Robust optimization model for closed-loop supply chain planning with collected material quality uncertainty

This study develops a robust optimization framework for closed-loop supply chain (CLSC) planning that explicitly accounts for uncertainty in the quality of recycled and remanufactured inputs. While such materials are critical for sustainability, their variable quality poses risks to production feasibility and supply reliability. To address this challenge, we propose an ordering-proportion-based robust model that distributes uncertainty across sourcing proportions and leverages the Bertsimas-Sim budget of uncertainty to balance conservatism and flexibility. A reformulation ensures tractability and preserves robust feasibility. Computational experiments demonstrate that the proposed model reduces shortages and stabilizes performance under independently realized uncertainties, while quantity-based robust models are more effective when uncertainties are correlated. Additional scalability tests confirm that the model remains computationally tractable for medium-sized networks. The findings highlight practical implications for managers, showing how proportion-based sourcing improves resilience, supports reliable demand fulfillment, and strengthens sustainability in CLSCs facing quality risks.