A double bootstrap data envelopment analysis model with stochastic reducible outputs and expandable inputs: An application to power plants

Clean production of electricity is not only cost-effective but also effective in reducing pollutants. Toward this end, the use of clean fuels is strongly recommended by environmentalists. Benchmarking techniques, especially data envelopment analysis, are an appropriate tool for measuring the relative efficiency of firms with environmental pollutants. In classic data envelopment analysis models, decision-makers are faced with production processes in which reducible inputs are used to produce expandable outputs. In this contribution, we consider production processes when the input and output data are given in stochastic form and some throughputs are reducible and some others are expandable. A stochastic directional distance function model is proposed to calculate the relative technical efficiency of firms. In order to evaluate firm-specific technical efficiency, we apply bootstrap DEA. We first calculate the technical efficiency scores of firms by classic DEA model. Then, the double bootstrap DEA model is applied to determine the impact of explanatory variables on firm efficiency. To demonstrate the applicability of the procedure, we present an empirical application wherein we employ power plants.