Jahanshahloo, G. R.; Hosseinzadeh Lotfi, F.; Jafari, Y.; Maddahi, R. Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation. (English) Zbl 1202.90249 Appl. Math. Modelling 35, No. 1, 544-549 (2011). 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. Cited in 22 Documents MSC: 90C32 Fractional programming 90C05 Linear programming 90B50 Management decision making, including multiple objectives Keywords:data envelopment analysis; cross-efficiency; ranking PDFBibTeX XMLCite \textit{G. R. Jahanshahloo} et al., Appl. Math. Modelling 35, No. 1, 544--549 (2011; Zbl 1202.90249) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.