sustainable closed-loop supply chain network considering disruption risk under uncertainty

This paper investigates the design of sustainable closed-loop supply chain networks (clscns) under disruption risks and uncertainty. we propose a multi-objective mixed-integer linear programming (milp) model that optimizes economic, environmental, and social sustainability objectives while minimizing the expected cost and maximizing network resilience against disruptions. the model incorporates various uncertainties, such as demand fluctuations, return rates, and disruption probabilities. we employ a scenario-based stochastic programming approach to address these uncertainties and identify robust solutions. the numerical results demonstrate the effectiveness of the proposed model in designing sustainable and resilient clscns. the model provides valuable insights for decision-makers in optimizing network configuration, resource allocation, and risk mitigation strategies within a closed-loop environment.