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Open AccessArticle

An Entropy-Based Cross-Efficiency under Variable Returns to Scale

by Chun-Hsiung Su 1 and Tim Lu 2,*
1
Department of Tourism and Leisure Management, Vanung University, Zhongli, Taoyuan 320, Taiwan
2
Department of Marketing and Logistics, Vanung University, Zhongli, Taoyuan 320, Taiwan
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1205; https://doi.org/10.3390/e21121205
Received: 4 November 2019 / Revised: 4 December 2019 / Accepted: 5 December 2019 / Published: 7 December 2019
Cross-efficiency evaluation is an effective methodology for discriminating among a set of decision-making units (DMUs) through both self- and peer-evaluation methods. This evaluation technique is usually used for data envelopment analysis (DEA) models with constant returns to scale due to the fact that negative efficiencies never happen in this case. For cases of variable returns to scale (VRSs), the evaluation may generate negative cross-efficiencies. However, when the production technology is known to be VRS, a VRS model must be used. In this case, negative efficiencies may occur. Negative efficiencies are unreasonable and cause difficulties in calculating the final cross-efficiency. In this paper, we propose a cross-efficiency evaluation method, with the technology of VRS. The cross-efficiency intervals of DMUs were derived from the associated aggressive and benevolent formulations. More importantly, the proposed approach does not produce negative efficiencies. For comparison of DMUs with their cross-efficiency intervals, a numerical index is required. Since the concept of entropy is an effective tool to measure the uncertainty, this concept was employed to build an index for ranking DMUs with cross efficiency intervals. A real-case example was used to illustrate the approach proposed in this paper. View Full-Text
Keywords: data envelopment analysis; cross efficiency; Shannon’s entropy; variable returns to scale; ranking data envelopment analysis; cross efficiency; Shannon’s entropy; variable returns to scale; ranking
MDPI and ACS Style

Su, C.-H.; Lu, T. An Entropy-Based Cross-Efficiency under Variable Returns to Scale. Entropy 2019, 21, 1205.

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