Evaluating performance of two-stage supply chain in presence of stochastic and undesired data

Conventional data envelopment analysis approaches often overlook the inherent uncertainty and the impact of undesired values on performance assessments, which can significantly affect a system's performance. Stochastic data envelopment analysis is an extension of conventional data envelopment analysis that incorporates uncertainty and randomness into the performance assessments. Recognizing the significance of undesirable data and uncertainty in management and decision-making processes, this study presents a novel extension of network data envelopment by integrating stochastic data and addressing the implications of undesirable outputs with weak disposability. Our research on the following key aspects: a) developing a two-stage network model that accommodates stochastic data; b) incorporating weak disposability for undesirable outputs and inputs; c) treating intermediate measures as freely disposable; and d) enabling performance evaluation across diverse probity levels. We demonstrate the applicability and effectiveness of our model through a case study involving 27 pasta manufacturing companies. By assessing efficiency across various probability levels, we offer insights into how different degrees of uncertainty influence operational performance metrics. The results reveal critical variations in efficiency scores, underscoring the importance of incorporating stochastic elements and undesirable outputs in management and decision-making processes.