Cross-efficiency in DEA: A maximum resonated appreciative model

The occurrence of multiple optimal solutions is an important and interesting issue in data envelopment analysis (DEA), for it allows flexibility to estimate the optimal cross-efficiencies of all decision making units (DMUs). This paper uses the advantage of multiple optimal solutions, be in the cases of efficient and/or inefficient DMUs, to integrate both the first and second-order voices of all DMUs and proposes a most appreciative cross-efficiency DEA method. The paper deals with multiple optimal solution cases within the context of cross-efficiency models and suggest a model that is most appreciative for all DMUs being cross-evaluated by all others. The merits and appreciative superiority of the proposed method is proven theoretically; and illustrated practically through a ranking study chosen from the literature.