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Data Envelopment Analysis : A Handbook of Models and Methods.

By: Material type: TextTextSeries: International Series in Operations Research and Management Science SeriesPublisher: New York, NY : Springer, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (472 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781489975539
Subject(s): Genre/Form: Additional physical formats: Print version:: Data Envelopment AnalysisDDC classification:
  • 658.5036
LOC classification:
  • T57.6-.97
Online resources:
Contents:
Intro -- Preface -- Contents -- Contributors -- Chapter 1 Distance Functions in Primal and Dual Spaces -- 1.1 Introduction -- 1.2 Cost and Distance Functions in the Primal and Dual Spaces: An Introductory Example -- 1.3 Distance Functions and Their Duals -- 1.4 Distance Functions and Efficiency Measurement -- 1.5 DEA Estimators -- 1.6 Endogenous Directional Vectors -- 1.7 Appendix: Parametric Distance Functions -- References -- Chapter 2 DEA Cross Efficiency -- 2.1 Introduction -- 2.2 Cross Efficiency -- 2.3 Numerical Example -- 2.4 Maximum Log Cross Efficiency -- 2.5 Multiplicative DEA Model -- 2.6 Maximum Log Cross Efficiency -- 2.7 Game Cross Efficiency -- 2.8 Conclusions -- References -- Chapter 3 DEA Cross Efficiency Under Variable Returns to Scale -- 3.1 Introduction -- 3.2 Negative Cross Efficiency and Free Production -- 3.3 DEA and Coordinate Systems: A Geometric Link Between the VRS and CRS Models -- 3.4 Cross Efficiency in the VRS Model -- 3.5 Conclusions -- References -- Chapter 4 Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis -- 4.1 Introduction -- 4.2 Axioms -- 4.2.1 Free Disposability and Natural Disposability -- 4.2.2 Convexity and Natural Convexity -- 4.2.3 Returns to scale -- 4.2.4 Envelopment -- 4.3 Continuous, Integer-Valued and Hybrid DEA Technologies -- 4.4 Efficiency Measures and Distance Functions -- 4.4.1 Modified Farrell Input Efficiency Measure -- 4.4.2 MILP Formulation -- 4.4.3 Numerical Examples -- 4.5 Alternative Efficiency Metrics -- 4.5.1 Modified Farrell Output Efficiency Measure and its Implementation -- 4.5.2 Modified Directional Distance Function and its Implementation -- 4.5.3 Additive and Slack Based Measures -- 4.6 Stochastic Noise -- 4.7 Conclusion and Directions for Future Research -- 4.8 Appendix: Proofs of theorems and lemmas -- References.
Chapter 5 DEA Models with Production Trade-offs and Weight Restrictions -- 5.1 Introduction -- 5.2 Production Trade-offs -- 5.3 Illustrative Example -- 5.3.1 Undergraduate and Master Students -- 5.3.2 Research Staff and Publications -- 5.3.3 Academic Staff and Students -- 5.3.4 Students and Publications -- 5.3.5 Computational Results -- 5.4 Graphical Illustrations -- 5.5 CRS and VRS Technology with Production Trade-offs -- 5.5.1 Axiomatic Definitions -- 5.5.2 Some Properties of CRS and VRS Technologies with Trade-offs -- 5.6 Weight Restrictions and the Infeasibility Problem -- 5.6.1 Definitions and Examples -- 5.6.2 Theoretical Results -- 5.6.3 Free Production with Not Linked Trade-offs -- 5.6.4 Free Production with Linked Trade-offs -- 5.7 Solving DEA Models with Production Trade-offs -- 5.7.1 Stage 1: Assessing the Radial Efficiency -- 5.7.2 Stage 2: Identifying Efficient Targets -- 5.7.3 Stage 3: Identifying Reference Sets of Efficient Peer Units -- 5.8 Conclusion -- References -- Chapter 6 Facet Analysis in Data Envelopment Analysis -- 6.1 Introduction -- 6.2 Primal and Dual Description of the Production Possibility Set TCCR -- 6.3 Primal and Dual Description of the Production Possibility Set TBCC -- 6.4 Interior and Exterior Facets -- 6.5 Procedures for Identification of the Total Set of FDEFs -- 6.5.1 Convex Hull Generation -- 6.6 An Efficiency Evaluation Relative to a Technology Spanned by FDEFs -- 6.6.1 The CRS Case: Extending the CCR-Model with Facet Extensions -- 6.6.2 The VRS Case: Extending the BCC-Model with Facet Extensions -- 6.7 Use of Efficient Faces and Facets in DEA -- References -- Chapter 7 Stochastic Nonparametric Approach to Efficiency Analysis: A Unified Framework -- 7.1 Introduction -- 7.2 Unified Frontier Model -- 7.3 Convex Nonparametric Least Squares -- 7.3.1 CNLS Estimator for the Observed Data Points.
