Dominance relations and ranking of units by using interval number ordering with cross-efficiency intervals

This paper proposes an approach to the cross‐efficiency evaluation that considers all the optimal data envelopment analysis (DEA) weights of all the decision‐making units (DMUs), thus avoiding the need to make a choice among them according to some alternative secondary goal. To be specific, we develop a couple of models that allow for all the possible weights of all the DMUs simultaneously and yield individual lower and upper bounds for the cross‐efficiency scores of the different units. As a result, we have a cross‐efficiency interval for the evaluation of each unit. Existing order relations for interval numbers are used to identify dominance relations among DMUs and derive a ranking of units based on the cross‐efficiency intervals provided. The approach proposed may also be useful for assessing the stability of the cross‐efficiency scores with respect to DEA weights that can be used for their calculation.