Ranking efficient DMUs using the infinity norm and virtual inefficient DMU in DEA

In many applications, ranking of decision making units (DMUs) is a problematic technical task procedure to decision makers in data envelopment analysis (DEA), especially when there are extremely efficient DMUs. In such cases, many DEA models may usually get the same efficiency score for different DMUs. Hence, there is a growing interest in ranking techniques yet. The purpose of this paper is ranking extreme efficient DMUs in DEA based on exploiting the leave-one out and minimizing the maximum distance between DMU under evaluation and boundary efficient in input and output directions. The proposed method has been able to overcome the lacks of infeasibility and unboundedness in some DEA ranking methods.