of substitution

FIGURE 22.3 Explorative analysis (a) The proposed approach does not need prior information for multiplier restriction. The analytical feature is different from a conventional use of the AR analysis that needs prior information. See Chapter 4 on the AR analysis. (b) The explorative analysis implies that we investigate computational results by utilizing both a data set and additional information so that computational results can fit with our expectation and reality. (c) It is possible for us to change a combination on multiplier restriction for explorative analysis until we can satisfy MRT and RSU estimates in our expected ranges. Equations (22.8) can work most of data sets because each production factor is divided by each factor average. An exception is a data set with many zeros. In this case, we must depend on the methodologies listed in Chapters 26 and 27.

FIGURE 22.4 Sustainability enhancement

Chapter 23

FIGURE 23.1 UC and DC (a) See Figure 21.1. Figure 23.1 changes Figure 21.1 by a smooth curve for our visual convenience and pays attention to the bottom of Figure 21.1, that is, a visual description of UC and DC. (b) For our visual convenience, part of input

x

is not shown in this figure (see Figure 21.1). For example, on the left‐hand side of Figure 23.1, the supporting hyperplane visually specifies the shape of the production curve and the possible occurrence of UC between desirable output (

g

) and undesirable output (

b

). A negative slope indicates the occurrence of UC, so being considered as “strong UC.” The occurrence of strong UC implies that enlarged input (

x

) increases undesirable output (

b

) and decreases the desirable output vector (

g

), as visually specified by the negative slope of the supporting line. In contrast, a positive slope implies an opposite case (i.e., no congestion), so being referred to as “no UC.” When the slope of a supporting hyperplane is zero, this chapter considers it as “weak UC,” being between strong UC and no UC. See Chapter 21, which explains this as the starting position of UC. The visual description on UC is extendable to a description on DC, or eco‐technology innovation for pollution reduction, as found on the right‐hand side of the figure. The three categories of DC include no (a positive slope), weak (a zero slope) and strong (a negative slope). (c) The occurrence of UC, or a capacity limit, becomes a serious problem in energy sectors so that it is necessary for us to identify such an occurrence in discussing energy policy. Meanwhile, the occurrence of DC, or eco‐technology innovation, may be more important than UC in terms of environmental protection and assessment because it is necessary for us to reduce the level of various types of pollution. (d) For our visual description, the figure uses a smooth curve to express the relationship between two production factors. The figure also depicts a single component of the three production factors. All the DEA formulations proposed in this chapter can handle their multiple components.

FIGURE 23.2 Undesirable Congestion (UC) (a) See Figure 21.2. (b) The figure visually specifies the relationship between the supporting hyperplane and the production and pollution possibility set. The types of UC include “no,” “weak” and “strong”. No UC is found at D, weak UC is found at A and strong UC is found on F. The occurrence of strong UC is identified by negative RTD if the three production factors have a single component, as depicted in the figure. (c) The figure does not incorporate the input (

x

) for our visual convenience. Hence, each dotted line can be considered as a supporting hyperplane.

FIGURE 23.3 Returns to damage (RTD) (a) IRTD: Increasing RTD, CRTD: constant RTD and DRTD: decreasing RTD in the case of a desirable output (

g

) and undesirable output (

b

), all of which belong to “positive RTD.” In addition, there are no RTD and negative RTD. The negative RTD indicates an occurrence of strong UC due to a capacity limit in part or all of a whole production system. (b) A use of scale elasticity for RTD classification indicates that

dg/db

becomes zero on {A} and negative on {F}, where

d

stands for a derivative of a functional form between two components. The derivative mathematically indicates the slope of a supporting hyperplane. The other three points ({C}, {D} and {E}) have a positive slope. Thus, Figure 23.3 indicates a mathematical linkage between strong UC and negative RTD in the case of a single component of the three production factors. The case of multiple components is discussed by the proposed formulations for DEA environmental assessment in this chapter.

FIGURE 23.4 Desirable congestion (DC) (a) See Figure 21.3. (b) Figure 23.4 visually specifies the relationship between a supporting hyperplane and the types of DC, including “no,” “weak” and “strong” DC. No DC is found on {D}, weak DC is found on {A}. Strong DC occurs on {F} and such an occurrence may be identified by negative DTR if the three production factors have a single component. (c) An important feature of Figures 23.4 and 23.5 is that they have an assumption of byproducts. That is, undesirable outputs are byproducts of the desirable outputs. Hence, the figures have a convex form to express efficiency frontiers. Without this assumption, they should be structured by a concave form to express an efficiency frontier for undesirable outputs.

FIGURE 23.5 Damages to return (DTR) (a) IDTR: Increasing DTR, CDTR: constant DTR and DDTR: decreasing DTR in the case of an undesirable output (

b

) and desirable output (

g

). In addition, there is no DTR and negative DTR. A negative DTR indicates the occurrence of DC due to eco‐technology innovation for reducing the amount of undesirable outputs.

