Introduction to Data Envelopment Analysis and Its Uses : With DEA-Solver Software and References,9780387285801

Introduction to Data Envelopment Analysis and Its Uses : With DEA-Solver Software and References

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ISBN13: 9780387285801
ISBN10: 0387285806
Format: Paperback
Pub. Date: 2006-01-31
Publisher(s): Springer Verlag
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Summary

Recent years have seen a great variety of applications of DEA (Data Envelopment Analysis) for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. One reason is that DEA has opened up possibilities for use in cases which have been resistant to other approaches because of the complex (often unknown) nature of the relations between multiple inputs and multiple outputs involved in many of these activities (which are often reported in non-commeasurable units). Examples include the maintenance activities of U.S. Air Force bases in different geographic locations, or police forces in England and Wales as well as performances of branch banks in Cyprus and Canada and the efficiency of universities in performing their education and research functions in the U.S., England, and France. These kinds of applications extend to evaluating the performance of cities, regions and countries with many different kinds of inputs and outputs that include "social" and "safety-net" expenditures as inputs and various "quality-of-life" dimensions as outputs which, in turn, have led to dealing with important issues such as identifying sites for new locations (away from Tokyo) for the capital of Japan.Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References has been carefully designed by the authors to provide a systematic introduction to DEA and its uses as a multifaceted tool for evaluating problems in a variety of contexts. The authors have been involved in DEA's development from the beginning. William Cooper (with Abraham Charnes and Edwardo Rhodes) is a founder of DEA. Lawrence Seiford and Kaoru Tone have been actively involved as researchers and practitioners from its earliest beginnings. All have been deeply involved in uses of DEA in practical applications as well as in the development of its basic theory and methodologies. The result is a textbook grounded in authority, experience and substance.

