Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software: Second edition

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software: Second Edition

Volumn , Issue , 2007, Pages 1-490

  Cooper, William W ^a   Seiford, Lawrence M ^b   Tone, Kaoru ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b University of IVIichigan   (United States)

^c NATIONAL GRADUATE INSTITUTE FOR POLICY STUDIES   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891424949     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-0-387-45283-8     Document Type: Book

References (325)

1. This example is taken from A. Charnes, W. W. Cooper and E. Rhodes, "Measuring the Efficiency of Decision Making Units", European Journal of Operational Research 2, 1978, pp. 429-444.
2. Our measures of distance and their uses are related to each other and discussed in W. W. Cooper, L. M. Seiford, K. Tone and J. Zhu "Some Models and Measures for Evaluating Performances with DEA: Past Accomplishments and Future Prospects", Journal of Productivity Analysis (forthcoming).
3. nd ed. (New York. W. W. Norton & Co., 1984.)
4. th Edition (Englewood Cliffs, N. J., Prentice-Hall, Inc., 1981.)
5. After Charnes, Cooper and Rhodes (1978) above.
6. See H. D. Sherman, "Measurement of Hospital Technical Efficiency: A Comparative Evaluation of Data Envelopment Analysis and Other Techniques for Measuring and Locating Efficiency in Health Care Organizations", Ph. D. Thesis (Boston: Harvard University Graduate School of Business, 1981.) Also available from University Microfilms, Inc., Ann Arbor, Michigan.
7. A. Charnes, W. W. Cooper and E. Rhodes (1978), "Measuring the Efficiency of Decision Making Units", European Journal of Operational Research 2, pp. 429-444.
8. A. Charnes, W. W. Cooper and E. Rhodes (1978), "A Data Envelopment Analysis Approach to Evaluation of the Program Follow Through Experiments in U. S. Public School Education", Management Science Research Report No. 432, Carnegie-Mellon University, School of Urban and Public Affairs, Pittsburgh, PA.
9. E. L. Rhodes (1978), "Data Envelopment Analysis and Related Approaches for Measuring the Efficiency of Decision-Making Units with an Application to Program Follow Through in U. S. Education", unpublished Ph. D. thesis, Carnegie-Mellon University, School of Urban and Public Affairs, Pittsburgh, PA.
10. A. Charnes, W. W. Cooper and E. Rhodes (1979), "Short Communication: Measuring the Efficiency of Decision Making Units", European Journal of Operational Research 3, p. 339.
11. A. Charnes, W. W. Cooper and E. Rhodes (1981), "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through", Management Science 27, pp. 668-697.
12. A. Charnes and W. W. Cooper (1985), "Preface to Topics in Data Envelopment Analysis", Annals of Operations Research 2, pp. 59-94
13. S. Bulla, W. W. Cooper, K. S. Park and D. Wilson (2000), Journal of Propulsion and Power 16, pp. 431-439.
14. See Research Report CCS 532 (Austin, Texas: University of Texas at Austin, Graduate School of Business, 1986) "Data Envelopment Analysis Approaches to Policy Evaluation and Management of Army Recruiting Activities I: Tradeoff between Joint Service and Army Advertising" by A. Charnes, W. W. Cooper, B. Golany, Major R. Halek, G. Klopp, E. Schmitz and Captain D. Thomas.
15. Farrell also restricted his treatments to the single output case. See M. J. Farrell (1957), "The Measurement of Production Efficiency", Journal of the Royal Statistical Society A, 120, pp. 253-281.
16. In the linear programming literature this is called the "complementary slackness" condition. This terminology is given by A. W. Tucker who is responsible for formulating and proving this. See E. D. Nering and A. W. Tucker Linear Programs and Related Problems, (Harcourt Brace, 1993).
17. Although empirical studies show the uniqueness of the reference set for most DMUs, there may be multiple reference sets and improvement plans (projections) in the existence of multiple optimal solutions.
18. K. Tone "An Extension of the Two Phase Process in the CCR Model", in Proceedings of the 1999 Fall National Conference of the Operations Research Society of Japan.
19. T. Coelli (1998), "A Multi-stage Methodology for the Solution of Oriented DEA Models", Operations Research Letters 22, pp. 143-149.
20. "Aborts" were treated as reciprocals so that an increase in their output would reduce the value of the numerator in the (FP0) objective represented in (2.3). They could also have been subtracted from a dominatingly large positive constant. See A. Charnes, T. Clark, W. W. Cooper and B. Golany "A Development Study of Data Envelopment Analysis in Measuring the Efficiency of Maintenance Units in the U. S. Air Forces", Annals of Operational Research 2, 1985, pp. 59-94.
