Journal of Productivity Analysis

, Volume 28, Issue 3, pp 151–163 | Cite as

Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

  • W. W. Cooper
  • L. M. Seiford
  • K. Tone
  • J. Zhu


This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.


Efficiency Effectiveness Social Indicators Engineering-science Welfare economics Distance measures 



Professor Cooper would like to express his appreciation to the IC2 Institute of the University of Texas for support of his research.


  1. Ahn T, Charnes A, Cooper WW (1988) Efficiency characterizations in different DEA models. Soc-Econ Plan Sci 22:253–257CrossRefGoogle Scholar
  2. Ali I, Seiford LM (1990a) Computational accuracy and infinitesimals in Data Envelopment Analysis. INFORMS 31:290–297Google Scholar
  3. Ali I, Seiford LM (1990b) Translational invariance in data envelopment analysis. Oper Res Lett 9:403–405CrossRefGoogle Scholar
  4. Arnold V, Bardhan I, Cooper WW, Gallegos A (1997) Primal and dual optimality in computer codes using two-stage solution procedure in DEA. In: Aronson JA, Zionts S (eds) Operations research methods, models and applications. Quorum Books, New YorkGoogle Scholar
  5. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale efficiencies in DEA. Manage Sci 30:1078–1092Google Scholar
  6. Banker RD, Cooper WW, Seiford LM, Zhu J (2004) Returns to scale in DEA, Chapter 2. In Cooper, Seiford, Zhu (eds) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  7. Banker RD, Natarajan R (2004) Statistical tests based on DEA efficiency scores. In: Cooper WW, Seiford LM, Zhu J (eds) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  8. Bardhan I, Bowlin WF, Cooper WW, Sueyoshi T (1996) Models and measures for efficiency dominance in DEA, Part II: free disposal hull (FDH) and Russell measure (RM) approaches. J Oper Res Soc Jpn 39:333–345Google Scholar
  9. Bardhan I, Cooper WW, Kumbhakar SC (1998) A simulation study of joint uses of DEA and statistical regressions for production function estimation and efficiency evaluation. J Prod Anal 9:249–278CrossRefGoogle Scholar
  10. Blackorby C, Russell RR (1999) Aggregation of efficiency indexes. J Prod Anal 12:5–20CrossRefGoogle Scholar
  11. Bowlin WF (1984) A Data Envelopment Analysis approach to performance evaluation in not-for-profit entities with an illustrative application to the U.S. Air Force. Ph.D. Thesis University of Texas Graduate School of Business, Austin Texas. Also available from University Micro-Films, Inc. in Ann Arbor, MichiganGoogle Scholar
  12. Brockett PL, Cooper WW, Golden L, Kumbhakar SC, Kwinn MJ, Layton B (2007) Estimating elasticities with frontier and other regression for use in evaluating alternative advertising strategies for use in U.S. Army recruitment. Soc-Econ Plan Sci (to appear)Google Scholar
  13. Brockett PL, Cooper WW, Deng H, Golden L, Kwinn MJ, Thomas DA (2002) The efficiency of joint advertising vs. service-specific advertising. Military Oper Res 7:57–75Google Scholar
  14. Brockett PL, Cooper WW, Kumbhakar SC, Kwinn MJ, Jr, McCarthy D (2004) Alternative statistical regression studies of the effects of joint and service specific advertising in military recruitment. J Oper Res Soc 55:1039–1048CrossRefGoogle Scholar
  15. Bulla S, Cooper WW, Park KS, Wilson D (2000) Evaluating efficiencies of turbofan jet engines: a data envelopment analysis approach. J Prop Power 16:431–439CrossRefGoogle Scholar
  16. Charnes A, Clarke RL, Cooper WW (1989) An approach to testing for organizational slack with R.D. Banker’s game theoretic formulation of DEA. Res Governm Non-Profit Account 5:211–230Google Scholar
  17. Charnes A, Cooper WW (1961) Management models and industrial applications of linear programming, vol 2, with A. Charnes. John Wiley and Sons, Inc., New YorkGoogle Scholar
  18. Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Naval Res Logist Quart 9:181–186CrossRefGoogle Scholar
  19. Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J Econ 30:91–l07Google Scholar
  20. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. J Oper Res 2:429–444CrossRefGoogle Scholar
  21. Charnes A, Cooper WW, Seiford LM, Stutz J (1983) Invariant multiplicative efficiency and piecewise Cobb-Douglas envelopments. Oper Res Lett 2:101–103CrossRefGoogle Scholar
  22. Charnes A, Cooper WW, Sueyoshi T (1985) Least squares/ridge regression and goal programming/constrained regression altenatives. Eur J Oper Res 27:144–157Google Scholar
  23. Coelli TJ (1998) A multi-stage methodology for the solution of orientated DEA models. Oper Res Lett 23:143–149CrossRefGoogle Scholar