7.3.2 Extrapolating to Unobserved Points -- 7.3.3 Computational Issues -- 7.4 Deterministic Frontiers -- 7.4.1 DEA as Sign-Constrained CNLS -- 7.4.2 Corrected CNLS -- 7.5 Stochastic Nonparametric Envelopment of Data (StoNED) -- 7.5.1 Step 1: CNLS Regression -- 7.5.2 Step 2: Estimation of the Expected Inefficiency -- 7.5.2.1 Method of Moments -- 7.5.2.2 Quasi-likelihood Estimation -- 7.5.2.3 Nonparametric Kernel Density Estimation for the Convoluted Residual -- 7.5.3 Step 3: Estimating the Frontier Production Function -- 7.5.4 Step 4: Estimating Firm-Specific Inefficiencies -- 7.5.5 Statistical Specification Tests of the Frontier Model -- 7.6 Extensions -- 7.6.1 Multiplicative Composite Error Term -- 7.6.2 Panel Data -- 7.6.3 Multiple Outputs (DDF Formulation) -- 7.6.4 Convex Nonparametric Quantile Regression and Asymmetric Least Squares -- 7.7 Contextual Variables -- 7.7.1 Two-Stage DEA -- 7.7.2 One-Stage DEA -- 7.7.3 StoNED With z-Variables (StoNEZD) -- 7.8 Heteroscedasticity -- 7.8.1 White Test of Heteroscedasticity Applied to CNLS -- 7.8.2 Doubly-Heteroscedastic Model -- 7.8.3 Stepwise StoNED Estimation Under Heteroscedasticity -- 7.9 Directions for Future Research -- References -- Chapter 8 Translation Invariance in Data Envelopment Analysis -- 8.1 Introduction -- 8.2 Translation Invariance for Dealing with Data Which Have Value Zero -- 8.3 Translation Invariant Models for Dealing with Non-Positive Data -- 8.4 Non-Translation Invariant Models for Dealing with Negative Data -- 8.5 The Linear Loss Distance Function Model and the Property of Translation Invariance -- 8.6 Conclusions -- References -- Chapter 9 Scale Elasticity in Non-parametric DEA Approach -- 9.1 Introduction -- 9.2 Technology Specification and Scale Elasticity -- 9.2.1 Technology -- 9.2.2 Primal Measure of Scale Elasticity -- 9.2.3 Dual Measure of Scale Elasticity.