21. R. D. Banker and R. C. Morey (1986), "Efficiency Analysis for Exogenously Fixed Inputs and Outputs", Operations Research 34, 1986, pp. 513-521. See also Chapter 10 in R. Fare, S. Grosskopf and C. A. Knox Lovell Production Frontiers (Cambridge University Press, 1994) where this is referred to as "sub-vector optimizations."
22. I. R. Bardhan (1995), "DEA and Stochastic Frontier Regression Approaches Applied to Evaluating Performances of Public Secondary Schools in Texas", Ph. D. Thesis. Austin Texas: Graduate School of Business, the University of Texas at Austin. Also available from University Microfilms, Inc. in Ann Arbor, Michigan.
23. V. L. Arnold, I. R. Bardhan and W. W. Cooper "A Two-Stage DEA Approach for Identifying and Rewarding Efficiency in Texas Secondary Schools" in W. W. Cooper, S. Thore, D. Gibson and F. Phillips, eds., IMPACT: How IC2 Research Affects Public Policy and Business Practices (Westport, Conn.: Quorum Books, 1997)
24. See Arnold et al. (1997) for further suggestions and discussions.
25. See Governmental Accounting Standards Board (GASB) Research Report: "Service Efforts and Accomplishments Reporting: Its Time Has Come", H. P. Hatry, J. M. Sullivan, J. M. Fountain and L. Kremer, eds. (Norwell, Conn., 1990).
26. C. A. K. Lovell, L. C. Walters and Lisa Wood, "Stratified Models of Education Production Using Modified DEA and Regression Analysis", in A. Charnes, W. W. Cooper, A. Y. Lewin and L. M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass.: Kluwer Academic Publishers, 1994).
27. W. W. Cooper (2005), "Origin, Uses of and Relations Between Goal Programming and DEA (Data Envelopment Analysis)", Journal of Multiple Criteria Decision Analysis (to appear).
28. R. D. Banker, A. Charnes and W. W. Cooper (1984) "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis", Management Science 30, pp. 1078-1092
29. SBM was first proposed by K. Tone (1997), "A Slacks-based Measure of Efficiency in Data Envelopment Analysis", Research Reports, Graduate School of Policy Science, Saitama University and subsequently published in European Journal of Operational Research 130(2001), pp. 498-509.
30. For a discussion of this constant-returns-to-scale Additive model see A. I. Ali and L. M. Seiford, "The Mathematical Programming Approach to Efficiency Measurement", in The Measurement of Productive Efficiency: Techniques and Applications, H. Fried, C. A. Knox Lovell, and S. Schmidt (editors), Oxford University Press, London, (1993).
31. T. Ahn, A. Charnes and W. W. Cooper (1988) "Efficiency Characterizations in Different DEA Models", Socio-Economic Planning Sciences, 22, pp. 253-257.
32. P. L. Brockett, W. W. Cooper, L. L. Golden, J. J. Rousseau and Y. Wang "DEA Evaluation of Organizational Forms and Distribution System in the U. S. Property and Liability Insurance Industry", International Journal of Systems Science, 1998.
33. A. I. Ali and L. M. Seiford (1990) "Translation Invariance in Data Envelopment Analysis", Operations Research Letters 9, pp. 403-405.
34. This term is taken from the literature on dimensional analysis. See pp. 123-125, in R. M. Thrall "Duality, Classification and Slacks in DEA" Annals of Operations Research 66, 1996.
35. See R. S. Färe and C. A. K. Lovell (1978) "Measuring the Technical Efficiency of Production", Journal of Economic Theory 19, pp. 150-162.
36. See also R. R. Russell (1985) "Measures of Technical Efficiency", Journal of Economic Theory 35, pp. 109-126.
37. "Hybrid" is proposed in K. Tone (2004), "A Hybrid Measure of Efficiency in DEA", GRIPS Research Report Series 1-2004-0003.
38. J. T. Pastor, J. L. Ruiz and I. Sirvent (1999), "An Enhanced DEA Russell Graph Efficiency Measure "European Journal of Operational Research 115, pp. 596-607.
39. R. S. Färe, S. Grosskopf and C. A. K Lovell (1985), The Measurement of Efficiency of Production Boston: Kluwer-Nijhoff.
40. I. Bardhan, W. F. Bowlin, W. W. Cooper and T. Sueyoshi (1996), "Models and Measures for Efficiency Dominance in DEA. Part II: Free Disposal Hull (FDI) and Russell Measure (RM) Approaches" Journal of the Operations Research Society of Japan 39, pp. 333-344.
