Obtaining a Unique Solution for Cross Efficiency in order to rank DMUs in Data Envelopment Analysis

Abstract

In Data Envelopment Analysis (DEA), weights are generally chosen in a manner that assigns a best set of weights to each Decision Making Unit (DMU). Although total freedom of weights is one of the advantages of DEA, it gives rise to some practical limitations such as: the high number of efficient DMUs and contradiction to prior observations or available information. For solving these problems, various ranking and weight restriction methods have been introduced before. Cross efficiency which is used for evaluation and ranking is a method that uses the idea of peer evaluation instead of a self-evaluation and as a result reduces the effects of total freedom of weights in this way. But since DEA weights are generally not unique, cross efficiency which uses optimal weights corresponding to evaluation of DMUs may not be unique either. This defect decreases the usefulness of the cross-evaluation method. In this paper, we present a method for obtaining a unique solution for cross efficiency and then try to rank all DMUs including efficient (extreme or non-extreme) and inefficient units. Our method is based upon maximizing the efficiency of each DMU over the set of alternative optimal solution of other DMUs when they were evaluated by CCR model. Then, we try to obtain ranking scores for under evaluation DMUs by using SAW and TOPSIS methods.