Data envelopment analysis cross efficiency evaluation with reciprocal behaviors

Data envelopment analysis (DEA) has proven to be a powerful technique for performance evaluation since its inception. Since the traditional DEA approaches lack discrimination power among efficient decision-making units (DMUs), the cross efficiency method has been proposed for peer appraisal in the literature. However, the previous cross efficiency approaches imposed a single and identical evaluation strategy across all DMUs simultaneously. In addition, all the related studies have considered a static issue without the dynamic alternation of evaluation strategies. In this paper, the reciprocal behaviors among DMUs are considered to address the cross efficiency evaluation, and a novel threshold value is used to determine positive or negative reciprocal behaviors by comparing the peer-evaluated efficiency with the threshold value based efficiency. This study assumes that a DMU would show positive behavior and apply a benevolent strategy toward other DMUs that evaluate it friendly, while it also shows negative behavior and apply an aggressive strategy toward DMUs that evaluate it hostilely. Furthermore, a game-like iteration process is developed for each DMU to determine and further adjust its evaluation strategy toward other DMUs in the evaluation process. Afterward, we calculate the optimal ultimate cross efficiency score with reciprocal behaviors. Finally, the proposed approach is applied to both a numerical example and an empirical study of 31 Chinese manufacturing industries to demonstrate its usefulness and efficacy.