Inverse DEA based resource allocation method for nonhomogeneous decision-making units

Inverse data envelopment analysis (DEA) method is a useful tool for analyzing the optimization of resource allocation of a set of homogeneous decision-making units (DMUs). However, the assumption of homogeneity for DMUs is not necessarily applied in reality. For example, universities with the same input structure cultivate students with different orientations; power plants consume different resources to generate electricity. Therefore, how to handle nonhomogeneous DMUs in inverse DEA becomes an issue when analyzing the optimization of resource allocation. In this study, an inverse DEA method for nonhomogeneous DMUs under constant returns to scale (CRS) is proposed to handle the aforementioned issue. Furthermore, the inverse DEA method for nonhomogeneous DMUs is extended to the case of variable returns to scale (VRS). The adjustment range of inputs-outputs under VRS is discussed to avoid the problem of infeasibility, and relevant properties of our method are proved. Moreover, the effect of frontier changes on the proposed method is also discussed. Finally, numerical examples are provided to illustrate the effectiveness of our method.