  24. Cook WD, Kress M, Seiford LM (1993) On the use of ordinal Data Envelopment Analysis. J Oper Res Soc 44:133–140CrossRefGoogle Scholar
  25. Cooper WW (2005) Origins, uses of and relations between goal programming and Data Envelopment Analysis. J Multi-Criteria Decision Anal 13:3–11CrossRefGoogle Scholar
  26. Cooper WW, Huang Z, Li S (1996) Satisficing DEA models under chance constraints. In Annals of operations research, vol. 66, 1996, pp. 279–295. Special issue on Extensions and New Developments in DEA edited by W.W. Cooper, R.G. Thompson and R.M. ThrallGoogle Scholar
  27. Cooper WW, Huang ZM, Li S, Parker B, Pastor JT (2007) Efficiency aggregation with enhanced Russell measures in DEA. Socio-Economic Planning Sciences (to appear)Google Scholar
  28. Cooper WW, Huang Z, Li S, Zhu J (2006) Critique of Dmitruk and Koshevoy and of Bol Plus Expanded Opportunities for Efficiency and Effectiveness Evaluations with DEA. Working paper% W.W. Cooper, The Red McCombs School of Business, The University of Texas at Austin, Texas 78712Google Scholar
  29. Cooper WW, Park KS, Pastor JT (2000) Marginal rates and elasticities of substitution in DEA. J Prod Anal 13:105–123CrossRefGoogle Scholar
  30. Cooper WW, Park KS, Pastor JT (1999a) RAM: a range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA. J Prod Anal 11:5–42CrossRefGoogle Scholar
  31. Cooper WW, Park KS, Pastor JT (2001) The range adjusted measure (RAM) in DEA: A response to the comments by Steinmann and Zweifl. J Prod Anal 15:145–152CrossRefGoogle Scholar
  32. Cooper WW, Park KS, Yu G (1999b) IDEA and AR-IDEA: Models for dealing with imprecise data in DEA. Manage Sci 45:597–607Google Scholar
  33. Cooper WW, Park KS, Yu G (2001) An illustrative application of IDEA (Imprecise Data Envelopment Analysis) to a Korean mobile telecommunication company. Oper Res 49:807–820CrossRefGoogle Scholar
  34. Cooper WW, Seiford LM, Tone K (2000) Data envelopment analysis: a comprehensive text with models, applications, references and DEA Solver Software. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  35. Cooper WW, Seiford LM, Tone K (2006) Introduction to data envelopment analysis and its uses. Springer Science and Business Media. Inc., New YorkGoogle Scholar
  36. Cooper WW, Seiford LM, Zhu J (2004) Handbook on data envelopment analysis. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  37. Dantzig G (1963) Linear programming and extensions. Princeton University Press, Princeton, NJGoogle Scholar
  38. Debreu G (1951) The Coefficient of resource utilization. Econometrica 9:273–292CrossRefGoogle Scholar
  39. Despotis DK (2005) Measuring human development via Data Envelopment Analysis, the Case of Asia and the Pacific. Omega 33:285–390CrossRefGoogle Scholar
  40. Dmitruk AV, Koshevaz GA (1991) On the existence of a technical efficiency criteria. J Econ Theory 55:121–144CrossRefGoogle Scholar
  41. Emrouznejad A, Parker B, Tavares G (2007) A bibliography of Data Envelopment Analysis (1978–2001). Soc-Econ Plan Sci (to appear)Google Scholar
  42. Färe R, Grosskopf S (1996) Intertemporal production functions with dynamic DEA. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  43. Färe R, Grosskopf S, Lovell CAK (1994) Production frontiers. Press Syndicate of the University of Cambridge, CambridgeGoogle Scholar
  44. Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  45. Färe R, Lovell CAK (1978) Measuring the technical efficiency of production. J Econ Theory 19:156–162CrossRefGoogle Scholar
  46. Farrell MJ (1957) The measurement of production efficiency. J Roy Stat Soc 120:253–290CrossRefGoogle Scholar
  47. Gattoufi S, Oral M, Reisman A (2004) Data Envelopment Analysis literature, A bibliography update (1951–2001). Soc-Econ Plan Sci 38:159–229CrossRefGoogle Scholar
  48. Gigerenzer G (2004) Striking a blow for sanity in theories of rationality. In: Augier M, March JG (eds) Models of a man, essays in memory of Herbert A. Simon. The MIT Press, Cambridge MassGoogle Scholar
  49. Golany B, Thore S (1997) The economic and social performance of nations: efficiency and returns to scale. Soc-Econ Plan Sci 31:191–204CrossRefGoogle Scholar
  50. Grosskopf S, Hayes KJ, Taylor LL, Weber WL (1999) Anticipating the consequences of school reform: a new use of DEA. Manage Sci 45:605–620Google Scholar
  51. Koopmans T (1951) Activity analysis of production and allocation. John Wiley & Sons, New YorkGoogle Scholar
  52. Lancaster KJ (1966) A new approach to consumer theory. J Political Econ 74:132–157CrossRefGoogle Scholar
