The cross-efficiency in the optimistic–pessimistic framework

In spite of strong discrimination power, the cross-efficiency methods suffer from some drawbacks that may limit their usefulness. The possible existence of multiple optimal weights may lead to the non-uniqueness of cross-efficiency scores and rankings. Also, some of these methods evaluate decision making units (DMUs) according to an optimistic approach. In this approach, the strengths of DMUs are considered, whereas their weaknesses are ignored. To reflect the real performance of DMUs, both weaknesses and strengths of them must be considered. In this study, an optimistic–pessimistic approach is applied for presenting a new cross-efficiency method. In the proposed method, the estimated scores are based on both weaknesses and strengths of DMUs. Also, using the proposed models, the optimal weights are uniquely determined. So, the proposed method can fully rank DMUs without needing to any secondary goal. Finally, our method is illustrated using two examples.