FIGURE 23.6 Computational flow from disposability to RTD and DTR (a) This figure visually describes the computational flow from the two disposability concepts to RTD under natural disposability and DTR under managerial disposability. (b) The possible occurrence of undesirable congestion is measured under natural disposability by assigning equality to the undesirable output (

B

). The occurrence indicates a technology limit on part or all of a whole production capability. (c) The possible occurrence of desirable congestion is measured under managerial disposability by assigning equality to the desirable output (

G

). The occurrence indicates an opportunity to reduce the amount of undesirable outputs by eco‐technology. (d) Strong, weak or no UC correspond to negative, no or positive RTD, respectively, in the case of a single component of three production factors. The UC is a necessary condition of RTD in the case of multiple components in the three production factors. (d) Strong, weak or no DC corresponds to negative, no or positive DTR, respectively, in the case of a single component of three production factors. The DC is a necessary condition of DTR in the case of multiple components in the three production factors. (e) I, C and D indicate increasing, constant and decreasing.

FIGURE 23.7 Returns to damage (RTD) under undesirable congestion (UC) (a) The increase in some component(s) of the input vector (

X

) increases the components of the other two production factors. The occurrence of UC is “undesirable” because some component(s) of the desirable output vector (

G

) decrease and those of the undesirable output vector (

B

) increase along with such a change of input vector. That is, the occurrence of UC is due to a capacity limit on part or whole in a production facility. (b) The occurrence and type of UC are identified by the sign of dual variables (

). The type of UC is classified into three categories. Meanwhile, these measures related to RTD are determined by not only the sign of dual variables (

) but also the sign of

. The type of RTD is classified into five categories.

FIGURE 23.8 Damages to return (DTR) under desirable congestion (DC) (a) An increase in some component(s) of the input vector (

X

) increases the components of the other two production factors. The occurrence of DC is desirable because some component(s) of the desirable output vector (

G

) increase but those of the undesirable output vector (

B

) decrease along with such a change in input vector. That is an occurrence of DC. We look for such an occurrence by eco‐technology innovation in a broad sense, including managerial challenges. (b) The occurrence and type of DC are identified by the sign of dual variables (

). The type of DC is classified into three categories. Meanwhile, these measures related to DTR are determined by not only the sign of dual variables (

), but also the sign of

. The type of DTR is classified into five categories.

Chapter 24

FIGURE 24.1 Disposability unification (stage III)

FIGURE 24.2 Desirable congestion for eco‐technology innovation (a) The three supporting lines (a–c, d–e and f–h) indicate no, weak and strong DC, respectively. The line indicates supporting hyperplanes if it includes an input (

x

). The figure drops the input for our visual description. (b) It is possible to depict the figure by

b

on the horizontal axis and

g

on the vertical axis. In the case, the right‐hand side indicates the occurrence of undesirable congestion (UC). See Chapter 21 for a detailed description on UC. UC is a conventional concept of congestion.

FIGURE 24.3

UENM(DC)

and efficiency measures (a) It is possible for us to apply the proposed approach to both radial and non‐radial measurements. Therefore, this chapter does not specify R (radial) and NR (non‐radial) in the figure.

FIGURE 24.4

SENM(DC)

measurement (a) RTS: returns to scale; DTS: damages to scale; DC: desirable congestion. (b) DMU {P} is projected onto N on the contour line segments {A}–{B}–{C}–{D}–{E} (the efficiency frontier for the desirable output under variable RTS). Meanwhile, it is projected onto L on the line from the origin O to L. The level of efficiency is determined by the distance between the observed point and the projected point. After disposability unification, the distance is measured by the desirable output. (c) The line segments, or {F}–{G}–{H}–{I}–{J}–{K}, consist of the efficiency frontier for the undesirable output. The frontier is shaped by variable DTS and the possible occurrence of desirable congestion (DC), or eco‐technology innovation. (d) This figure incorporates the possible occurrence of DC, but excludes UC. As a result, the frontier for desirable output has an increasing shape and the frontier for undesirable output has an increasing and decreasing shape. This figure incorporates the assumption that the undesirable output is a byproduct of the desirable output. Without this assumption, the efficiency frontier has a concave shape, not a convex shape as depicted in this figure. See Figure 15.6.

Chapter 25

FIGURE 25.1 Computational flow of proposed approach (a) The incorporation of SCSCs into DEA is not necessary if the primal model incorporates data range adjustments on slacks, as found in radial and non‐radial measurements proposed by DEA environmental assessment. See Chapters in Section II. They can always produce positive multipliers (i.e., dual variables) so that the environmental assessment discussed in this book can fully utilize all production factors. Hence, the proposed approaches can omit the computational part on DEA/SCSCs and starts from the DMU classification by DEA‐DA. A problem is that the subjectivity of a user may be included in the range adjustments. The use of SCSCs can avoid such a difficulty related to a conventional use of DEA. See Chapter 7 on the use of SCSCs.

FIGURE 25.2 Visual difference between supporting line and discriminant line (a) The O indicates efficient DMUs and the X indicates inefficient DMUs. The two groups correspond to G1 and G2, respectively, in all formulations of Chapter 11. A supporting line (s–s′) can be expressed by the supporting hyperplane in the case where production factors have multiple components. In a similar manner, a supporting line (d–d′) becomes a discriminant hyperplane in the multiple components.

