Ranking of units by corrected cross-efficiency method using optimal weights in the smallest interval

Abstract

An important method for ranking of decision making units (DMUs) in data envelopment analysis (DEA) is cross-efficiency method. This study proposes a secondary multi-objective model for calculating optimal weights with least dispersion. Firstly, these weights are placed in the smallest interval. Secondly, the cross-efficiency of each of the other units has the least deviation from the CCR efficiency of the same unit. Therefore, optimal weights are obtained which have the least dispersion. As result, the zero optimal weights which lead to the triviality of the relevant index, are avoided as far as possible. Hence, using the average cross-efficiency, the results of the ranking would be more reasonable. Using the proposed model for ranking of six nursing homes, the results show that this model is more accurate. Finally, in order to improve performance of the emergency department of a hospital, the proposed model is used to rank 11 defined scenarios.