41. See the paper by T. Ahm and L. M. Seiford "Sensitivity of DEA Results to Models and Variable Sets in a Hypothesis Test Setting: The Efficiency of University Operations" in Y. Ijiri, ed., Creative and Innovative Approaches to the Science of Management (New York: Quorum Books, 1993). In this paper Ahn and Seiford find that U. S. public universities are more efficient than private universities when student outputs are emphasized but the reverse is true when research is emphasized. The result, moreover, is found to be invariant over all of the DEA models used in this study. For "methods" cross-checking, C. A. K. Lovell, L. Walters and L. Wood compare statistical regressions with DEA results in "Stratified Models of Education Production Using Modified DEA and Regression Analysis", in Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass.: Kluwer Academic Publishers, 1994.)
42. J. T. Pastor (1996), "Translation Invariance in DEA: A Generalization", Annals of Operations Research 66, pp. 93-102.
43. R. M. Thrall (1996) "The Lack of Invariance of Optimal Dual Solutions Under Translation", Annals of Operations Research 66, pp. 103-108.
44. Deprins D., L. Simar and H. Tulkens (1984), "Measuring Labor Efficiency in Post Offices", in M. Marchand, P. Pestieau and H. Tulkens, eds. The Performance of Public Enterprises: Concepts and Measurement (Amsterdam, North Holland), pp. 243-267.
45. in C. A. K. Lovell "Linear Programming Approaches to the Measurement and Analysis of Productive Efficiency", TOP 2, 1994, pp. 175-243.
46. Bowlin, W. F., J. Brennan, A. Charnes, W. W. Cooper and T. Sueyoshi (1984), "A Model for Measuring Amounts of Efficiency Dominance", Research Report, The University of Texas at Austin, Graduate School of Business.
47. See also Bardhan I., W. F. Bowlin, W. W. Cooper and T. Sueyoshi "Models and Measures for Efficiency Dominance in DEA", Journal of the Operations Research Society of Japan 39, 1996, pp. 322-332.
48. R. M. Thrall (1999), "What is the Economic Meaning of FDH?" Journal of Productivity Analysis, 11, pp. 243-250.
49. R. D. Banker and R. M. Thrall (1992) "Estimating Most Productive Scale Size Using Data Envelopment Analysis", European Journal of Operational Research 62, pp. 74-84.
50. R. D. Banker, I. Bardhan and W. W. Cooper (1996) "A Note on Returns to Scale in DEA", European Journal of Operational Research 88, pp. 583-585.
51. R. D. Banker, H. Chang and W. W. Cooper (1996) "Equivalence and Implementation of Alternative Methods for Determining Returns to Scale in Data Envelopment Analysis", European Journal of Operational Research 89, pp. 473-481.
52. R. D. Banker and R. Morey (1986) "Efficiency Analysis for Exogenously Fixed Inputs and Outputs" Operations Research 34, pp. 513-521.
53. T. Ahn, A. Charnes and W. W. Cooper (1989), "A Note on the Efficiency Characterizations Obtained in Different DEA Models", Socio-Economic Planning Sciences 22, pp. 253-257.
54. See R. D. Banker (1984), "Estimating Most Productive Scale Size Using Data Envelopment Analysis", European Journal of Operational Research 17, pp. 35-44.
55. See also R. D. Banker, A. Charnes and W. W. Cooper (1984), "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis", Management Science 30, pp. 1078-1092.
56. A brief review of the history of this and related concepts is to be found in F. R. Førsund - "On the Calculation of the Scale Elasticity in DEA Models", Journal of Productivity Analysis 7, 1996, pp. 283-302 - who traces the idea of a technically optimal scale to R. Frisch's classical volume, Theory of Production (Dordrecht: D. Reidel, 1965).
57. See also L. M. Seiford and J. Zhu (1999) "An Investigation of Returns to Scale in Data Envelopment Analysis", Omega 27, pp. 1-11.
58. This transformation is done explicitly in the Appendix to W. W. Cooper, R. G. Thompson and R. M. Thrall (1996) "Extensions and New Developments in DEA", Annals of Operations Research 66, pp. 3-45.
59. K. Tone (1996) "A Simple Characterization of Returns to Scale in DEA" Journal of the Operations Research Society of Japan 39, pp. 604-613.
60. R. M. Thrall (1996a), "Duality, Classification and Slacks in DEA", Annals of Operations Research 66, pp. 109-138.
61. W. W. Cooper, K. S. Park and J. T. Pastor (1999), "RAM: A Range Adjusted Measure of Efficiency", Journal of Productivity Analysis 11, pp. 5-42.
62. R. M. Thrall (1996b), "The Lack of Invariance of Optimal Dual Solutions under Translation Invariance", Annals of Operations Research 66, pp. 109-138.
63. R. D. Banker, A. Charnes and W. W. Cooper (1984), "Some Models for Estimating Technical and Scale Efficiencies in Data Envelopment Analysis", Management Science 30, pp. 1078-1092.
