Determination of Weights for the Ultimate Cross Efficiency: A Use of Principal Component Analysis Technique

Data Envelopment Analysis (DEA) has becoming more and more important in evaluating the performance of homogenous Decision Making Units (DMUs). Cross efficiency evaluation method, a DEA extension technique, can be utilized to identify efficient DMUs and to rank DMUs in a peer appraisal mode, instead of a pure self-evaluation of traditional DEA models. Traditionally, the ultimate cross efficiency is determined based on the average assumption. However it cannot ensure this result contains the most information of the cross-efficiency matrix (CEM). In the current paper, we use principal component analysis (PCA) to determine the ultimate cross-efficiency of each DMU and then rank them. Compared with the tradition average cross efficiency evaluation method, the method proposed in this paper can contain the most of the information of CEM. Finally, an empirical example is illustrated to examine the validity of the proposed method.