9.2.4 Scale Elasticity in DEA Models -- 9.2.4.1 Scale Elasticity in Production DEA Models -- 9.2.4.2 Scale Elasticity in Multiplicative DEA Model -- 9.2.4.3 Scale Elasticity in Production DEA Models with Indivisibilities -- 9.2.4.4 Scale Elasticity in Cost DEA Models -- 9.2.4.5 Scale Elasticity in Alternative Cost DEA Model -- 9.3 Concluding Remarks -- References -- Chapter 10 DEA Based Benchmarking Models -- 10.1 Introduction -- 10.2 Context-Dependent Data Envelopment Analysis -- 10.2.1 Stratification DEA Model -- 10.2.2 Attractiveness and Progress -- 10.2.3 Output Oriented Context-Dependent DEA Model -- 10.2.4 Context-Dependent DEAWith Value Judgment -- 10.3 Variable and Fixed Benchmarking Models -- 10.3.1 Variable-Benchmark Model -- 10.3.2 Fixed-Benchmark Model -- 10.4 Concluding Remarks -- References -- Chapter 11 Data Envelopment Analysis with Non-Homogeneous DMUs -- 11.1 Introduction -- 11.2 Manufacturing Plants with Variable Output Sets -- 11.3 A DEA Model for DMUs with Variable Output Sets -- 11.4 AR Restrictions on Pairs of Input Variables -- 11.5 Other Considerations -- 11.6 Application -- 11.7 Conclusions -- 11.8 Appendix 1: Generating the Maximal Output Groupings -- 11.9 Appendix 2: Generating a Single Set of AR Constraints -- 11.10 Appendix 3: Tables -- References -- Chapter 12 Efficiency Measurement in Data Envelopment Analysis with Fuzzy Data -- 12.1 Introduction -- 12.2 The Problem -- 12.3 The Membership Grade Approach -- 12.4 The α-cut Approach -- 12.5 Discussion and Conclusion -- References -- Chapter 13 Partial Input to Output Impacts in DEA: Production Considerations and Resource Sharing Among Business Sub-Units -- 13.1 Introduction -- 13.2 Efficiency Measurement in Steel Fabrication Plants -- 13.3 Modeling Efficiency in the Presence of Partial Input to Output Interactions -- 13.4 AR Restrictions on Pairs of Input Variables.
13.5 Other Considerations -- 13.6 Application -- 13.7 Discussion and Conclusions -- 13.8 Appendix 1: Proofs of Theorems -- 13.9 Appendix 2: Algorithms -- 13.10 Appendix 3: Tables -- References -- Chapter 14 Super-Efficiency in Data Envelopment Analysis -- 14.1 Introduction -- 14.2 Infeasibility -- 14.3 Alternative VRS Super-Efficiency Models -- 14.3.1 Equivalent Standard Super-Efficiency Models (Lovell and Rouse 2003) -- 14.3.2 Super-Efficiency Based on Efficient Projections (Chen 2004, 2005) -- 14.3.3 A Modified Super-Efficiency Measure (Cook et al. 2009) -- 14.3.4 Two-Stage Procedure (Lee et al. 2011) and Its One Model Approach (Chen and Liang 2011) -- 14.3.5 DDF-Based Super-Efficiency and SBM Super-Efficiency -- 14.3.6 A Numerical Example for Comparison -- 14.4 Slacks-Based Super-Efficiency -- 14.4.1 SBM Super-Efficiency -- 14.4.2 Additive Super-Efficiency -- 14.4.3 A Numerical Example -- 14.5 DDF-Based Super-Efficiency -- 14.5.1 N-L Super-Efficiency -- 14.5.2 Modified DDF-Based Super-Efficiency -- 14.6 Integer Super-Efficiency -- 14.6.1 Integer-Valued Additive Super-Efficiency -- 14.6.2 Additive Super-Efficiency for Undesirable Integer-Restricted Data -- 14.6.3 DDF-Based Integer Super-Efficiency -- 14.7 Conclusions -- References -- Chapter 15 DEA Models with Undesirable Inputs, Intermediates, and Outputs -- 15.1 Introduction -- 15.2 Single-Stage DEA Models with Undesirable Variables -- 15.2.1 Desirability and Disposability -- 15.2.1.1 Desirability Determination -- 15.2.1.2 Disposability Assumptions in DEA -- 15.2.2 DEA Models with Undesirable Inputs/Outputs for Single-Stage Systems -- 15.3 Two-Stage DEA Models with Undesirable Variables -- 15.3.1 Desirability of Inputs and Outputs in Two-Stage Systems -- 15.3.2 Production Possibility Sets of Two-Stage Systems with Undesirable Variables -- 15.3.3 Two-Stage DEA Models with Undesirable Variables.
