DEA cross-efficiency aggregation method based upon Shannon entropy

Abstract

Existing approaches for DEA cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each Decision Making Unit (DMU) and view it as the overall performance measurement of the DMU. This paper focuses on the aggregation process of the efficiencies in the cross-efficiency matrix and proposes the use of Shannon entropy for cross-efficiency aggregation. In the study, we propose an entropy model to generate a set of weights for aggregating and determining the ultimate cross-efficiency instead of the traditional average cross-efficiency. We prove that the set of weight is a unique global optimal solution which can reflect the goodness of this method. Finally, two examples of a flexible manufacturing system and 27 industrial robots are illustrated to examine the validity of the proposed method.

Keywords:

• data envelopment analysis (DEA)
• cross-evaluation
• cross-efficiency
• Shannon entropy

Acknowledgements

The research is supported by National Natural Science Funds of China for Innovative Research Groups (No. 70821001), National Natural Science Funds of China (No. 70901069) and The Fundamental Research Funds for the Central Universities (No. WK2040150007).