A regret cross-efficiency ranking method considering consensus consistency

Abstract

Data envelopment analysis (DEA) is a powerful nonparametric approach for assessing the performance of decision making units (DMUs). Traditional DEA models usually utilize a self-evaluation mode to evaluate DMUs, which have the following shortcomings such as efficiency overestimation and incomplete ranking. As the extension of traditional DEA, cross-efficiency (CE) evaluation remedies these limitations. It connects self-evaluation with peer-evaluation to appraise DMUs and rank them. However, most existing studies on CE evaluation utilize the arithmetic average method to aggregate self-evaluation efficiency and peer-evaluation efficiency, while ignoring the significance of self-efficiency and the irrational psychology of decision-makers (DMs). Observed by the aforementioned phenomena, this paper employs regret theory to portray the regret aversion behavior of DMs and further proposes a novel regret cross-efficiency aggregation (RCEA) method. Considering aggressive and benevolent cross-efficiency models, we apply the RCEA method to calculate the regret-based aggressive cross-efficiency and the regret-based benevolent cross-efficiency, and introduce a parameter reflecting the psychological preference of DMs to aggregate them. To attain consensus between DMUs’ expectations for efficiency and the ultimate integration results, we design a regret cross-efficiency adjustment algorithm. This algorithm provides a more acceptable evaluation result and derives a full ranking for all DMUs. Finally, the validity and feasibility of the proposed model are illustrated by evaluating the efficiency of scientific research activities in 13 universities in China.