Robust DEA under discrete uncertain data: a case study of Iranian electricity distribution companies

摘要

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the real-world problems often deal with imprecise or ambiguous data. In this paper, we propose a novel robust data envelopment model (RDEA) to investigate the efficiencies of decision-making units (DMU) when there are discrete uncertain input and output data. The method is based upon the discrete robust optimization approaches proposed by Mulvey et al. (1995) that utilizes probable scenarios to capture the effect of ambiguous data in the case study. Our primary concern in this research is evaluating electricity distribution companies under uncertainty about input/output data. To illustrate the ability of proposed model, a numerical example of 38 Iranian electricity distribution companies is investigated. There are a large amount ambiguous data about these companies. Some electricity distribution companies may not report clear and real statistics to the government. Thus, it is needed to utilize a prominent approach to deal with this uncertainty. The results reveal that the RDEA model is suitable and reliable for target setting based on decision makers (DM’s) preferences when there are uncertain input/output data.;In the highly competitive and dynamic markets derived from globalization, the domestic firms should find a competitive edge that enables them to survive in the market. Moreover, limited natural resources and growing environmental concerns and regulations about production processes are new considerations influence the firms’ operations. Therefore, the operational efficiencies would play an important role in survival and growth of firms. Especially in electricity distribution companies, operational efficiency is the most crucial issue among regulators (Sadjadi and Omrani 2008).;Data envelopment analysis (DEA) is a well-known non-parametric technique that measures the relative operational efficiency of similar decision-making units (DMUs). The most important capability of DEA is its ability to compare several parameters (inputs/outputs) concurrently and sum up them into a scalar measure of relative efficiency. The efficiencies of DMUs are obtained from weights corresponding to each input and output that computed through the optimal solution of linear programming (LP) problems. In fact, DEA is a data-oriented method for measuring and benchmarking the relative efficiency of peer DMUs. Target setting and improvement of DMU’s performance are important features of DEA technique. There are several successful real-world applications of DEA method in different public and private sector industries such as banks, software development, health care, pharmacies, auto manufacturing, fisheries and search engines (Saranga and Phani 2009). Sadjadi and Omrani (2008), for instance, used DEA method for measuring the relative efficiency of energy companies in Iran. Roghanian and Foroughi (2010) implemented DEA to compare efficiencies of all regional and international airports in Iran using different input/output data. Goto and Tsutsui (1998) employed DEA approach to measure overall cost and technical efficiencies between Japanese and US electricity power plants. Saranga and Phani (2009) employed non-parametric DEA models and parametric methods such as regression analysis to specify the factors that have contributed to the internal operational efficiencies of firms in Indian pharmaceutical industry.;One of the most important issues associated with DEA is the uncertainty associated with the data. Since the resulted formulation of DEA technique is in form of LP, one can use traditional sensitivity analysis when there are one or a few uncertain parameters. However, when all input data are subject to uncertain, it is practically impossible to use sensitivity analysis method to handle all uncertainties. There are several methods for estimating the efficiencies of DMUs under data uncertainty.;In the real-world problems, data are often