Cross-efficiency evaluation in data envelopment analysis (DEA) is a useful tool in evaluating the performance of decision-making units (DMUs). It is generally assumed that decision makers (DMs) are completely rational in common cross-efficiency evaluation models, which fail to consider the DM's risk attitude that plays an important role in the evaluation process. To fill this gap, we investigate the cross-efficiency evaluation in DEA based on prospect theory. First, we introduce a prospect value of the DMU to capture the non-rational psychological aspects of a DM under risk. Second, based on the prospect value, we propose a new cross-efficiency model termed the prospect cross-efficiency (PCE) model. Particularly, some existing cross-efficiency evaluation models can be deemed as the special cases of the PCE model with suitable adjustments of the parameters. Furthermore, this paper provides an empirical example to evaluate cross-efficiency with several selected universities directly managed by the Ministry of Education of China to illustrate the effectiveness of the PCE model in ranking DMUs.
Cross-efficiency evaluation, developed by Sexton, Silkman, and Hogan (1986), has been widely accepted as a discriminative assessment tool for data envelopment analysis (DEA). It is generally used for distinguishing efficient decision-making units (DMUs) from one another (Despotis, 2002). Each DMU in cross-efficiency evaluation has a self-evaluated efficiency derived by its own set of optimal weights and n 1 peer-evaluated efficiencies obtained by the optimal weights of other DMUs. Consequently, a final efficiency for ranking DMUs is aggregated based on n efficiencies. The major characteristics of cross-efficiency evaluation are the following: (1) ranking the DMUs in a unique order (Doyle & Green, 1995), (2) eliminating unrealistic weight schemes without predetermining any weight restrictions (Anderson, Hollingsworth, & Inman, 2002), and (3) effectively differentiating between good and poor performers among the DMUs (Boussofiane, Dyson, & Thanassoulis, 1991). Due to these advantages, cross-efficiency evaluation has been used in a variety of applications, including project ranking (Green, Doyle, & Cook, 1996), the measurement of the labour assignment in a cellular manufacturing system (Ertay & Ruan, 2005), sports rankings (Wu, Liang, & Chen, 2009), corporate philanthropic selection (Partovi, 2011), the supplier selection problem in public procurement (Falagario, Sciancalepore, Costantino, & Pietroforte, 2012), and portfolio selection (Lim, Oh, & Zhu, 2014; Mashayekhi & Omrani, 2016). Despite the many advantages and wide applications of cross-efficiency, its usefulness is possibly reduced by the non-uniqueness of the optimal weights (Doyle & Green, 1994). Specifically, the possible existence of multiple optimal weights in the evaluation leads to different sets of cross-efficiency scores for each DMU.