Cross-Efficiency Evaluation Based on an Interval Method

Subject Areas : International Journal of Data Envelopment Analysis

M  Khodadadi ¹ (Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran)
Ghasem  Tohidi ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, Iran)

Received: 2017-05-30 Accepted : 2017-05-30 Published : 2016-09-01

Keywords: Data envelopment analysis (DEA, Cross-efficiency evaluation, Interval numbers,

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.

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