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

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. (C) 2016 Elsevier B.V. All rights reserved.