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Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. (English) Zbl 1202.90249

Summary: In data envelopment analysis (DEA), the cross-efficiency evaluation method introduces a cross-efficiency matrix, in which the units are self and peer evaluated. A problem that possibly reduces the usefulness of the cross-efficiency evaluation method is that the cross-efficiency scores may not be unique due to the presence of alternate optima. So, it is recommended that secondary goals be introduced in cross-efficiency evaluation. In this paper we propose the symmetric weight assignment technique (SWAT) that does not affect feasibility and rewards decision making units (DMUs) that make a symmetric selection of weights. A numerical example is solved by our proposed method and its solution is compared with those of alternative approaches.

MSC:

90C32 Fractional programming
90C05 Linear programming
90B50 Management decision making, including multiple objectives
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[1] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. Oper. Res., 2, 429-444 (1978) · Zbl 0416.90080
[2] Dimitrov, S.; Sutton, W., Promoting symmetric weight selection in data envelopment analysis: a penalty function approach, Eur. J. Oper. Res., 200, 1, 281-288 (2010) · Zbl 1183.90227
[3] Sexton, T. R.; Silkman, R. H.; Hogan, A. J., Data envelopment analysis: critique and extensions, (Silkman, R. H., Measuring Efficiency: An Assessment of Data Envelopment Analysis, vol. 32 (1986), Jossey-Bass: Jossey-Bass San Francisco, CA), 73-105
[4] Anderson, T. R.; Hollingsworth, K. B.; Inman, L. B., The fixed weighting nature of a cross-evaluation model, J. Product. Anal., 18, 1, 249-255 (2002)
[5] Doyle, J. R.; Green, R., Efficiency and cross-efficiency in data envelopment analysis: derivatives, meanings and uses, J. Oper. Res. Soc., 45, 5, 567-578 (1994) · Zbl 0807.90016
[6] Liang, L.; Wu, J.; Cook, W. D.; Zhu, J., Alternative secondary goals in DEA cross-efficiency evaluation, Int. J. Prod. Econ., 113, 1025-1030 (2008)
[7] Wu, J.; Liang, L.; Zha, Y.; Yang, F., Determination of cross-efficiency under the principle of rank priority in cross-evaluation, Expert Syst. Appl., 36, 4826-4829 (2009)
[8] Alder, N.; Friedman, L.; Sinuany-Stern, Z., Review of ranking methods in the data envelopment analysis context, Eur. J. Oper. Res., 140, 249-265 (2002) · Zbl 1001.90048
[9] R. Allen, R.G. Dyson, A.R. Santos, E. Shale, Pitfalls and protocols in the application of DEA, in: Presented at the 39th Annual Conference of the Operational Research Society, Bath, UK, September 1997.; R. Allen, R.G. Dyson, A.R. Santos, E. Shale, Pitfalls and protocols in the application of DEA, in: Presented at the 39th Annual Conference of the Operational Research Society, Bath, UK, September 1997.
[10] Andersen, P.; Petersen, N. C., A procedure for ranking efficient units in data envelopment analysis, Manage. Sci., 39, 10, 1261-1294 (1993) · Zbl 0800.90096
[11] Friedman, L.; Sinuany-Stern, Z., Scaling units via the canonical correlation analysis and the data envelopment analysis, Eur. J. Oper. Res., 100, 3, 629-637 (1997) · Zbl 0918.90003
[12] Sinuany-Stern, Z.; Friedman, L., Data envelopment analysis and the discriminant analysis of ratios for ranking units, Eur. J. Oper. Res., 111, 470-478 (1998) · Zbl 0939.91112
[13] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage. Sci., 30, 9, 1078-1092 (1984) · Zbl 0552.90055
[14] Charnes, A.; Cooper, W. W.; Golany, B.; Seiford, L.; Stutz, J., Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, J. Econom., 30, 91-107 (1985) · Zbl 0582.90007
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