Noura, A. A.; Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Fanati Rashidi, S. Super-efficiency in DEA by effectiveness of each unit in society. (English) Zbl 1207.90066 Appl. Math. Lett. 24, No. 5, 623-626 (2011). Summary: One of the most important topics in management science is determining the efficiency of Decision Making Units (DMUs). The Data Envelopment Analysis (DEA) technique is employed for this purpose. In many DEA models, the best performance of a DMU is indicated by an efficiency score of one. There is often more than one DMU with this efficiency score. To rank and compare efficient units, many methods have been introduced under the name of super-efficiency methods. Among these methods, one can mention P. Andersen and N. C. Petersen’s [Manage. Sci. 39, No. 10, 1261–1264 (1993; Zbl 0800.90096)] super-efficiency model, and the slack-based measure introduced by K. Tone [Eur. J. Oper. Res. 130, No. 3, 498–509 (2001; Zbl 0990.90523)]. Each of the methods proposed for ranking efficient DMUs has its own advantages and shortcomings. In this paper, we present a super-efficiency method by which units that are more effective and useful in society have better ranks. In fact, in order to determine super-efficiency by this method, the effectiveness of each unit in society is considered rather than the cross-comparison of the units. To do so, we divide the inputs and outputs into two groups, desirable and undesirable, at the discretion of the manager, and assign weights to each input and output. Then we determine the rank of each DMU according to the weights and the desirability of inputs and outputs. Cited in 2 Documents MSC: 90B50 Management decision making, including multiple objectives 90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) Keywords:efficiency; decision making unit; data envelopment analysis; ranking; super efficiency Citations:Zbl 0800.90096; Zbl 0990.90523 PDFBibTeX XMLCite \textit{A. A. Noura} et al., Appl. Math. Lett. 24, No. 5, 623--626 (2011; Zbl 1207.90066) Full Text: DOI 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] Doyle, J.; Green, R., Data envelopment analysis and multiple criteria decision making, Omega, 21, 713-715 (1993) [3] Tofallis, C., Improving discernment in DEA using profiling, Omega, 24, 361-364 (1996) [4] Tone, K., A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 130, 498-509 (2002) · Zbl 0990.90523 [5] Du, J.; Liang, L.; Zhu, J., A slacks-based measure of efficiency in data envelopment analysis: a comment, European Journal of Operational Research, 204, 694-697 (2010) · Zbl 1181.90148 [6] 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 [7] Ringuest, J. L., Multi Objective Optimization: Behavioral and Computational Considering (1992), Kluwer Academic Publishers 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.