Data envelopment analysis cross-efficiency method of non-homogeneous decision-making units

Faced with a large number of the efficiency evaluation problems with non-homogeneous decision-making units (DMUs) in reality, the existing efficiency evaluation methods are always unfair in terms of evaluation perspective and inputs/outputs allocation. Therefore, this paper adopts the concept of network data envelopment analysis (DEA) to define the inclusion relationship of production structure between non-homogeneous DMUs. Sequentially, the DEA cross-efficiency model and its corresponding cross-evaluation strategy are constructed by combining the self-evaluation perspective with peer-evaluation perspective, and then the efficiency of these DMUs can be evaluated in a more objective and reasonable way. Actually, the cross-evaluation perspective can fully reflect the effect of non-homogeneous structure on efficiency. In addition, the inclusion relationship is extended to a mixed relationship, and the application scope of the new cross-efficiency method is thus further expended. Finally, two examples are provided to illustrate the effectiveness of the new method.