Data Envelopment Analysis: History, Models, and Interpretations

  • William W. Cooper
  • Lawrence M. Seiford
  • Joe ZhuEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 164)


In about 30 years, Data Envelopment Analysis (DEA) has grown into a powerful quantitative, analytical tool for measuring and evaluating the performance. DEA has been successfully applied to a host of many different types of entities engaged in a wide variety of activities in many contexts worldwide. This chapter discusses the basic DEA models and some of their extensions.


Data envelopment analysis Efficiency Performance 


  1. Afriat S. Efficiency estimation of production functions. Int Econ Rev. 1972;13:568–98.CrossRefGoogle Scholar
  2. Ahn T, Charnes A, Cooper WW. Efficiency characterizations in different DEA models. Soc Econ Plann Sci. 1988;22:253–7.CrossRefGoogle Scholar
  3. Arnold V, Bardhan I, Cooper WW, Gallegos A. Primal and dual optimality in computer codes using two-stage solution procedures in DEA. In: Aronson J, Zionts S, editors. Operations research methods, models and applications. Westpost, CT: Quorum Books; 1998.Google Scholar
  4. Banker R, Charnes A, Cooper WW. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci. 1984;30:1078–92.CrossRefGoogle Scholar
  5. Banker RD, Morey RC. Efficiency analysis for exogenously fixed inputs and outputs. Oper Res. 1986a;34(4):513–21.CrossRefGoogle Scholar
  6. Banker RD, Morey RC. The use of categorical variables in data envelopment analysis. Manag Sci. 1986b;32(12):1613–27.CrossRefGoogle Scholar
  7. Bardhan I, Bowlin WF, Cooper WW, Sueyoshi T. Models and measures for efficiency dominance in DEA, part I: additive models and MED measures. J Oper Res Soc Jpn. 1996;39:322–32.Google Scholar
  8. Bessent A, Bessent W, Charnes A, Cooper WW, and Thorogood (1983). Evaluation of Educational Proposals by means of DEA, Educational Administrative Quarterly 14, 82–107. Reprinted in Management Science in Higher Education: Methods and Studies (New York: Elsevier Publishing co., 1987).Google Scholar
  9. Brockett PL, Charnes A, Cooper WW, Huang ZM, Sun DB. Data transformations in DEA cone ratio envelopment approaches for monitoring bank performances. Eur J Oper Res. 1997;98(2):250–68.CrossRefGoogle Scholar
  10. Bulla S, Cooper WW, Parks KS, Wilson D. Evluating efficiencies in Turbo-Fan jet engines in multiple inputs–outputs context approaches. Propul Power. 2000;16:431–9.CrossRefGoogle Scholar
  11. Charnes A, Cooper WW. Management models and industrial applications of linear programming. New York, NY: Wiley; 1961.Google Scholar
  12. Charnes A, Cooper WW. Programming with linear fractional functionals. Nav Res Logist Q. 1962;9:181–5.CrossRefGoogle Scholar
  13. Charnes A, Cooper WW, Rhodes E. 1978, Measuring the efficiency of decision making units, European Journal of Operational Research 2, 429–444. Also, 1979, Short Communication, European Journal of Operational Research 3, 339–340.Google Scholar
  14. Charnes A, Clarke CT, Cooper WW, Golany B. A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US air forces. Annals of operation research. 1985. Vol. 2 p. 95–112.Google Scholar
  15. Charnes A, Cooper WW, Sun DB, Huang ZM. Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks. J Econ. 1990;46:73–91.Google Scholar
  16. Charnes A, Cooper WW, Wei QL, Huang ZM. Cone ratio data envelopment analysis and multi-objective programming. Int J Syst Sci. 1989;20:1099–118.CrossRefGoogle Scholar
  17. Charnes A, Cooper WW, Golany B, Seiford L, Stutz J. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. J Econ. 1985b;30:91–l07.Google Scholar
  18. Chen Y, Zhu J. Measuring information technology’s indirect impact on firm performance. Inform Technol Manag J. 2004;5(1–2):9–22.CrossRefGoogle Scholar
  19. Cook WD, Seiford LM. Data envelopment analysis (DEA) – Thirty years on. Eur J Oper Res. 2009;192:1–17.CrossRefGoogle Scholar
  20. Cook WD, Kress M, Seiford LM. On the use of ordinal data in data envelopment analysis. J Oper Res Soc. 1993;44:133–40.Google Scholar
  21. Cook WD, Kress M, Seiford LM. Data envelopment analysis in the presence of both quantitative and qualitative factors. J Oper Res Soc. 1996;47:945–53.Google Scholar
  22. Cook WD, Zhu J. Context-dependent assurance regions in DEA. Oper Res. 2008;56(1):69–78.CrossRefGoogle Scholar
  23. Cook WD, Liang L, Zhu J. Measuring performance of two-stage network structures by DEA: a review and future perspective. Omega. 2010;38:423–30.CrossRefGoogle Scholar
  24. Cook WD, Hababou M, Tuenter H. Multi-component efficiency measurement and shared inputs in data envelopment analysis: an application to sales and service performance in bank branches. J Product Anal. 2000;14:209–24.CrossRefGoogle Scholar
  25. Cook WD, Green RH. Evaluating power plant efficiency: a hierarchical model. Comput Oper Res. 2005;32:813–23.CrossRefGoogle Scholar
  26. Cook WD, Chai D, Doyle J, Green RH. Hierarchies and groups in DEA. J Product Anal. 1998;10:177–98.CrossRefGoogle Scholar
  27. Cook WD, Zhu J. Rank order data in DEA: a general framework. Eur J Oper Res. 2006;174(2):1021–38.CrossRefGoogle Scholar
