Improving the evaluation of cross efficiencies: A method based on Shannon entropy weight

- Cross-efficiency evaluation method for DEA analysis has been proposed.
- Two cross efficiency models, MAX and MIN are proposed.
- The aggregation problem of cross efficiency a Shannon entropy approach is applied.
- Results on production data from 15 thermoelectric enterprises in China are discussed.

Data envelopment analysis (DEA) is a non-parametric statistical method used to assess the production frontiers of decision-making units (DMUs) and evaluate their relative efficiencies. However, using traditional DEA models to evaluate efficiency has certain deficiencies. For example, some DMUs cannot be ranked fully using traditional DEA models. To solve such problems, the cross-efficiency evaluation method has been proposed to replace the self-evaluation system. Nevertheless, this method, which uses a mutual evaluation system to overcome the ranking issue, still has shortcomings such as non-unique cross efficiency weights, which may result in multiple cross efficiency values. Further, providing adequate performance improvement tools to decision makers is difficult using only the average efficiency values. To address the problems of uniqueness and aggregation, this study proposes two cross efficiency models, designated MAX and MIN models. The self-evaluated optimal weight of a certain DMU derived from these MAX and MIN models can maximize or minimize the efficiency of the DMU to form two cross efficiency matrices, which can partially solve the problem that results from multiple optimal weights. To solve the aggregation problem of cross efficiency, the study also applies Shannon entropy, which classifies all cross efficiency values into one group of acquired common objective weights to avoid subjective factors. Finally, the present study confirms an improvement when using the proposed method by examining production data on 15 thermoelectric enterprises in China.