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A New Ranking Approach with a modified Cross Evaluation Matrix

Cross evaluation matrix was suggested to resolve a ranking problem in the data envelopment analysis (DEA) context. The cross evaluation matrix is composed of simple efficiency and cross-efficiency (CE) values of decision making units (DMUs). However, simple efficiency cannot discriminate efficient DMUs because of the nature of basic DEA models. To make complete use of the efficiency information of DMUs, a modified cross evaluation matrix is proposed. The modified matrix consists of super-efficiency (SE) values for diagonal elements and CE values for nondiagonal elements. As the efficiency values are not limited to "1" in SE approach, the proposed matrix can explain the difference of efficiency of efficient DMUs. The proposed matrix can be more accurate than the original cross evaluation matrix. Consequently, the rank order of DMUs generated by the suggested matrix reflects differences in relative efficiency of DMUs. A numerical example is given to show the superiority of the proposed approach. This is done by comparing with other available ranking methods in the DEA context. Several distance measures are utilized to compare rank consistency of the ranking methods. Finally, a case study is presented to explain how our approach is applied to real ranking problems.