An output oriented super-efficiency measure in stochastic data envelopment analysis: Considering Iranian electricity distribution companies

In this paper, the concept of chance constrained programming approaches is used to develop output oriented super-efficiency model in stochastic data envelopment analysis. Output oriented super-efficiency model is one of the classic models in data envelopment analysis widely used by DEA people and practitioners. However, in many real applications, data is often imprecise. A successful method to address uncertainty in data is replacing deterministic data by random variables, leading to stochastic DEA. Therefore, in this paper, output oriented super-efficiency model is developed in stochastic data envelopment analysis, and its deterministic equivalent which is a nonlinear program is derived. Moreover, it is shown that the deterministic equivalent of the stochastic super-efficiency model can be converted to a quadratic program. Furthermore, sensitivity analysis of the proposed super-efficiency model is also discussed with respect to changes on parameter variables. Finally, data related to seventeen Iranian electricity distribution companies is used to illustrate the methods developed in this article.