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

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 t...

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Autores principales: Su, Chun-Hsiung, Lu, Tim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514551/
http://dx.doi.org/10.3390/e21121205
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author Su, Chun-Hsiung
Lu, Tim
author_facet Su, Chun-Hsiung
Lu, Tim
author_sort Su, Chun-Hsiung
collection PubMed
description 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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spelling pubmed-75145512020-11-09 An Entropy-Based Cross-Efficiency under Variable Returns to Scale Su, Chun-Hsiung Lu, Tim Entropy (Basel) Article 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. MDPI 2019-12-07 /pmc/articles/PMC7514551/ http://dx.doi.org/10.3390/e21121205 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Su, Chun-Hsiung
Lu, Tim
An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title_full An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title_fullStr An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title_full_unstemmed An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title_short An Entropy-Based Cross-Efficiency under Variable Returns to Scale
title_sort entropy-based cross-efficiency under variable returns to scale
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514551/
http://dx.doi.org/10.3390/e21121205
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