An optimistic-pessimistic DEA model based on game cross efficiency approach
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 1215-1230.

The ranking of the decision making units (DMUs) is an essential problem in data envelopment analysis (DEA). Numerous approaches have been proposed for fully ranking of units. Majority of these methods consider DMUs with optimistic approach, whereas their weaknesses are ignored. In this study, for fully ranking of the units, a modified optimistic–pessimistic approach, which is based on game cross efficiency idea is proposed. The proposed game like iterative optimistic-pessimistic DEA procedure calculates the efficiency scores according to weaknesses and strengths of units and is based on non-cooperative game. This study extends the optimistic-pessimistic DEA approach to obtain robust rank values for DMUs. The proposed approach yields Nash equilibrium solution, thus overcomes the problem of non-uniqueness of the DEA optimal weights that can possibly reduce the usefulness of cross efficiency. Finally, in order to verify the validity of the proposed model and to show the practicability of algorithm, we apply a real-world example for selection of industrial R&D projects. The proposed model can increase the discriminating power of DMUs and can fully rank the DMUs.

DOI : 10.1051/ro/2019052
Classification : 90C05, 90C90, 91A80
Mots-clés : Optimistic-pessimistic DEA, game cross efficiency, fully ranking 
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     title = {An optimistic-pessimistic {DEA} model based on game cross efficiency approach},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Örkcü, Mediha; Özsoy, Volkan Soner; Örkcü, H. Hasan. An optimistic-pessimistic DEA model based on game cross efficiency approach. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 4, pp. 1215-1230. doi : 10.1051/ro/2019052. http://archive.numdam.org/articles/10.1051/ro/2019052/

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