64. F. R. Førsund (1996), "On the Calculation of Scale Elasticities in DEA Models", Journal of Productivity Analysis 7, pp. 283-302.
65. R. D. Banker and R. M. Thrall (1992), "Estimation of Returns to Scale Using Data Envelopment Analysis", European Journal of Operational Research 62, pp. 74-84.
66. R. Färe, S. Grosskopf and C. A. K. Lovell (1985), The Measurement of Efficiency of Production, Boston: Kluwer Nijhoff. Publishing Co., and Production Frontiers, Cambridge University Press.
67. H. Fukuyama (2000), "Returns to Scale and Scale Elasticity in Data Envelopment Analysis", European Journal of Operational Research 125, pp. 93-112.
68. J. C. Panzar and R. D. Wiliig (1977), "Economies of Scale in Multi-Output Production", Quarterly Journal of Economics XLI, pp. 481-493.
69. W. J. Baumol, J. C. Panzar and R. D. Willig (1982), Contestable Markets, New York: Harcourt Brace Jovanovich.
70. A. Charnes, W. W. Cooper, L. M. Seiford and J. Stutz (1982), "A Multiplicative Model for Efficiency Analysis", Socio-Economic Planning Sciences 16, pp. 213-224.
71. R. D. Banker, A. Charnes, W. W. Cooper and A. Schinnar (1981), "A Bi-Extremal Principle for Frontier Estimation and Efficiency Evaluation", Management Science 27, pp. 1370-1382.
72. A. Charnes, W. W. Cooper, L. M. Seiford and J. Stutz (1983), "Invariant Multiplicative Efficiency and Piecewise Cobb-Douglas Envelopments", Operations Research Letters 2, pp. 101-103.
73. R. D. Banker and A. Maindiratta (1986), "Piecewise Loglinear Estimation of Efficient Production Surfaces", Management Science 32, pp. 126-135.
74. R. D. Banker, W. W. Cooper, L. M. Seiford, R. M. Thrall and J. Zhu (2003), "Returns to Scale In Different DEA Models", European Journal of Operational Research (to appear).
75. W. W. Cooper, R. G. Thompson and R. M. Thrall (1996), "Extensions and New Developments in DEA, Appendix", The Annals of Operations Research 66, pp. 3-45.
76. H. Varian (1984), Microeconomic Analysis, New York: W. W. Norton.
77. R. D. Banker and R. Morey (1986), "Efficiency Analysis for Exogenously Fixed Inputs and Outputs", Operations Research 34, pp. 513-521.
78. K. Tone (2001), "On Returns to Scale under Weight Restrictions in Data Envelopment Analysis", Journal of Productivity Analysis 16, pp. 31-47.
79. T. Sueyoshi (1999), "DEA Duality on Returns to Scale (RTS) in Production and Cost Analyses: An Occurrence of Multiple Solutions and Differences between Production-based and Cost-based RTS Estimates", Management Science 45, 1593-1608.
80. K. Tone and B. K. Sahoo (2005), "Cost-Elasticity: A Re-Examination in DEA", Annals of Operations Research (forthcoming).
81. S. Ray (2005), "Are Some Indian Banks too Large? An Examination of Size Efficiency in Indian Banking", Journal of Productivity Analysis (forthcoming).
82. A. Maindiratta (1990), "Scale and Size Efficiencies of Decision Making Units in Data Envelopment Analysis", Journal of Econometrics 46, pp. 39-56.
83. P. Bogetoft and D. Wang (2005), "Estimating the Potential Gains from Mergers", Journal of Productivity Analysis 23, pp. 145-171.
84. J. Zhu and Z. Shen (1995), "A Discussion of Testing DMU's Returns to Scale", European Journal of Operational Research 81, pp. 590-596.
85. L. M. Seiford and J. Zhu (1999), "An Investigation of Returns to Scale under Data Envelopment Analysis", Omega 27, pp. 1-11.
86. J. Zhu (2002), Quantitative Models for Performance Evaluation and Benchmarking: Data Envelopment Analysis with Spreadsheets and DEA Excel Solver, Kluwer Academic Publishers, Boston.
87. R. D. Banker, W. W. Cooper, L. M. Seiford, R. M. Thrall and J. Zhu, "Returns to scale in different DEA models", European Journal of Operational Research (2004), 154, pp. 345-362.
88. R. G. Thompson, F. D. Singleton, Jr., R. M. Thrall and B. A. Smith (1986), "Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas", Interfaces 16, pp. 35-49.
