DEA cross-efficiency ranking method considering satisfaction and consensus degree

Cross-efficiency evaluation in data envelopment analysis is an effective way to rank decision-making units (DMUs). However, different cross-efficiency evaluation models derived from different perspectives generate different cross-efficiency rankings. The information resulting from the various perspectives may be valuable and should not be ignored. In this paper, we propose an innovative composite method for ranking DMUs by calculating the Shannon entropy of the obtained cross-efficiency scores derived from the perspectives of satisfaction and consensus. Also, we adopt grey incidence analysis to compare the rankings of different cross-efficiency models. The calculation procedure using Shannon entropy and grey incidence analysis is illustrated on an example to generate the composite ranking result and compare it to other cross-efficiency model rankings. The cross-efficiency ranking using both satisfaction and consensus information provides a new comprehensive perspective in group evaluation. A practical example is used to show that the cross-efficiency results obtained from the composite perspective of satisfaction and consensus should be widely accepted in practical decision-making.