Sensitivity Analysis in DEA

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


This chapter presents some of the recently developed analytical methods for studying the sensitivity of DEA results to variations in the data. The focus is on the stability of classification of DMUs (decision making units) into efficient and inefficient performers. Early work on this topic concentrated on developing algorithms for conducting such analyses after it was noted that standard approaches for conducting sensitivity analyses in linear programming could not be used in DEA. However, recent work has bypassed the need for such algorithms. It has also evolved from the early work that was confined to studying data variations in one input or output for one DMU. The newer methods described in this chapter make it possible to analyze the sensitivity of results when all data are varied simultaneously for all DMUs.


Data envelopment analysis Efficiency Stability Sensitivity 


  1. Ahn T, Seiford LM. Sensitivity of DEA to models and variable sets in an hypothesis test setting: The efficiency of university operations. In: Ijiri Y, editor. Creative and innovative approaches to the science of management. New York: Quorum Books; 1993.Google Scholar
  2. Banker RD. Maximum likelihood, consistency and data envelopment analysis: a statistical foundation, this volume.Google Scholar
  3. Banker RD, Chang H, Cooper WW. Simulation studies of efficiency, returns to scale and misspecification with nonlinear functions in DEA. Ann Oper Res. 1996;66:233–53.Google Scholar
  4. Charnes A, Cooper WW. Management models and industrial applications of linear programmer. New York: John Wiley and Sons; 1961.Google Scholar
  5. Charnes A, Cooper WW. Structural sensitivity analysis in linear programming and an exact product form left inverse. Naval Res Log Quart. 1968;15:517–22.Google Scholar
  6. Charnes A, Cooper WW, Li S. Using DEA to evaluate relative efficiencies in the economic performance of Chinese cities. Socio-Econ Plann Sci. 1989;23:325–44.CrossRefGoogle Scholar
  7. Charnes A, Neralic L. Sensitivity analysis of the proportionate change of inputs (or outputs) in data envelopment analysis. Glasnik Matematicki. 1992;27:393–405.Google Scholar
  8. Charnes A, Cooper WW, Lewin AY, Morey RC, Rousseau JJ. Sensitivity and stability analysis in DEA. Ann Oper Res. 1985;2:139–50.CrossRefGoogle Scholar
  9. Charnes A, Haag S, Jaska P, Semple J. Sensitivity of efficiency calculations in the additive model of data envelopment analysis. J Syst Sci. 1992;23:789–98.CrossRefGoogle Scholar
  10. Charnes A, Rousseau JJ, Semple JH. Sensitivity and stability of efficiency classifications in DEA. J Prod Anal. 1996;7:5–18.CrossRefGoogle Scholar
  11. Charnes A, Cooper WW, Thrall RM. A Structure for characterizing and classifying efficiencies in DEA. J Prod Anal. 1991;3:197–237.CrossRefGoogle Scholar
  12. Cooper WW, Seiford LM, Tone K. Data envelopment analysis: a comprehensive text with models references and DEA-solver software applications. Boston: Kluwer Academic Publishers; 2000.Google Scholar
  13. Neralic L. Sensitivity in data envelopment analysis for arbitrary perturbations of data. Glasnik Matematicki. 1997;32:315–35.Google Scholar
  14. Seiford LM, Zhu J. Stability regions for maintaining efficiency in data envelopment analysis. Eur J Oper Res. 1998a;108:127–39.CrossRefGoogle Scholar
  15. Seiford LM, Zhu J. Sensitivity analysis of DEA models for simultaneous changes in all of the data. J Oper Res Soc. 1998b;49:1060–71.Google Scholar
  16. Seiford LM, Zhu J. Infeasibility of super-efficiency data envelopment analysis models. INFOR. 1998c;37(2):174–87.Google Scholar
  17. Sexton TR, Silkman RH, Hogan RH. Measuring efficiency: an assessment of data envelopment analysis, new directions for program evaluations. In: Silkman RH, editor. Measuring efficiency: an assessment of data envelopment analysis. Publication No. 32 in the series New Directions for Program Evaluations. A publication of the American Evaluation Association. San Francisco: Jossy Bass; 1986.Google Scholar
  18. Simar L, Wilson P. DEA Bootstrapping, this volume.Google Scholar
  19. Thompson RG, Dharmapala PS, Diaz J, Gonzalez-Lima MD, Thrall RM. DEA multiplier analytic center sensitivity analysis with an illustrative application to independent oil Cos. Ann Oper Res. 1996;66:163–80.CrossRefGoogle Scholar
  20. Thompson RG, Dharmapala PS, Thrall RM. Sensitivity analysis of efficiency measures with applications to Kansas farming and Illinois coal mining. In: Charnes A, Cooper WW, Lewin AY, Seiford LM, editors. Data envelopment analysis: theory, methodology and applications. Massachusetts: Norwell Kluwer Academic Publishers; 1994. p. 393–422.Google Scholar
  21. Wilson PW. Detecting influential observations in data envelopment analysis. J Prod Anal. 1995;6:27–46.CrossRefGoogle Scholar
  22. Zhu J. Robustness of the efficient DMUs in data envelopment analysis. Eur J Oper Res. 1996a;90:451–60.CrossRefGoogle Scholar
  23. Zhu J. DEA/AR analysis of the 1988–1989 performance of Nanjing textile corporation. Ann Oper Res. 1996b;66:311–35.CrossRefGoogle Scholar
  24. Zhu J. Super-efficiency and DEA sensitivity analysis. Eur J Oper Res. 2001;129(2):443–55.CrossRefGoogle Scholar
  25. Zhu J. Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets. Boston: Springer Science; 2009.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • William W. Cooper
    • 1
  • Shanling Li
    • 2
  • Lawrence M. Seiford
    • 3
  • Joe Zhu
    • 4
    Email author
  1. 1.Red McCombs School of BusinessUniversity of Texas at AustinAustinUSA
  2. 2.Faculty of ManagementMcGill UniversityMontrealCanada
  3. 3.Department of Industrial and Operations EngineeringUniversity of Michigan at Ann ArborAnn ArborUSA
  4. 4.School of BusinessWorcester Polytechnic InstituteWorcesterUSA

Personalised recommendations