An aggressive game cross-efficiency evaluation in data envelopment analysis

Cross-efficiency evaluation is an effective method for ranking decision making units (DMUs) in data envelopment analysis, which is performed with peer-evaluation and self-evaluation. From different points of view, various cross-efficiency evaluations have been proposed with different secondary goals...

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Bibliographic Details
Published in:Annals of operations research 2017-12, Vol.259 (1-2), p.241-258
Main Authors: Liu, Wenli, Wang, Ying-Ming, Lv, Shulong
Format: Article
Language:English
Subjects:
Business and Management
Combinatorics
Data envelopment analysis
Decision analysis
Decision making
Efficiency
Game theory
Games
Iterative algorithms
Iterative methods
Mathematical models
Methods
Operations research
Operations Research/Decision Theory
Original Paper
Ranking
Retail sales
Theory of Computation
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Summary:Cross-efficiency evaluation is an effective method for ranking decision making units (DMUs) in data envelopment analysis, which is performed with peer-evaluation and self-evaluation. From different points of view, various cross-efficiency evaluations have been proposed with different secondary goals. Yet they usually lead to different average cross-efficiencies and different rankings. In this paper, we develop a concept of the aggressive game cross-efficiency, and propose an aggressive secondary model to minimize the cross-efficiencies of other DMUs under the constraints that the aggressive game cross-efficiency of the evaluated DMU is guaranteed. To achieve the aggressive game cross-efficiency, we develop an iterative algorithm. Mathematically, it is proved that all conventional average cross-efficiencies are sure to converge to the same aggressive game cross-efficiency by the iterative algorithm. Finally, numerical examples are presented to show the effectiveness of our approach in evaluating and ranking DMUs.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-017-2524-1