Non-cooperative two-stage network DEA model: Linear vs. parametric linear

Abstract

In the data envelopment analysis (DEA) literature, linear fractional non-cooperative network DEA models for two-stage network structures are often transformed into parametric linear models. The transformed parametric linear models are then solved by computing a series of linear models when the parameter is varied. For example, Wu, Zhu, Ji, Chu and Liang (2016) provide a linear fractional non-cooperative DEA model for analyzing the reuse of undesirable intermediate outputs in a two-stage production process with a shared resources and feedback. They transformed the linear fractional model into a parametric linear model. Such approaches do not guarantee that the global optimal solution is found. We show that (variants of) linear fractional non-cooperative network DEA models can be directly transformed into a linear programing model, without the need for solving parametric linear models. This greatly reduces the computational burden and the global optimal solution is always guaranteed.