89. See also R. G. Dyson and E. Thanassoulis (1988), "Reducing Weight Flexibility in Data Envelopment Analysis", Journal of the Operational Research Society, 39, pp. 563-576. Finally, see Notes and Selected Bibliography in Section 6.9 of this chapter for references on uses of DEA for site selection.
90. A. Charnes, W. W. Cooper, Z. M. Huang and D. B. Sun (1990), "Polyhedral Cone-Ratio DEA Models with an Illustrative Application to Large Commercial Banks", Journal of Econometrics 46, pp. 73-91.
91. For a treatment that studies this approach as an alternative to the more rigid approach to risk evaluation under the "Basel Agreement" for controlling risks in bank portfolios see P. L. Brockett, A. Charnes, W. W. Cooper, Z. M. Huang and D. B. Sun, "Data Transformations in DEA Cone-Ratio Approaches for Monitoring Bank Performance", European Journal of Operational Research, 98, 1997, pp. 250-268.
92. Y. Roll, W. D. Cook and B. Golany (1991), "Controlling Factor Weights in Data Envelopment Analysis", IIE Transactions 23, pp. 2-9.
93. R. Allen, A. Athanassopoulos, R. G. Dyson and E. Thanassoulis (1997), "Weights restrictions and value judgements in data envelopment analysis", Annals of Operations Research 73, pp. 13-34.
94. P. L. Brockett, A. Charnes, W. W. Cooper, Z. Huang and D. B. Sun (1997), "Data Transformations in DEA Cone Ratio Envelopment Approaches for Monitoring Bank Performance", European Journal of Operational Research 98, pp. 250-268.
95. For detailed discussions see the references cited in Brockett et al. (1997).
96. R. S. Barr, L. M. Seiford and T. F. Siems (1994), "Forcasting Bank Failure: A Non-Parametric Frontier Estimation Approach", Recherches Economiques de Louvain 60, pp. 417-429
97. and R. S. Barr, L. M. Seiford and T. F. Siems (1993), "An Envelopment-Analysis Approach to Measuring the Managerial Efficiency of Banks", Annals of Operations Research, 45, pp. 1-19 for details.
98. th Edition (Englewood Cliffs, N. J., Prentice-Hall Inc., 1983.)
99. R. M. Nun (1989), "Bank Failure: The Management Factor" (Austin, TX., Texas Department of Banking).
100. See A. Ben Israel and T. N. Greville, Generalized Inverses (New York, John Wiley & Sons Inc., 1974).
101. Y. Takamura and K. Tone (2003), "A Comparative Site Evaluation Study for Relocating Japanese Government Agencies out of Tokyo", Socio-Economic Planning Sciences 37, pp. 85-102.
102. AHP (Analytic Hierarchy Process) was invented by T. L. Saaty (1980), Analytic Hierarchy Process, New York: McGraw-Hill. See also K. Tone (1989), "A Comparative Study on AHP and DEA", International Journal of Policy and Information 13, pp. 57-63.
103. See J. A. Dewar and J. A. Friel (2001), "Delphi Method", in S. I. Gass and CM. Harris, eds., Encyclopedia of Operations Research and Management Science (Norwell, Mass., Kluwer Academic Publishers) pp. 208-209.
104. Y. Yamada, T. Matsui and M. Sugiyama (1994), "An Inefficiency Measurement Method for Management Systems", Journal of the Operations Research Society of Japan 37, 2, pp. 158-167.
105. R. G. Thompson, L. N Langemeir, C. Lee, E. Lee and R. M. Thrall (1990), "The Role of Multiplier Bounds in Efficiency Analysis with Application to Kansas Farming", Journal of Econometrics 46, pp. 93-108.
106. Y. Roll and B. Golany (1993), "Alternate Methods of Treating Factor Weights in DEA", OMEGA 21, pp. 99-109.
107. R. G. Dyson and E. Thanassoulis (1988), "Reducing Weight Flexibility in Data Envelopment Analysis", Journal of the Operational Research Society 39, pp. 563-576.
108. A. D. Athanassopoulos and J. E. Storbeck (1995), "Non-Parametric Models for Spatial Efficiency", The Journal of Productivity Analysis 6, pp. 225-245.
109. A. Desai, K. Haynes and J. E. Storbeck "A Spatial Efficiency Framework for the Support of Locational Decisions", in Data Envelopment Analysis: Theory, Methodology, and Applications, A. Charnes, W. W. Cooper, Arie Y. Lewin, and Lawrence M. Seiford (editors), Kluwer Academic Publishers, Boston, 1994.
110. D. B. Sun (1988), "Evaluation of Managerial Performance in Large Commercial Banks by Data Envelopment Analysis", Ph. D. dissertation, Graduate School of Business, University of Texas, Austin, TX.
