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A slacks-based measure of super-efficiency in data envelopment analysis. (English) Zbl 1073.90520

Summary: In most models of Data Envelopment Analysis (DEA), the best performers have the full efficient status denoted by unity (or 100%), and, from experience, we know that usually plural Decision Making Units (DMUs) have this ”efficient status”. To discriminate between these efficient DMUs is an interesting subject. This paper addresses this ”super-efficiency” issue by using the slacks-based measure (SBM) of efficiency, which the author proposed in his previous paper [Eur. J. Oper. Res. 130, No. 3, 498–509 (2001; Zbl 0990.90523)]. The method differs from the traditional one based on the radial measure, e.g. Andersen and Petersen model, in that the former deals directly with slacks in inputs/outputs, while the latter does not take account of the existence of slacks. We will demonstrate the rationality of our approach by comparing it with the radial measure of super-efficiency. The proposed method will be particularly useful when the number of DMUs are small compared with the number of criteria employed for evaluation.

MSC:

90B50 Management decision making, including multiple objectives

Citations:

Zbl 0990.90523
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References:

[1] Andersen, P.; Petersen, N.C., A procedure for ranking efficient units in data envelopment analysis, Management science, 39, 1261-1264, (1993) · Zbl 0800.90096
[2] Charnes, A.; Cooper, W.W., Management models and industrial applications of linear programming, (1961), Wiley New York · Zbl 0107.37004
[3] Charnes, A.; Cooper, W.W., Programming with linear fractional functionals, Naval research logistics quarterly, 15, 333-334, (1962) · Zbl 0127.36901
[4] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, European journal of operational research, 2, 429-444, (1978) · Zbl 0416.90080
[5] Cooper, W.W.; Seiford, L.M.; Tone, K., Data envelopment analysis - A comprehensive text with models, applications, references and DEA-solver software, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0990.90500
[6] Doyle, J.; Green, R., Data envelopment analysis and multiple criteria decision making, Omega, 21, 713-715, (1993)
[7] Doyle, J.; Green, R., Efficiency and cross-efficiency in DEA: derivations, meanings and uses, Journal of the operational research society, 45, 567-578, (1994) · Zbl 0807.90016
[8] Seiford, L.M.; Zhu, J., Infeasibility of super-efficiency data envelopment analysis models, Infors, 37, 174-187, (1999)
[9] Stewart, T.J., Data envelopment analysis and multiple criteria decision-making - A response, Omega, 22, 205-206, (1994)
[10] Tofallis, C., Improving discernment in DEA using profiling, Omega, 24, 361-364, (1996)
[11] Tone, K., A slacks-based measure of efficiency in data envelopment analysis, European journal of operational research, 130, 498-509, (2001) · Zbl 0990.90523
[12] Zhu, J., Super-efficiency and DEA sensitivity analysis, European journal of operational research, 129, 443-455, (2001) · Zbl 0985.90058
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