Table of Contents

List of Tables
xiii
List of Figures
xvii
Preface xix
General Discussion
1(20)
Introduction
1(1)
Single Input and Single Output
2(4)
Two Inputs and One Output Case
6(2)
One Input and Two Outputs Case
8(4)
Fixed and Variable Weights
12(1)
Summary and Conclusion
13(2)
Problem Supplement for Chapter 1
15(6)
Basic CCR Model
21(20)
Introduction
21(1)
Data
22(1)
The CCR Model
23(1)
From a Fractional to a Linear Program
23(2)
Meaning of Optimal Weights
25(1)
Explanatory Examples
25(5)
Example 2.1 (1 Input and 1 Output Case)
26(1)
Example 2.2 (2 Inputs and 1 Output Case)
27(3)
Illustration of Example 2.2
30(2)
Summary of Chapter 2
32(1)
Selected Bibliography
33(1)
Problem Supplement for Chapter 2
34(7)
CCR Model and Production Correspondence
41(42)
Introduction
41(1)
Production Possibility Set
42(1)
The CCR Model and Dual Problem
43(4)
The Reference Set and Improvement in Efficiency
47(1)
Theorems on CCR-Efficiency
48(2)
Computational Aspects of the CCR Model
50(3)
Computational Procedure for the CCR Model
50(2)
Data Envelopment Analysis and the Data
52(1)
Determination of Weights (=Multipliers)
52(1)
Reasons for Solving the CCR Model Using the Envelopment Form
52(1)
Example
53(5)
The Output-Oriented Model
58(2)
Discretionary and Non-Discretionary Inputs
60(4)
Summary of Chapter 3
64(1)
Notes and Selected Bibliography
65(2)
Related DEA-Solver Models for Chapter 3
67(1)
Problem Supplement for Chapter 3
68(15)
Alternative Dea Models
83(36)
Introduction
83(2)
The BCC Models
85(5)
The BCC Model
87(2)
The Output-oriented BCC Model
89(1)
The Additive Model
90(5)
The Basic Additive Model
90(3)
Translation Invariance of the Additive Model
93(2)
A Slacks-Based Measure of Efficiency (SBM)
95(7)
Definition of SBM
96(1)
Interpretation of SBM as a Product of Input and Output Inefficiencies
97(1)
Solving SBM
97(2)
SBM and the CCR Measure
99(1)
The Dual Program of the SBM Model
100(1)
Oriented SBM Models
101(1)
A Weighted SBM Model
101(1)
Numerical Example (SBM)
102(1)
Russell Measure Models
102(2)
Summary of the Basic DEA Models
104(2)
Summary of Chapter 4
106(1)
Notes and Selected Bibliography
107(1)
Appendix: Free Disposal Hull (FDH) Models
107(2)
Related DEA-Solver Models for Chapter 4
109(1)
Problem Supplement for Chapter 4
110(9)
Returns to Scale
119(46)
Introduction
119(3)
Geometric Portrayals in DEA
122(2)
BCC Returns to Scale
124(2)
CCR Returns to Scale
126(5)
Most Productive Scale Size
131(4)
Further Considerations
135(3)
Relaxation of the Convexity Condition
138(2)
Decomposition of Technical Efficiency
140(4)
Scale Efficiency
140(2)
Mix Efficiency
142(1)
An Example of Decomposition of Technical Efficiency
143(1)
An Example of Returns to Scale Using a Bank Merger Simulation
144(6)
Background
144(1)
Efficiencies and Returns to Scale
144(3)
The Effects of a Merger
147(3)
Summary
150(1)
Additive Models
150(3)
Multiplicative Models and ``Exact'' Elasticity
153(5)
Summary of Chapter 5
158(1)
Appendix: FGL Treatment and Extensions
159(1)
Related DEA-Solver Models for Chapter 5
160(1)
Problem Supplement for Chapter 5
161(4)
Models with Restricted Multipliers
165(38)
Introduction
165(1)
Assurance Region Method
166(7)
Formula for the Assurance Region Method
166(3)
General Hospital Example
169(2)
Change of Efficient Frontier by Assurance Region Method
171(1)
On Determining the Lower and Upper Bounds
172(1)
Another Assurance Region Model
173(1)
Cone-Ratio Method
174(3)
Polyhedral Convex Cone as an Admissible Region of Weights
174(1)
Formula for Cone-Ratio Method
175(1)
A Cone-Ratio Example
176(1)
How to Choose Admissible Directions
177(1)
An Application of the Cone-Ratio Model
177(5)
Negative Slack Values and Their Uses
182(2)
A Site Evaluation Study for Relocating Japanese Government Agencies out of Tokyo
184(9)
Background
184(1)
The Main Criteria and their Hierarchy Structure
185(1)
Scores of the 10 Sites with respect to the 18 Criteria
186(1)
Weights of the 18 Criteria by the 18 Council Members (Evaluators)
187(2)
Decision Analyses using Averages and Medians
189(1)
Decision Analyses using the Assurance Region Model
189(1)
Evaluation of ``Positive'' of Each Site
190(1)
Evaluation of ``Negative'' of Each Site
190(1)
Uses of ``Positive'' and ``Negative'' Scores
191(1)
Decision by the Council
191(1)
Concluding Remarks
192(1)
Summary of Chapter 6
193(1)
Notes and Selected Bibliography
194(1)
Related DEA-Solver Models for Chapter 6
194(1)
Problem Supplement for Chapter 6
195(8)
