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

Cheng, Gang and Qian, Zhenhua and Zervopoulos, Panagiotis (2011): Overcoming the infeasibility of super-efficiency DEA model: a model with generalized orientation.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Data envelopment analysis (DEA); Super-efficiency (SE); Infeasibility; Orientation
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C67 - Input-Output Models

References

Charnes A, Cooper WW,Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research. 1978, 2(6): 429-444.

Andersen P,Petersen NC. A procedure for ranking efficient units in data envelopment analysis. Management Science. 1993, 39(10): 1261-1265.

Xue M,Harker PT. Note: Ranking DMUs with infeasible super-efficiency DEA models. Management Science. 2002, 48(5): 705-710.

Chen Y. Measuring super-efficiency in DEA in the presence of infeasibility. European Journal of Operational Research. 2005, 161(2): 545-551.

Ray SC. The directional distance function and measurement of super-efficiency: an application to airlines data. Journal of the Operational Research Society. 2008, 59(6): 788-797.

Wilson PW. Detecting Influential Observations in Data Envelopment Analysis. Journal of Productivity Analysis. 1995, 6(1): 27-45.

Banker RD,Chang H. The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operational Research. 2006, 175(2): 1311-1320.

Charnes A, Haag S, Jaska P,Semple J. Sensitivity of Efficiency Classifications in the Additive-Model of Data Envelopment Analysis. International Journal of Systems Science. 1992, 23(5): 789-798.

Seiford LM,Zhu J. Sensitivity analysis of DEA models for simultaneous changes in all the data. Journal of the Operational Research Society. 1998, 49(10): 1060-1071.

Seiford LM,Zhu J. Stability regions for maintaining efficiency in data envelopment analysis. European Journal of Operational Research. 1998, 108(1): 127-139.

Zhu J. Robustness of the efficient DMUs in data envelopment analysis. European Journal of Operational Research. 1996, 90(3): 451-460.

Zhu J. Super-efficiency and DEA sensitivity analysis. European Journal of Operational Research. 2001, 129(2): 443-455.

Färe R, Grosskopf S, Lindgren B,Roos P. Productivity changes in Swedish pharamacies 1980–1989: A non-parametric Malmquist approach. Journal of Productivity Analysis. 1992, 3(1-2): 85-101.

Berg SA, Forsund FR,Jansen ES. Malmquist Indexes of Productivity Growth during the Deregulation of Norwegian Banking, 1980-89. Scandinavian Journal of Economics. 1992, 94: S211-S228.

Rousseau JJ,Semple JH. Two-person ratio efficiency games. Management Science. 1995, 41(3):435-441.

Lovell CAK,Rouse APB. Equivalent standard DEA models to provide superefficiency scores. Journal of the Operational Research Society. 2003, 54(1): 101-108.

Cook WD, Liang L, Zha Y,Zhu J. A modified super-efficiency DEA model for infeasibility. Journal of the Operational Research Society. 2009, 60(2): 276-281.