111. A. Charnes, W. W. Cooper, Q. L. Wei and Z. M. Huang (1989), "Cone Ratio Data Envelopment Analysis and Multi-objective Programming", International Journal of Systems Science 20, pp. 1099-1118.
112. K. Tone (2001), "On Returns to Scale under Weight Restrictions in Data Envelopment Analysis", Journal of Productivity Analysis 16, pp. 31-47.
113. R. D. Banker and R. Morey (1986a), "Efficiency Analysis for Exogenously Fixed Inputs and Outputs", Operations Research 34(4), pp. 513-521
114. A. Charnes, W. W. Cooper, J. J. Rousseau and J. Semple (1987), "Data Envelopment Analysis and Axiomatic Notions of Efficiency and Reference Sets", CCS Research Report 558 (Austin, Texas: University of Texas, Graduate School of Business, Center for Cybernetic Studies, Austin, Texas 78712).
115. H. Deng (2003), "Evaluating and Managing Congestion in Chinese Production", Ph. D. Thesis (Austin, TX: The Red McCombs School of Business in The University of Texas at Austin). Also available from University Micro Films, Inc., Ann Arbor, Mich.
116. Exceptions are the FDH and multiplicative models discussed in Chapter 4 and Chapter 5.
117. E. F. Fama and M. C. Jensen (1983a), "Separation of Ownership and Control", Journal of Law and Economics 26, pp. 301-325.
118. See also Fama and Jensen (1983b), "Agency Problems and Residual Claims", Journal of Law and Economics 26, pp. 327-349.
119. P. L. Brockett, W. W. Cooper, J. J. Rousseau and Y. Wang (1998), "DEA Evaluations of the Efficiency of Organizational Forms and Distribution Systems in the U. S. Property and Liability Insurance Industry", International Journal of System Science 29, pp. 1235-1247.
120. See P. L. Brockett, W. W. Cooper, L. Golden, J. J. Rousseau and Y. Wang "Evaluating Solvency and Efficiency Performances by U. S. Property-Liability Insurance Companies", Journal of Risk and Insurance (submitted).
121. Thte Mann-Whitney statistic does not require equal sample size. See E. L. Lehman (1979) Nonparametrization: Statistical Methods Based on Ranks (New York: Holden-Day).
122. D. L. Adolphson, G. C. Cornia, L. C. Walters, "A Unified Framework for Classifying DEA Models", Operational Research'90, edited by H. E. Bradley, Pergamon Press, pp. 647-657 (1991).
123. K. Tone (1993), "On DEA Models", (in Japanese) Communications of the Operations Research Society of Japan 38, pp. 34-40.
124. ll. R. D. Banker and R. C. Morey (1986b), "The Use of Categorical Variables in Data Envelopment Analysis", Management Science 32(12), pp. 1613-1627.
125. W. A. Kamakura (1988), "A Note on The Use of Categorical Variables in Data Envelopment Analysis", Management Science 34(10), pp. 1273-1276.
126. J. J. Rousseau and J. Semple (1993), "Categorical Outputs in Data Envelopment Analysis", Management Science 39(3), pp. 384-386.
127. K. Tone (1997), "DEA with Controllable Category Levels", in Proceedings of the 1997 Spring National Conference of the Operations Research Society of Japan pp. 126-127.
128. K. Tone (1995), "DEA Models Revisited", Communications of the Operations Research Society of Japan 40, pp. 681-685 (in Japanese).
129. K. Tone (1993), Data Envelopment Analysis (in Japanese) (Tokyo: JUSE Press, Ltd.).
130. A. Charnes, W. W. Cooper and E. Rhodes (1981), "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through", Management Science 27, pp. 668-697.
131. P. L. Brockett and B. Golany (1996), "Using Rank Statistics for Determining Programmatic Efficiency Differences in Data Envelopment Analysis", Management Science 42, pp. 466-472.
132. P. L. Brockett and A. Levine (1984) Statistics and Probability and Their Applications (Fort Worth, TX. CBS College Publishing). The concepts of cost efficiency related subjects were introduced by M. J. Farrell (1957) and G. Debreu (1951) and developed into implementable form by Fare, Grosskopf and Lovell (1985) using linear programming technologies. Cooper, Park and Pastor (1999) 8 extended these treatments to the Additive models with a new "translation invariant" measure named "RAM." Inadequacies in attempts to move from "technical" to price based or cost based efficiencies were identified by Tone (2002). In response a new approach to cost efficiency was developed by Tone (2002) and further extended to decompositions of cost, efficiency by Tone and Tautsui (2664) in a form they applied to Japan-US electric utilities comparisons. Tone and Sahoo (2005) 9 applied the new cost efficiency model to examine the performance of Life Insurance Corporation (LIC) of India and found a significant heterogeneity in the cost efficiency scores over the course of 19 years. See also Tone and Sahoo (2005) 10 in which the issues of cost elasticity are extensively discussed based on the new cost efficiency model. Fukuyama and Weber (2004) u developed a variant of the new cost efficiency model using "directional distance functions " introduced in Chambers, Chung and Fare (1996) 12 to measure inefficiency. See Fare, Grosskopf and Whittaker (2004) 13 for an updated survey. See, however, Ray (2004), 14 p. 95, who identified a deficiency in the failure of "directional distance functions " to account for nonzero slacks in the measures of efficiency.