Non-Discretionary and Categorical Variables
203(42)
Introduction
203(2)
Examples
205(2)
Non-controllable, Non-discretionary and Bounded Variable Models
207(8)
Non-controllable Variable (NCN) Model
207(1)
An Example of a Non-Controllable Variable
208(2)
Non-discretionary Variable (NDSC) Model
210(2)
Bounded Variable (BND) Model
212(1)
An Example of the Bounded Variable Model
212(3)
DEA with Categorical DMUs
215(4)
An Example of a Hierarchical Category
215(1)
Solution to the Categorical Model
216(1)
Extension of the Categorical Model
217(2)
Comparisons of Efficiency between Different Systems
219(2)
Formulation
219(1)
Computation of Efficiency
220(1)
Illustration of a One Input and Two Output Scenario
220(1)
Rank-Sum Statistics and DEA
221(7)
Rank-Sum-Test (Wilcoxon-Mann-Whitney)
222(1)
Use of the Test for Comparing the DEA Scores of Two Groups
223(1)
Use of the Test for Comparing the Efficient Frontiers of Two Groups
224(1)
Bilateral Comparisons Using DEA
224(1)
An Example of Bilateral Comparisons in DEA
225(1)
Evaluating Efficiencies of Different Organization Forms
226(2)
Summary of Chapter 7
228(1)
Notes and Selected Bibliography
228(1)
Related DEA-Solver Models for Chapter 7
228(2)
Problem Supplement for Chapter 7
230(15)
Allocation Models
245(26)
Introduction
245(1)
Overall Efficiency with Common Prices and Costs
246(4)
Cost Efficiency
246(2)
Revenue Efficiency
248(1)
Profit Efficiency
248(1)
An Example
249(1)
New Cost Efficiency under Different Unit Prices
250(7)
A New Scheme for Evaluating Cost Efficiency
250(2)
Differences Between the Two Models
252(1)
An Empirical Example
253(2)
Extensions
255(2)
Decomposition of Cost Efficiency
257(3)
Loss due to Technical Inefficiency
257(1)
Loss due to Input Price Inefficiency
258(1)
Loss due to Allocative Inefficiency
259(1)
Decomposition of the Actual Cost
259(1)
An Example of Decomposition of Actual Cost
260(1)
Summary of Chapter 8
260(1)
Notes and Selected Bibliography
261(1)
Related DEA-Solver Models for Chapter 8
262(2)
Problem Supplement for Chapter 8
264(7)
Data Variations
271(30)
Introduction
271(1)
Sensitivity Analysis
271(8)
Degrees of Freedom
271(1)
Algorithmic Approaches
272(1)
Metric Approaches
272(3)
Multiplier Model Approaches
275(4)
Statistical Approaches
279(7)
Chance-Constrained Programming and Satisficing in DEA
286(6)
Introduction
286(1)
Satisficing in DEA
286(1)
Deterministic Equivalents
287(3)
Stochastic Efficiency
290(2)
Window Analysis
292(4)
An Example
292(1)
Application
293(2)
Analysis
295(1)
Summary of Chapter 9
296(1)
Related DEA-Solver Models for Chapter 9
297(4)
Super-Efficiency Models
301(44)
Introduction
301(1)
Radial Super-efficiency Models
302(3)
Non-radial Super-efficiency Models
305(4)
Definition of Non-radial Super-efficiency Measure
306(1)
Solving Super-efficiency
307(1)
Input/Output-Oriented Super-efficiency
308(1)
An Example of Non-radial Super-efficiency
308(1)
Extensions to Variable Returns-to-Scale
309(2)
Radial Super-efficiency Case
309(1)
Non-radial Super-efficiency Case
310(1)
Summary of Chapter 10
311(1)
Notes and Selected Bibliography
311(1)
Related DEA-Solver Models for Chapter 10
311(1)
Problem Supplement for Chapter 10
312(3)
Appendices
Linear Programming and Duality
315(11)
Linear Programming and Optimal Solutions
315(1)
Basis and Basic Solutions
315(1)
Optimal Basic Solutions
316(1)
Dual Problem
317(1)
Symmetric Dual Problems
318(1)
Complementarity Theorem
319(1)
Farkas' Lemma and Theorem of the Alternative
320(1)
Strong Theorem of Complementarity
321(2)
Linear Programming and Duality in General Form
323(3)
Introduction to DEA-Solver
326(17)
Platform
326(1)
Installation of DEA-Solver
326(1)
Notation of DEA Models
326(1)
Included DEA Models
327(1)
Preparation of the Data File
327(1)
The CCR, BCC, IRS, DRS, GRS, SBM, Super-Efficiency and FDH Models
328(1)
The AR Model
329(1)
The ARG Model
330(1)
The NCN and NDSC Models
331(1)
The BND Model
332(1)
The CAT, SYS and Bilateral Models
332(1)
The Cost and New-Cost Models
333(1)
The Revenue and New-Revenue Models
334(1)
The Profit, New-Profit and Ratio Models
334(1)
The Window Models
334(1)
Weighted SBM Model
335(1)
Starting DEA-Solver
336(1)
Results
336(4)
Data Limitations
340(1)
Problem Size
340(1)
Inappropriate Data for Each Model
340(2)
Sample Problems and Results
342(1)
Summary of Headings to Inputs/Outputs
342(1)
Bibliography
343(2)
Author Index 345(2)
Topic Index 347

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