Cross-efficiency evaluation in data envelopment analysis based on the perspective of fairness utility

摘要

Data envelopment analysis (DEA) has been widely applied as an effective data-driven tool in evaluating the efficiency of decision making units (DMUs). However, traditional DEA models evaluate DMU efficiencies in a self-evaluation mode. As an extension of traditional DEA, cross-efficiency evaluation links one DMU's performance with others and has the appeal that scores arise from peer evaluation. Unfortunately, the problem of non-unique optimal weights has reduced the usefulness of this extended method. Although, some current secondary goal approaches have reduced the non-uniqueness of optimal weights, they are mostly based on the perspectives of improving or worsening the evaluated DMU's or other DMUs' position or efficiency, which fails to consider DMU's fairness mentality that plays an important role in guiding human interaction in behavioral economics. To fill this gap, we propose the concept of a fairness utility to construct our secondary goal model. Specifically, the secondary goal is to maximize the minimum fairness of the other DMUs when keeping the evaluated DMU's optimal efficiency. Two algorithms are proposed. One is used to solve the nonlinear fairness utility model. The other is used to guarantee the unique optimal weights. Finally, a numerical example is presented, and an empirical application is given to verify the proposed method.