A Ranking DEA model based on cross-weights evaluation

The cross-efficiency method in data envelopment analysis (DEA) has widely been used as a suitable utility for ranking decision-making units (DMUs). In cross-efficiency, the average of n efficiency values for each DMU is considered as the overall efficiency score. Another method based on the concept of cross-efficiency for calculating the efficiency score for each DMU is to use the average comparable weights to calculate the efficiency, which is called the cross-weight evaluation. In the cross-weight method, as in the cross-efficiency method, there is the issue of multiple optimal solutions. In this paper, for overcoming this issue, we use the neutral strategy for cross-weight evaluation. Unlike the aggressive and benevolent formulations, the neutral way is only concerned with its own interests and is indifferent to other DMUs. This study proposes a new cross-weight evaluation by maximizing the minimum of the output weights while keeping the efficiency of the unit under evaluation unchanged. Numerical examples are provided to illustrate the potential application of this new model and its effectiveness in ranking DMUs.