15.4 Conclusions.
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Intro -- Preface -- Contents -- Contributors -- Chapter 1 Distance Functions in Primal and Dual Spaces -- 1.1 Introduction -- 1.2 Cost and Distance Functions in the Primal and Dual Spaces: An Introductory Example -- 1.3 Distance Functions and Their Duals -- 1.4 Distance Functions and Efficiency Measurement -- 1.5 DEA Estimators -- 1.6 Endogenous Directional Vectors -- 1.7 Appendix: Parametric Distance Functions -- References -- Chapter 2 DEA Cross Efficiency -- 2.1 Introduction -- 2.2 Cross Efficiency -- 2.3 Numerical Example -- 2.4 Maximum Log Cross Efficiency -- 2.5 Multiplicative DEA Model -- 2.6 Maximum Log Cross Efficiency -- 2.7 Game Cross Efficiency -- 2.8 Conclusions -- References -- Chapter 3 DEA Cross Efficiency Under Variable Returns to Scale -- 3.1 Introduction -- 3.2 Negative Cross Efficiency and Free Production -- 3.3 DEA and Coordinate Systems: A Geometric Link Between the VRS and CRS Models -- 3.4 Cross Efficiency in the VRS Model -- 3.5 Conclusions -- References -- Chapter 4 Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis -- 4.1 Introduction -- 4.2 Axioms -- 4.2.1 Free Disposability and Natural Disposability -- 4.2.2 Convexity and Natural Convexity -- 4.2.3 Returns to scale -- 4.2.4 Envelopment -- 4.3 Continuous, Integer-Valued and Hybrid DEA Technologies -- 4.4 Efficiency Measures and Distance Functions -- 4.4.1 Modified Farrell Input Efficiency Measure -- 4.4.2 MILP Formulation -- 4.4.3 Numerical Examples -- 4.5 Alternative Efficiency Metrics -- 4.5.1 Modified Farrell Output Efficiency Measure and its Implementation -- 4.5.2 Modified Directional Distance Function and its Implementation -- 4.5.3 Additive and Slack Based Measures -- 4.6 Stochastic Noise -- 4.7 Conclusion and Directions for Future Research -- 4.8 Appendix: Proofs of theorems and lemmas -- References.

Chapter 5 DEA Models with Production Trade-offs and Weight Restrictions -- 5.1 Introduction -- 5.2 Production Trade-offs -- 5.3 Illustrative Example -- 5.3.1 Undergraduate and Master Students -- 5.3.2 Research Staff and Publications -- 5.3.3 Academic Staff and Students -- 5.3.4 Students and Publications -- 5.3.5 Computational Results -- 5.4 Graphical Illustrations -- 5.5 CRS and VRS Technology with Production Trade-offs -- 5.5.1 Axiomatic Definitions -- 5.5.2 Some Properties of CRS and VRS Technologies with Trade-offs -- 5.6 Weight Restrictions and the Infeasibility Problem -- 5.6.1 Definitions and Examples -- 5.6.2 Theoretical Results -- 5.6.3 Free Production with Not Linked Trade-offs -- 5.6.4 Free Production with Linked Trade-offs -- 5.7 Solving DEA Models with Production Trade-offs -- 5.7.1 Stage 1: Assessing the Radial Efficiency -- 5.7.2 Stage 2: Identifying Efficient Targets -- 5.7.3 Stage 3: Identifying Reference Sets of Efficient Peer Units -- 5.8 Conclusion -- References -- Chapter 6 Facet Analysis in Data Envelopment Analysis -- 6.1 Introduction -- 6.2 Primal and Dual Description of the Production Possibility Set TCCR -- 6.3 Primal and Dual Description of the Production Possibility Set TBCC -- 6.4 Interior and Exterior Facets -- 6.5 Procedures for Identification of the Total Set of FDEFs -- 6.5.1 Convex Hull Generation -- 6.6 An Efficiency Evaluation Relative to a Technology Spanned by FDEFs -- 6.6.1 The CRS Case: Extending the CCR-Model with Facet Extensions -- 6.6.2 The VRS Case: Extending the BCC-Model with Facet Extensions -- 6.7 Use of Efficient Faces and Facets in DEA -- References -- Chapter 7 Stochastic Nonparametric Approach to Efficiency Analysis: A Unified Framework -- 7.1 Introduction -- 7.2 Unified Frontier Model -- 7.3 Convex Nonparametric Least Squares -- 7.3.1 CNLS Estimator for the Observed Data Points.