  53. Lee J-D, Seogwon H, Kim T-Y (2005) The measurement of consumer efficiency considering the discrete choice of consumers. J Prod Anal 23:65–84Google Scholar
  54. Lovell CAK, Pastor JT (1995) Units invariant and translation invariant DEA models. Oper Res Lett 18:147–151CrossRefGoogle Scholar
  55. Mattingly JD (1996) Elements of gas turbine propulsion. McGraw-Hill, New YorkGoogle Scholar
  56. Pareto V (1909) Manuel d’Economie Politique. Giars & Briere, ParisGoogle Scholar
  57. Park KS (2004) Simplification of the transformations and redundancy of assurance regions in IDEA (Imprecise DEA). J Oper Res Soc 55:1333–1336CrossRefGoogle Scholar
  58. Pastor JT, Ruiz JL, Sirvent I (1999) An enhanced DEA Russell graph efficiency measure. J Oper Res Soc 115:596–607Google Scholar
  59. Portela MCAS, Borges PC, Thanassoulis E (2003) Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. J Prod Anal 19(2–3):251–269CrossRefGoogle Scholar
  60. Portela MCAS, Thanassoulis E, Simpson G (2004) Negative data in DEA: a directional distance approach applied to bank branches. J Oper Res Soc 55:1111–1121CrossRefGoogle Scholar
  61. Prieto AM, Zofio JL (2001) Evaluating effectiveness in public provision of infrastructure and equipment: the case of Spanish municipalities. J Prod Anal 15:41–58CrossRefGoogle Scholar
  62. Ramanathan R (2007) An application of Data Envelopment Analysis for Evaluating comparative performances of countries of the Middle East and North Africa. Soc-Econ Plan Sci (to appear)Google Scholar
  63. Robinson J (1933) The economics of imperfect competition. Cambridge University Press, CambridgeGoogle Scholar
  64. Russell RR (1985) Measure of technical efficiency. J Econ Theory 35:109–126CrossRefGoogle Scholar
  65. Saaty TL, Braun J (1964) Nonlinear mathematics. Dover Publications, New YorkGoogle Scholar
  66. Schaible S (1996) Fractional programming. In: Gass SI, Harris CM (eds) Encyclopedia of operations research and management science. Kluwer Academic Publishers, Boston, pp 234–237Google Scholar
  67. Sengupta JK (1995) Dynamics of data envelopment analysis: theory of system efficiency. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  68. Simar L, Wilson PW (2004) Performance of the bootstrap for DEA estimates and iterating the principle. In: Cooper WW, Seiford LM, Joe Zhu (eds) Handbook on DEA. Kluwer Academic Publishers, Norwell, MassGoogle Scholar
  69. Simon HA (1957) Models of man: social and rational. John Wiley & Sons, New YorkGoogle Scholar
  70. Sobczyk A (1956) Symmetrical types of convex regions. Mathemat Magaz 29:175–192CrossRefGoogle Scholar
  71. Steinmann L, Zweifel P (2001) The range adjusted measure (RAM) in DEA: comment. J Prod Anal 15:142–145CrossRefGoogle Scholar
  72. Sueyoshi T, Honma T (2003) DEA network computing in multi-stage parallel processes. Int Trans Oper Res 10:1–27CrossRefGoogle Scholar
  73. Sueyoshi T, Sekitani K (2007) Computational strategy for Russell measure in DEA: second order cone programming. Eur J Oper Res 180:459–471CrossRefGoogle Scholar
  74. Takamura Y, Tone K (2003) A comparative site evaluation study for relocating Japanese government agencies out of Tokyo. Soc-Econ Plan Sci 37:85–102CrossRefGoogle Scholar
  75. Thompson RG, Langmeier LM, Lee CT, Lee E, Thrall RM (1990) The role of multiplier bounds in efficiency analysis with applications to Kansas farming. J Econ 46:93–108Google Scholar
  76. Thompson RG, Singleton FDJ, Thrall RM, Smith BA (1986) Comparative site evaluations for locating a high-energy physics lab in Texas. Interfaces 16:35–49Google Scholar
  77. Tone K (2001) A slacks based measure of efficiency in Data Envelopment Analysis. Eur J Oper Res 130:498–509CrossRefGoogle Scholar
  78. Thrall RM (1996) Duality, classification and slacks in DEA. Ann Oper Res 66:109–128CrossRefGoogle Scholar
  79. Tulkens H (1993) On FDH efficiency analysis: some methodological issues and applications in retail banking, courts and urban transit. J Prod Anal 1/2:83–210CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • W. W. Cooper
    • 1
  • L. M. Seiford
    • 2
  • K. Tone
    • 3
  • J. Zhu
    • 4
  1. 1.The Red McCombs School of BusinessThe University of Texas at AustinAustinUSA
  2. 2.College of Engineering, Industrial and Operations EngineeringThe University of MichiganAnn ArborUSA
  3. 3.National Graduate Institute for Policy StudiesTokyoJapan
  4. 4.Department of ManagementWorcester Polytechnic InstituteWorcesterUSA

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