Ranking DMUs by combining cross-efficiency scores based on Shannon's entropy

Abstract

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.