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Overcoming the infeasibility of super-efficiency DEA model: a model with generalized orientation

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  • Cheng, Gang
  • Qian, Zhenhua
  • Zervopoulos, Panagiotis

Abstract

The super-efficiency (SE) model is identical to the standard model, except that the unit under evaluation is excluded from the reference set. This model has been used in ranking efficient units, identifying outliers, sensitivity and stability analysis, measuring productivity changes, and solving two-player games. Under the assumption of variable, non-increasing and non-decreasing returns to scale (VRS, NIRS, NDRS), the SE model may be infeasible for some efficient DMUs. Based on the necessary and sufficient conditions for the infeasibility of SE, in the current paper, we have developed a DEA model with generalized orientation to overcome infeasibility issues. The DEA model with generalized orientation extends the orientation of the DEA model from the traditional input-orientation and output-orientation to the modified input-orientation, input-prioritized non-orientation, modified output-orientation, and output-prioritized non-orientation. All of the extended orientations are always feasible in the associated super-efficiency models. In addition, the modified input-oriented and the modified output-oriented approaches are developed to deal with the problem of infeasibility in super-efficiency models while keeping the concordance with the traditional oriented models. The newly developed model is illustrated with a real world dataset.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31991.

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Date of creation: 03 Jul 2011
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Handle: RePEc:pra:mprapa:31991

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Keywords: Data envelopment analysis (DEA); Super-efficiency (SE); Infeasibility; Orientation;

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  1. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
  2. Zhu, Joe, 2001. "Super-efficiency and DEA sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 129(2), pages 443-455, March.
  3. Zhu, Joe, 1996. "Robustness of the efficient DMUs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 90(3), pages 451-460, May.
  4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  5. Seiford, Lawrence M. & Zhu, Joe, 1998. "Stability regions for maintaining efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 108(1), pages 127-139, July.
  6. Banker, Rajiv D. & Chang, Hsihui, 2006. "The super-efficiency procedure for outlier identification, not for ranking efficient units," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1311-1320, December.
  7. J. J. Rousseau & J. H. Semple, 1995. "Two-Person Ratio Efficiency Games," Management Science, INFORMS, vol. 41(3), pages 435-441, March.
  8. Chen, Yao, 2005. "Measuring super-efficiency in DEA in the presence of infeasibility," European Journal of Operational Research, Elsevier, vol. 161(2), pages 545-551, March.
  9. Mei Xue & Patrick T. Harker, 2002. "Note: Ranking DMUs with Infeasible Super-Efficiency DEA Models," Management Science, INFORMS, vol. 48(5), pages 705-710, May.
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