A new method for ranking non-extreme efficient units in data envelopment analysis

Data envelopment analysis (DEA) evaluates the performance of decision making units (DMUs). When DEA models are used to calculate efficiency of DMUs, a number of them may have the equal efficiency 1. In order to choose a winner among DEA efficient candidates, some methods have been proposed. But most of these methods are not able to rank non-extreme efficient DMUs. Since, the researches performed about ranking of non-extreme efficient units are very limited, incomplete and with some difficulties, we are going to develop a new method to rank these DMUs in this paper. Therefore, we suppose that DMU (o) is a non-extreme efficient under evaluating DMU. In continue, by using "Representation Theorem", DMU (o) can be represented as a convex combination of extreme efficient DMUs. So, we expect the performance of DMU (o) be similar to the performance of convex combination of these extreme efficient DMUs. Consequently, the ranking score of DMU (o) is calculated as a convex combination of ranking scores of these extreme efficient DMUs. So, the rank of this unit will be determined.