Stochastic data envelopment analysis in the presence of undesirable outputs: An application to the power industry

Performance analysis using data envelopment analysis is sensitive to data variability and uncertainty. Therefore, it is necessary to adapt classic data envelopment analysis models when dealing with data uncertainty. This paper aims to examine the technical efficiency and scale elasticity of production processes involving undesirable outputs in a stochastic environment. To achieve this, we employ a chance-constrained programming approach to develop measures of technical efficiency and scale elasticity for power plants. The analysis is conducted from the perspective of production theory, considering undesirable outputs and stochastic variability within the production set. We demonstrate the real-world applicability of our proposed approach for calculating technical efficiency and returns-to-scale (or scale elasticity) using data from 31 power plants. The results indicate significant differences between deterministic and proposed stochastic programmes at various confidence levels. However, the results are consistent when considering a confidence level of 0.5. Additionally, our findings support the hypothesis that combined cycle power plants outperform gas-fueled and steam power plants. Furthermore, the majority of all three types of plants operate under constant returns-to-scale.