A closer target setting approach to boundary problems with the Russell graph measure

Abstract

A Russell graph measure (RGM) is one of the standard DEA models, but its efficiency measure is not well-defined--or has unacceptable properties--at the boundary of the nonnegative orthant. This is known as a boundary problem. Existing studies have tackled this issue; however, their models may fail to identify an efficient target or fail to satisfy some desirable properties of efficiency measures. In this paper, we incorporate a closer target setting approach into the RGM model with production trade-offs to overcome such issues. We demonstrate that the efficiency measure of the proposed model overcomes the boundary problem and has stronger properties than existing models. We also demonstrate that the efficiency scores of the proposed model can be computed by solving a series of LPs. We conduct a numerical experiment with a real-world dataset to illustrate how targets provided by our model are realistic compared with the existing model, which also suggests the validity of our model in applications.