DEA Cross-Efficiency Ranking Method Based on Grey Correlation Degree and Relative Entropy

Abstract

The ranking of decision-making units (DMUs) is one of the most significant issues in efficiency evaluation. However, the calculation results from the traditional Data envelopment analysis(DEA), method sometimes include multiple efficient DMUs or multiple DMUs with the same efficiency value, in which case the approach is weak in distinguishing among these DMUs. Therefore, this study proposes a DEA cross-efficiency ranking method based on the relative entropy evaluation method and the grey relational analysis method. First, the approach uses the cross-efficiency matrix as the decision matrix of multiple criteria decision-making (MCDM), and the relationship between DMU and the ideal solution is analyzed by the grey relational analysis method and the relative entropy evaluation method. Then, the degree of the criteria is determined by Shannon entropy, and the weighted grey correlation degree and the weighted relative entropy are obtained. Finally, with the comprehensive relative closeness degree between the DMU and the ideal solution, we can sort all the DMUs accordingly. In a comparative analysis, it shows that this method analyzes the similarity between DMUs and the ideal solution from the information distance and the similarity of the data sequence curve, and has certain advantages for analyzing the ranking of DMUs.