Cross-Efficiency Evaluation Based on an Interval Method

Abstract

In data envelopment analysis (DEA), several secondary goals have already been proposed in order to overcome the problem of the DEA alternative optimal weights in the cross-efficiency evaluation. However, in the presence of different secondary goals, the rank assigned to some of decision making units (DMUs) may be non-unique. To overcome the shortcomings, this paper considers the elements of cross-efficiency matrix as interval numbers based on maximum and minimum cross-efficiency that each of the DMUs can achieve. Then, the study using a formula reorders the aggregated interval numbers in each row of the cross-efficiency matrix, and obtains the rank of each of DMUs. The new method removes the problem of the DEA alternative optimal weights in the cross-efficiency evaluation. Moreover, it provides a distinct and unique rank to each of the DMUs. Ultimately, the usefulness of the proposed method in comparison with the previous methods is demonstrated by using a numerical example.