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Entropy 2016, 18(12), 452;

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Department of Marketing and Logistics, Vanung University, Chung-Li, Tao-Yuan 320, Taiwan
Graduate School of Business and Management, Vanung University, Chung-Li, Tao-Yuan 320, Taiwan
Author to whom correspondence should be addressed.
Academic Editors: Kevin H. Knuth and Adom Giffin
Received: 7 November 2016 / Revised: 12 December 2016 / Accepted: 14 December 2016 / Published: 17 December 2016
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Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper. View Full-Text
Keywords: data envelopment analysis; cross-efficiency; entropy; ranking data envelopment analysis; cross-efficiency; entropy; ranking
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Lu, T.; Liu, S.-T. Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures. Entropy 2016, 18, 452.

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