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A note on robustness of the efficient DMUs in data envelopment analysis. (English) Zbl 1006.91043

Summary: Sensitivity analysis of extreme efficient DMUs was studied by J. Zhu [Eur. J. Oper. Res. 90, 451-460 (1996; Zbl 0907.90007)] using the modified CCR A. Charnes, W. W. Cooper and E. Rhodes [Eur. J. Oper. Res. 2, 429-444 (1978; Zbl 0443.90090)] model. Upward proportional variations of inputs and downward proportional variations of outputs were considered. The procedure suggested by Zhu is a new approach to sensitivity analysis and can result in sufficient and necessary conditions on the changes which do not alter the efficiency of DMUs. However, in certain instances the results presented by Zhu do not hold. The aim of this note is to point out shortcomings which can be met following procedure proposed by Zhu. This includes inefficiency of so-called projected points, domination of obtained hyperplane, case of simultaneous changes of inputs and outputs, and case of infeasibility even if all data are greater than 0.

MSC:

91B38 Production theory, theory of the firm
90C05 Linear programming
90C31 Sensitivity, stability, parametric optimization
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References:

[1] 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
[2] Zhu, J., Robustness of the efficient DMUs in data envelopment analysis, European Journal of Operational Research, 90, 3, 451-460 (1996) · Zbl 0907.90007
[3] Charnes, A.; Cooper, W. W.; Thrall, R. M., A structure for classifying and characterizing efficiency and inefficiency in data envelopment analysis, The Journal of Productivity Analysis, 2, 197-237 (1991)
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