  28. Cooper WW, Thompson RG, Thrall RM. Extensions and new developments in data envelopment analysis. Ann Oper Res. 1996;66:3–45.Google Scholar
  29. Cooper WW, Seiford LM, Tone 2nd K, editors. Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software. Boston: Kluwer; 2007.Google Scholar
  30. Cooper WW, Seiford LM, Zhu J. A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA. Soc Econ Plann Sci. 2000a;34(1):1–25.CrossRefGoogle Scholar
  31. Cooper WW, Park KS, Pastor JT. Marginal rates and Elasticities of substitution in DEA. J Product Anal. 2000b;13(2000):105–23.CrossRefGoogle Scholar
  32. Cooper WW, Park KS, Pastor JT. RAM: a range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA. J Product Anal. 1999a;11:5–42.CrossRefGoogle Scholar
  33. Cooper WW, Park KS, Yu G. IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Manag Sci. 1999b;45:597–607.CrossRefGoogle Scholar
  34. Debreu G. The coefficient of resource utilization. Econometrica. 1951;19:273–92.CrossRefGoogle Scholar
  35. Dyson RG, Thanassoulis E. Reducing weight flexibility in data envelopment analysis. J Oper Res Soc. 1988;39(6):563–76.Google Scholar
  36. Emrouznejad A, Parker BR, Tavares G. Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Soc Econ Plann Sci. 2008;42:151–7.CrossRefGoogle Scholar
  37. Färe R, Grosskopf S, Lovell CAK. The measurement of efficiency of production. Boston: Kluwer Nijhoff Publishing Co.; 1985.Google Scholar
  38. Färe R, Grosskopf S, Lovell CAK. Production frontiers. Cambridge: Cambridge University Press; 1994.Google Scholar
  39. Färe R, Grosskopf S. Intertemporal production frontiers: with dynamic DEA. Boston, MA: Kluwer Academic; 1996.Google Scholar
  40. Färe R, Grosskopf S. Modelling undesirable factors in efficiency evaluation: Comment. Eur J Oper Res. 2004;157:242–5.CrossRefGoogle Scholar
  41. Farrell MJ. The measurement of productive efficiency. J Roy Stat Soc A. 1957;120:253–81.CrossRefGoogle Scholar
  42. Hua Z, Bin Y. DEA with undesirable factors. (Chapter 6). In: Zhu J, Cook WD, editors. Modeling data irregularities and structural complexities in data envelopment analysis. Boston: Springer Science; 2007.Google Scholar
  43. Koopmans TC, editor. Analysis of production as an efficient combination of activities. New York: Wiley; 1951.Google Scholar
  44. Liang LF, Yang F, Cook WD, Zhu J. DEA models for supply chain efficiency evaluation. Ann Oper Res. 2006;145(1):35–49.CrossRefGoogle Scholar
  45. Liang L, Cook WD, Zhu J. DEA Models for two-stage processes: game approach and efficiency decomposition. Nav Res Logist. 2008;55:643–53.CrossRefGoogle Scholar
  46. Roll Y, Cook WD, Golany B. Controlling factor weights in data envelopment analysis. IIE Trans. 1991;23:2–9.CrossRefGoogle Scholar
  47. Scheel H. Undesirable outputs in efficiency valuations. Eur J Oper Res. 2001;132:400–10.CrossRefGoogle Scholar
  48. Seiford LM, Zhu J. Modeling undesirable factors in efficiency evaluation. Eur J Oper Res. 2002;142(1):16–20.CrossRefGoogle Scholar
  49. Shephard RW. Theory of cost and production functions. Princeton, NJ: Princeton University Press; 1970.Google Scholar
  50. Takamura T, Tone K. A comparative site evaluation study for relocating Japanese Government Agencies out of Tokyo. Soc Econ Plann Sci. 2003;37:85–102.CrossRefGoogle Scholar
  51. Thompson RG, Jr FD, Singleton RMThrall, Smith BA. Comparative site evaluation for locating a high-energy physics lab in Texas. Interfaces. 1986;16:35–49.CrossRefGoogle Scholar
  52. Thompson RG, Langemeier L, Lee C, Lee E, Thrall R. The role of multiplier bounds in efficiency analysis with application to Kansas farming. J Econ. 1990;46:93–108.Google Scholar
  53. Tone K Sahoo BK. A reexamination of cost efficiency and cost elasticity in DEA. 2003. Working paper. National Graduate Institute for Policy Studies, Tokyo, Japan.Google Scholar
  54. Wong Y-HB, Beasley JE. Restricting weight flexibility in data envelopment analysis. J Oper Res Soc. 1990;41:829–35.Google Scholar
  55. Zhu J. DEA/AR analysis of the 1988–1989 performance of the Nanjing Textiles Corporation. Ann Oper Res. 1996a;66:311–35.CrossRefGoogle Scholar
  56. Zhu J. Data envelopment analysis with preference structure. J Oper Res Soc. 1996b;47(1):136–50.Google Scholar
  57. Zhu J. Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets and DEA excel solver. Boston: Kluwer; 2003a.Google Scholar
  58. Zhu J. Imprecise data envelopment analysis (IDEA): a review and improvement with an application. Eur J Oper Res. 2003b;144(3):513–29.CrossRefGoogle Scholar
  59. Zhu J. Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets. 2nd ed. Boston: Springer Science; 2009.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • William W. Cooper
    • 1
  • Lawrence M. Seiford
    • 2
  • Joe Zhu
    • 3
    Email author
  1. 1.Red McCombs School of BusinessUniversity of Texas at AustinAustinUSA
  2. 2.Department of Industrial and Operations EngineeringUniversity of Michigan at Ann ArborAnn ArborUSA
  3. 3.School of BusinessWorcester Polytechnic InstituteWorcesterUSA

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