Ranking DMUs by Combining Cross-Efficiency Scores Based on Shannon’s Entropy

Cross-efficiency evaluation is an effective approach for ranking decision-making units (DMUs), and there exist different perspectives from different cross-efficiency evaluation models. However, efficiency ranking results derived from cross-efficiency models may not be the same, and these models may provide some precious information that we cannot ignore. In this case, it may not be easy for one to decide which method should be used in some underlying assumptions, and we need several cross-efficiency evaluation models to measure simultaneously the cross-efficiency scores of DMUs. Hence, combining different viewpoints for ranking DMUs is a possible way to apply cross-efficiency evaluation. Since Shannon’s entropy is an effective tool to measure uncertainty, in this study we adopt the idea of Shannon’s entropy to combine cross-efficiency scores, which are obtained from different evaluation models, for comparison of DMUs. An example of commercial banks in Taiwan is used to illustrate the idea proposed in this paper.

[1]  Amar Oukil,et al.  Ranking via composite weighting schemes under a DEA cross-evaluation framework , 2018, Comput. Ind. Eng..

[2]  Jie Wu,et al.  The DEA Game Cross-Efficiency Model and Its Nash Equilibrium , 2008, Oper. Res..

[3]  Shiang-Tai Liu,et al.  A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio , 2018, Ann. Oper. Res..

[4]  Rodney H. Green,et al.  Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses , 1994 .

[5]  Jie Wu,et al.  Alternative secondary goals in DEA cross-efficiency evaluation , 2008 .

[6]  Peng Jiang,et al.  Weight determination in the cross-efficiency evaluation , 2011, Comput. Ind. Eng..

[7]  Gholam R. Amin,et al.  Peer-judgment risk minimization using DEA cross-evaluation with an application in fishery , 2019, Ann. Oper. Res..

[8]  Lei Li,et al.  Entropy Cross-Efficiency Model for Decision Making Units with Interval Data , 2016, Entropy.

[9]  Andrés Camilo,et al.  Evaluación de la eficiencia relativa de los sistemas de producción porcícolas del departamento de Cundinamarca, utilizando análisis envolvente de datos (DEA) , 2020 .

[10]  Jie Wu,et al.  Extended secondary goal models for weights selection in DEA cross-efficiency evaluation , 2016, Comput. Ind. Eng..

[11]  Jie Wu,et al.  Cross efficiency evaluation method based on weight-balanced data envelopment analysis model , 2012, Comput. Ind. Eng..

[12]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .

[13]  Nuria Ramón,et al.  Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation , 2011 .

[14]  T. Sexton,et al.  Data Envelopment Analysis: Critique and Extensions , 1986 .

[15]  Yongjun Li,et al.  Increasing the Discriminatory Power of DEA Using Shannon's Entropy , 2014, Entropy.

[16]  Majid Soleimani-Damaneh,et al.  Shannon's entropy for combining the efficiency results of different DEA models: Method and application , 2009, Expert Syst. Appl..

[17]  Bo Guo,et al.  Determining Common Weights in Data Envelopment Analysis with Shannon's Entropy , 2014, Entropy.

[18]  Ying-Ming Wang,et al.  An aggressive game cross-efficiency evaluation in data envelopment analysis , 2017, Ann. Oper. Res..

[19]  Carreño Carreño,et al.  Evaluación de la diversidad taxonómica y funcional de la comunidad microbiana relacionada con el ciclo del nitrógeno en suelos de cultivo de arroz con diferentes manejos del tamo , 2020 .

[20]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[21]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[22]  Shiang-Tai Liu,et al.  Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures , 2016, Entropy.

[23]  A. Vannucci,et al.  BICS Bath Institute for Complex Systems A note on time-dependent DiPerna-Majda measures , 2008 .

[24]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[25]  T. Anderson,et al.  The Fixed Weighting Nature of A Cross-Evaluation Model , 2002 .