7.3.2 Extrapolating to Unobserved Points -- 7.3.3 Computational Issues -- 7.4 Deterministic Frontiers -- 7.4.1 DEA as Sign-Constrained CNLS -- 7.4.2 Corrected CNLS -- 7.5 Stochastic Nonparametric Envelopment of Data (StoNED) -- 7.5.1 Step 1: CNLS Regression -- 7.5.2 Step 2: Estimation of the Expected Inefficiency -- 7.5.2.1 Method of Moments -- 7.5.2.2 Quasi-likelihood Estimation -- 7.5.2.3 Nonparametric Kernel Density Estimation for the Convoluted Residual -- 7.5.3 Step 3: Estimating the Frontier Production Function -- 7.5.4 Step 4: Estimating Firm-Specific Inefficiencies -- 7.5.5 Statistical Specification Tests of the Frontier Model -- 7.6 Extensions -- 7.6.1 Multiplicative Composite Error Term -- 7.6.2 Panel Data -- 7.6.3 Multiple Outputs (DDF Formulation) -- 7.6.4 Convex Nonparametric Quantile Regression and Asymmetric Least Squares -- 7.7 Contextual Variables -- 7.7.1 Two-Stage DEA -- 7.7.2 One-Stage DEA -- 7.7.3 StoNED With z-Variables (StoNEZD) -- 7.8 Heteroscedasticity -- 7.8.1 White Test of Heteroscedasticity Applied to CNLS -- 7.8.2 Doubly-Heteroscedastic Model -- 7.8.3 Stepwise StoNED Estimation Under Heteroscedasticity -- 7.9 Directions for Future Research -- References -- Chapter 8 Translation Invariance in Data Envelopment Analysis -- 8.1 Introduction -- 8.2 Translation Invariance for Dealing with Data Which Have Value Zero -- 8.3 Translation Invariant Models for Dealing with Non-Positive Data -- 8.4 Non-Translation Invariant Models for Dealing with Negative Data -- 8.5 The Linear Loss Distance Function Model and the Property of Translation Invariance -- 8.6 Conclusions -- References -- Chapter 9 Scale Elasticity in Non-parametric DEA Approach -- 9.1 Introduction -- 9.2 Technology Specification and Scale Elasticity -- 9.2.1 Technology -- 9.2.2 Primal Measure of Scale Elasticity -- 9.2.3 Dual Measure of Scale Elasticity.

