Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies

This paper presents Data Envelopment Analysis (DEA) model with uncertain data for performance assessment of electricity distribution companies. During the past two decades, DEA has been widely used for benchmarking the electricity distribution companies. However, there is no study among many existing DEA approaches where the uncertainty in data is allowed and, at the same time, the distribution of the random data is permitted to be unknown. The proposed method of this paper develops a new DEA method with the consideration of uncertainty on output parameters. The method is based on the adaptation of recently developed robust optimization approaches proposed by Ben-Tal and Nemirovski [2000. Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming 88, 411–421] and Bertsimas et al. [2004. Robust linear optimization under general norms.Operations Research Letters 32, 510–516]. The results are compared with an existing parametric Stochastic Frontier Analysis (SFA) using data from 38 electricity distribution companies in Iran to show the effects of the data uncertainties on the performance of DEA outputs. The results indicate that the robust DEA approach can be a relatively more reliable method for efficiency estimating and ranking strategies.