Chapter 26

FIGURE 26.1 Computational process for fuel mix strategy (a) Many OECD nations do not have nuclear generation so that the data set used in this chapter contains many zeros. As a result, it is necessary for us to utilize the property of translation invariance. The property can be used only for the proposed non‐radial model. The property indicates that an efficiency measure should be not influenced even if inputs and/or outputs are shifted toward a same direction by adding or subtracting a specific real number. The property makes it possible that we can evaluate the performance of DMUs, whose production factors contain many zeros and negative values in a data set. (b) The proposed window analysis is useful in dealing with a data set in a time horizon.

FIGURE 26.2 Shift of period block (PB) in window analysis (a) W stands for Window. W1, W2,…, W6 are related to the first, second,…, sixth window. PB stands for a period block in which we measure unified efficiency and efficiency growth. (b) The number within each set of parentheses indicates the order of window to express the corresponding PB.

FIGURE 26.3 Upper and lower bounds of fuel mix strategy (a) TA stands for the total average that is, for example, listed at the right‐hand bottom of Tables 26.1 to 26.4. Sueyoshi and Goto (2015c) lists the computational results on cross sectional analysis that uses a pooled data set. (b) This chapter does not describe on the left part (on the pooled data) of the figure because this chapter focuses upon a description on the window analysis. See Sueyoshi and Goto (2015c) that provides a detailed description on the cross section analysis.

Chapter 27

FIGURE 27.1 Efficiency frontiers for desirable and undesirable outputs (Stage I) (a) The figures do not consider the existence of zero or negative values. (b) Source: Figure 15.6. The figure corresponds to Stage I. This chapter does not list Stage II. (c) This chapter adds efficiency frontiers under constant returns to scale (RTS) and damages to scale (DTS).

FIGURE 27.2 Efficiency frontiers under disposability unification (Stage III) (a) The right‐hand side of the figure assumes a same amount of an input, so not considering the input. The figure does not consider the existence of zero or negative values in all production factors. (b) Source: Figure 15.6. (c) This chapter uses the byproduct assumption that an undesirable output is a byproduct of a desirable output. (d) Pr&PoPS stands for a production and pollution possibility set. DC indicates the occurrence of desirable congestion, or eco‐technology innovation and managerial challenges to reduce the amount of undesirable outputs.

FIGURE 27.3 Efficiency frontier and damages to return (Stage III) (a) This figure does not consider the existence of zero or negative values. This chapter attempts to visually describe the type of DC. (b) This chapter uses the by‐product assumption that an undesirable output is a byproduct of a desirable output. (c) DTR stands for damages to return and DC stands for desirable congestion.

FIGURE 27.4 Two approaches for handling zero and negative values (a) Disaggregation requires more theoretical work to improve the reliability of research. For example, the selection of

ε

s

is subjective. None knows what the best selection is. (b) The property of translation invariance works only on non‐radial measurement, as discussed in Chapter 26. (c) The disaggregation works for both radial and non‐radial measurements. The proposed disaggregation needs to mathematically explore concerning how many DMUs with zero or negative values are appropriate in terms of making efficiency frontiers for desirable and undesirable outputs within the framework of DEA environmental assessment. It is necessary for us to consider which situation the proposed approach works or not. (d) It is easily imagined that the number of DMUs with positive values is larger than that of DMUs with zero or negative values. Such is just an assumption. (e) The proposed approach by disaggregation is a quick and easy method, not an exact method, to deal with zero and negative values. Mathematical justification is necessary on the property of disaggregation.

FIGURE 27.5 Corporate sustainability development (a) See Figure 15.5. The figure depicts a gradual improvement for sustainability development.

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Operations Research and Management Science (ORMS) is a broad, interdisciplinary branch of applied mathematics concerned with improving the quality of decisions and processes and is a major component of the global modern movement towards the use of advanced analytics in industry and scientific research. The Wiley Series in Operations Research and Management Science features a broad collection of books that meet the varied needs of researchers, practitioners, policy makers, and students who use or need to improve their use of analytics. Reflecting the wide range of current research within the ORMS community, the Series encompasses application, methodology, and theory and provides coverage of both classical and cutting edge ORMS concepts and developments. Written by recognized international experts in the field, this collection is appropriate for students as well as professionals from private and public sectors including industry, government, and nonprofit organizations who are interested in ORMS at a technical level.

Founding Series EditorJames J. Cochran, The University of Alabama

Advisory Editors

AnalyticsJennifer Bachner, Johns Hopkins UniversityKhim Yong Goh, National University of Singapore

Decision and Risk AnalysisGilberto Montibeller, Loughborough UniversityGregory S. Parnell, United States Military Academy at West Point

Optimization ModelsLawrence V. Snyder, Lehigh UniversityYa‐xiang Yuan, Chinese Academy of Sciences

Stochastic ModelsRaúl Gouet, University of ChileTava Olsen, The University of Auckland Business School

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