9.2.4 Scale Elasticity in DEA Models -- 9.2.4.1 Scale Elasticity in Production DEA Models -- 9.2.4.2 Scale Elasticity in Multiplicative DEA Model -- 9.2.4.3 Scale Elasticity in Production DEA Models with Indivisibilities -- 9.2.4.4 Scale Elasticity in Cost DEA Models -- 9.2.4.5 Scale Elasticity in Alternative Cost DEA Model -- 9.3 Concluding Remarks -- References -- Chapter 10 DEA Based Benchmarking Models -- 10.1 Introduction -- 10.2 Context-Dependent Data Envelopment Analysis -- 10.2.1 Stratification DEA Model -- 10.2.2 Attractiveness and Progress -- 10.2.3 Output Oriented Context-Dependent DEA Model -- 10.2.4 Context-Dependent DEAWith Value Judgment -- 10.3 Variable and Fixed Benchmarking Models -- 10.3.1 Variable-Benchmark Model -- 10.3.2 Fixed-Benchmark Model -- 10.4 Concluding Remarks -- References -- Chapter 11 Data Envelopment Analysis with Non-Homogeneous DMUs -- 11.1 Introduction -- 11.2 Manufacturing Plants with Variable Output Sets -- 11.3 A DEA Model for DMUs with Variable Output Sets -- 11.4 AR Restrictions on Pairs of Input Variables -- 11.5 Other Considerations -- 11.6 Application -- 11.7 Conclusions -- 11.8 Appendix 1: Generating the Maximal Output Groupings -- 11.9 Appendix 2: Generating a Single Set of AR Constraints -- 11.10 Appendix 3: Tables -- References -- Chapter 12 Efficiency Measurement in Data Envelopment Analysis with Fuzzy Data -- 12.1 Introduction -- 12.2 The Problem -- 12.3 The Membership Grade Approach -- 12.4 The α-cut Approach -- 12.5 Discussion and Conclusion -- References -- Chapter 13 Partial Input to Output Impacts in DEA: Production Considerations and Resource Sharing Among Business Sub-Units -- 13.1 Introduction -- 13.2 Efficiency Measurement in Steel Fabrication Plants -- 13.3 Modeling Efficiency in the Presence of Partial Input to Output Interactions -- 13.4 AR Restrictions on Pairs of Input Variables.

13.5 Other Considerations -- 13.6 Application -- 13.7 Discussion and Conclusions -- 13.8 Appendix 1: Proofs of Theorems -- 13.9 Appendix 2: Algorithms -- 13.10 Appendix 3: Tables -- References -- Chapter 14 Super-Efficiency in Data Envelopment Analysis -- 14.1 Introduction -- 14.2 Infeasibility -- 14.3 Alternative VRS Super-Efficiency Models -- 14.3.1 Equivalent Standard Super-Efficiency Models (Lovell and Rouse 2003) -- 14.3.2 Super-Efficiency Based on Efficient Projections (Chen 2004, 2005) -- 14.3.3 A Modified Super-Efficiency Measure (Cook et al. 2009) -- 14.3.4 Two-Stage Procedure (Lee et al. 2011) and Its One Model Approach (Chen and Liang 2011) -- 14.3.5 DDF-Based Super-Efficiency and SBM Super-Efficiency -- 14.3.6 A Numerical Example for Comparison -- 14.4 Slacks-Based Super-Efficiency -- 14.4.1 SBM Super-Efficiency -- 14.4.2 Additive Super-Efficiency -- 14.4.3 A Numerical Example -- 14.5 DDF-Based Super-Efficiency -- 14.5.1 N-L Super-Efficiency -- 14.5.2 Modified DDF-Based Super-Efficiency -- 14.6 Integer Super-Efficiency -- 14.6.1 Integer-Valued Additive Super-Efficiency -- 14.6.2 Additive Super-Efficiency for Undesirable Integer-Restricted Data -- 14.6.3 DDF-Based Integer Super-Efficiency -- 14.7 Conclusions -- References -- Chapter 15 DEA Models with Undesirable Inputs, Intermediates, and Outputs -- 15.1 Introduction -- 15.2 Single-Stage DEA Models with Undesirable Variables -- 15.2.1 Desirability and Disposability -- 15.2.1.1 Desirability Determination -- 15.2.1.2 Disposability Assumptions in DEA -- 15.2.2 DEA Models with Undesirable Inputs/Outputs for Single-Stage Systems -- 15.3 Two-Stage DEA Models with Undesirable Variables -- 15.3.1 Desirability of Inputs and Outputs in Two-Stage Systems -- 15.3.2 Production Possibility Sets of Two-Stage Systems with Undesirable Variables -- 15.3.3 Two-Stage DEA Models with Undesirable Variables.

15.4 Conclusions.

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