133. M. J. Farrell (1957), "The Measurement of Productive Efficiency", Journal of the Royal Statistical Society Series A, 120, III, pp. 253-281.
134. G. Debreu (1951), "The Coefficient of Resource Utilization", Econometrica 19, pp. 273-292.
135. R. Fare, S. Grosskopf and C. A. K. Lovell, Measurement of Efficiency of Production (Boston: Kluwer-Nijhoff Publishing Co., Inc., 1985).
136. This means that P lies below the production possibility surface and hence is inefficient.
137. K. Tone (2002), "A Strange Case of the Cost and Allocative Efficiencies in DEA", Journal of the Operational Research Society 53, pp. 1225-1231.
138. This ratio model was introduced in K. Tone (1993), Data Envelopment Analysis (in Japanese) (Tokyo: JUSE Press, Ltd.).
139. W. W. Cooper, Z. Huang, S. Li and J. T. Pastor (2005) "Aggregation with Enhanced Russell Measure in DEA", European Journal of Operational Research (forthcoming).
140. K. Tone and M. Tsutsui (2004), "Decomposition of Cost Efficiency and its Application to Japan-US Electric Utility Comparisons", Research Report Series 1-2004-0004, GRIPS (National Graduate Institute for Policy Studies), also forthcoming in Socio-Economic Planning Sciences.
141. W. W. Cooper, K. S. Park and J. T. Pastor (1999), "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models and Relations to Other Models and Measures in DEA", Journal of Productivity Analysis 11, pp. 5-42.
142. K. Tone and B. K. Sahoo (2005), "Evaluating Cost Efficiency and Returns to Scale in the Life Insurance Corporation of India Using Data Envelopment Analysis", Socio-Economic Planning Sciences 39, pp. 261-285.
143. K. Tone and B. K. Sahoo (2005), "Cost-Elasticity: A Re-Examination in DEA", Annals of Operations Research (forthcoming).
144. H. Fukuyama and W. L. Weber (2004), "Economic Inefficiency Measurement of Input Spending When Decision-making Units Face Different Input Prices", Journal of the Operational Research Society 55, pp. 1102-1110.
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146. R. Fare, S. Grosskopf and G. Whittaker (2004) "Distance Functions", Chapter 5 in W. W. Cooper, L. M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell Mass., Kluwer Academic Publishers).
147. S. Ray (2004) Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research (Cambridge University Press).
148. See also M. J. Farrell and M. Fieldhouse (1962), "Estimating Efficient Production F+unctions Under Increasing Returns to Scale", Journal of the Royal Statistical Society Series+ A, 125, Part 2, pp. 252-267.
149. See also R. Fare, S. Grosskopf and C. A. K. Lovell (1994), Production Frontiers (Cambridge: Cambridge University Press).
150. P. W. Wilson (1995), "Detecting Influential Observations in Data Envelopment Analysis", Journal of Productivity Analysis 6, pp. 27-46.
151. See, for instance, R. M. Thrall (1989), "Classification of Transitions under Expansion of Inputs and Outputs", Managerial and Decision Economics 10, pp. 159-162.
152. R. D. Banker, H. Chang and W. W. Cooper (1996), "Simulation Studies of Efficiency, Returns to Scale and Misspecification with Nonlinear Functions in DEA", Annals of Operations Research 66, pp. 233-253.
153. A. Charnes, W. W. Cooper, A. Y. Lewin, R. C. Morey and J. J. Rousseau (1985), "Sensitivity and Stability Analysis in DEA", Annals of Operations Research 2, pp. 139-156.
154. A. Charnes and W. W. Cooper (1968), "Structural Sensitivity Analysis in Linear Programming and an Exact Product Form Left Inverse", Naval Research Logistics Quarterly 15, pp. 517-522.
155. For a summary discussion see A. Charnes and L. Neralic (1992), "Sensitivity Analysis in Data Envelopment Analysis 3", Glasnik Matematicki 27, pp. 191-201.
156. A subsequent extension is L. Neralic (1997), "Sensitivity in Data Envelopment Analysis for Arbitrary Perturbations of Data", Glasnik Matematicki 32, pp. 315-335.
