Evaluating sustainability performance in fossil-fuel power plants using a two-stage data envelopment analysis

In this paper, we present a two-stage data envelopment analysis (DEA) to evaluate the efficiency of power generation facilities, where the first stage takes into consideration the financial mission of the plants facing their sustainable mission in the second stage. One common assumption of two-stage DEA models is the homogeneity of the values of the intermediate measures, i.e., the weights given to the intermediate measures are the same regardless of whether they are outputs or inputs. However, this assumption may not apply in some situations such as when one stage values the intermediates more than the other. This is the case in the application we address in this paper where we use a network model to develop performance measures for sustainability of the U.S. fossil-fuel power stations. We show that the resulting two-stage DEA model is a nonlinear program that is a particular case of indefinite fractional bilinear problems (IFBPs). To solve it, we propose an efficient algorithm that involves solving several univariate linear equations in each iteration. This model is then used to construct a comprehensive sustainability performance measure for the fossil-fuel power stations. Using nonparametric tests we also provide statistical evidence to show that neither existing two-stage DEA models nor traditional efficiency ratios adequately account for the environmental and social impacts of fossil-fuel power generation sources.