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

Lu, Tim; Liu, Shiang-Tai

doi:10.3390/e18120452

Cited by 9 publications

(16 citation statements)

References 51 publications

(72 reference statements)

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“…Wang et al [24] explored the DEA entropy model to construct the cross-efficiency intervals for ranking DMUs. Lu and Liu [25] considered the benevolent and aggressive and formulations simultaneously for obtaining a number of cross-efficiency intervals, and the entropy was used to build a numerical index for the DMUs to be comparable. Rotela Junior et al [26] adopted a DEA model in portfolio optimization, and Shannon entropy was included to ensure an efficient asset diversification while return and portfolio risk were maximized and minimized, respectively.…”

Section: The Entropymentioning

confidence: 99%

“…Since we take into account the aggressive and benevolent cross-efficiency at the same time, a family of cross-efficiency intervals is derived for each DMU. The idea of Lu and Liu [25], which calculated the entropy value of the cross-efficiency interval, is adopted to construct a numerical index for DMUs with cross efficiency intervals.…”

Section: The Entropymentioning

confidence: 99%

“…With the smallest entropy (uncertainty) of each DMU, we can discriminate DMUs more easily. Based on Lu and Liu [25], Equation (13) can be transformed intô…”

Section: The Entropymentioning

confidence: 99%

See 2 more Smart Citations

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

2019

Entropy

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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.

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Section: The Entropymentioning

confidence: 99%

Section: The Entropymentioning

confidence: 99%

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

2019

Entropy

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“…Data envelop analysis (DEA) is a linear programming model and non-parametric approach that evaluates relative technical efficiencies of decision making units (DMUs) on the basis of multiple inputs and outputs by computing the ratio of weighted sum of their outputs to their inputs [1]. This technique has been used in many fields successfully with crisp values, however in real application there are inaccurate data similar to probabilistic, interval, ordinal, qualitative, or fuzzy.…”

Section: Introductionmentioning

confidence: 99%

“…This technique has been used in many fields successfully with crisp values, however in real application there are inaccurate data similar to probabilistic, interval, ordinal, qualitative, or fuzzy. Hence, some researchers conducted several theoretical development of DEA model with data such as interval [1]. Nevertheless, there are many models and techniques to solve this problem, but there is a new problem for ranking the efficient DMUs with interval data, so that in some researches DMUs were ranked by these ideal points [2,3].…”

Section: Introductionmentioning

confidence: 99%

Hybrid cluster analyzing and data envelopment analysis with interval data

et al. 2017

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Data envelope analysis (DEA) is an approach to estimate the relative efficiency of decision making units (DMUs). Several studies were conducted in order to prioritize efficient units and some useful models such as cross-efficiency matrix (CEM) were presented. Besides, a number of DEA models with interval data have been developed and ranking DMUs with such data was solved. However, presenting an obtained crisp data derived interval data is a critical problem, so that many researches were implemented so as to compute weights and averaging the interval data. In this paper we propose the new algorithm to find more suitable weight applying a data mining approach of DMU's data. For this purpose, we employed clustering 2 and pair-wise comparison matrix on given relative efficiency from CEM. Results indicate there is meaningful different between efficiency of DMUs with lower bound and that of DMUs with upper bound.

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