157. See also L. Neralic (2004), "Preservation of Efficiency and Inefficiency Classification in Data Envelopment Analysis", Mathematical Communications 9, pp. 51-62.
158. A. Charnes, S. Haag, P. Jaska and J. Semple (1992), "Sensitivity of Efficiency Calculations in the Additive Model of Data Envelopment Analysis", International Journal of System Sciences 23, pp. 789-798.
159. Extensions to other classes of models may be found in A. Charnes, J. J. Rousseau and J. H. Semple (1996) "Sensitivity and Stability of Efficiency Classifications in DEA", Journal of Productivity Analysis 7, pp. 5-18.
160. The shape of this "ball" will depend on the norm that is used. For a discussion of these and other metric concepts and their associated geometric portrayals see Appendix A in A. Charnes and W. W. Cooper (1961), Management Models and Industrial Applications of Linear Programming (New York: John Wiley & Sons).
161. This omission of DMU0 is also used in developing a measure of "super efficiency" as it is called in P. Andersen and N. C. Petersen (1993), "A Procedure for Ranking Efficient Units in DEA", Management Science 39, pp. 1261-1264.
162. Their use is more closely associated with stability when a DMU is omitted, however, so we do not cover it here. See the next chapter, Chapter 10, in this text. See also R. M. Thrall (1996) "Duality Classification and Slacks in DEA", Annals of Operations Research 66, pp. 104-138.
163. A. Charnes, J. J. Rousseau and J. H. Semple (1996), "Sensitivity and Stability of Efficiency Classification in Data Envelopment Analysis", Journal of Productivity Analysis 7, pp. 5-18.
164. In fact, Seiford and Zhu propose an iterative approach to assemble an exact stability region in L. Seiford and J. Zhu, "Stability Regions for Maintaining Efficiency in Data Envelopment Analysis", European Journal of Operational Research 108, 1998, pp. 127-139.
165. R. G. Thompson, P. S. Dharmapala and R. M. Thrall (1994), "Sensitivity Analysis of Efficiency Measures with Applications to Kansas Farming and Illinois Coal Mining", in A. Charnes, W. W. Cooper, A. Y. Lewin and L. M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass., Kluwer Academic Publishers) pp. 393-422.
166. R. G. Thompson, P. S. Dharmapala, J. Diaz, M. D. Gonzales-Lina and R. M. Thrall (1996), "DEA Multiplier Analytic Center Sensitivity Analysis with an Illustrative Application to Independent Oil Cos.", Annals of Operations Research 66, pp. 163-180.
167. A. Charnes, W. W. Cooper and R. M. Thrall (1991), "A Structure for Classifying and Characterizing Efficiency in Data Envelopment Analysis", Journal of Productivity Analysis 2, pp. 197-237.
168. An alternate approach to simultaneous variations in all data effected by the envelopment model is available in L. M. Seiford and J. Zhu (1998), "Sensitivity Analysis of DEA Models for Simultaneous Changes in All Data", Journal of the Operational Research Society 49, pp. 1060-1071.
169. See also the treatments of simultaneous changes in all data for additive models in L. Neralic (2004), "Preservation of Efficiency and Inefficiency Classification in Data Envelopment Analysis", Mathematical Communications 9, pp. 51-62.
170. This status is easily recognized because 6\ = 6 = 6% - 1 are all associated with uniquely obtained solutions with zero slacks. See A. Charnes, W. W. Cooper and R. M. Thrall (1991) "A Structure for Classifying and Characterizing Efficiency in Data Envelopment Anaysis", Journal of Productivity Analysis 2, pp. 197-237.
171. W. W. Cooper, S. Li, L. M. Seiford and J. Zhu (2004), Chapter 3 in W. W. Cooper, L. M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell, Mass., Kluwer Academic Publishers).
172. R. D. Banker (1993), "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation", Management Science 39, pp. 1265-1273.
173. R. Banker and R. Natarasan (2004), "Statistical Tests Based on DEA Efficiency Scores", Chapter 11 in W. W. Cooper, L. M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis (Norwell, Mass., Kluwer Academic Publishers).
174. Quoted from p. 139 in R. D Banker (1996), "Hypothesis Tests Using Data Envelopment Analysis", Journal of Productivity Analysis pp. 139-159.
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178. L. Simar and P. W. Wilson (1998), "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models", Management Science 44, pp. 49-61.
179. See also Simar and Wilson (2004) "Performance of the Bootstrap for DEA Estimators and Iterating the Principle", Chapter 10 in W. W. Cooper, L. M. Seiford and J. Zhu, eds. Handbook on Data Envelopment Analysis (Norwell, Mass: Kluwer Academic Publishers).
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