A robust optimization model for leagile closedloop supply chain design under uncertainty

Purpose: This study aims to design a leagile closed-loop supply chain (CLSC) for a durable product by integrating reverse logistics into the forward supply chain (SC) network. The proposed framework is developed in alignment with circular economy (CE) principles to enhance both economic and environmental performance under uncertainty. Design/Methodology: A multi-tier, single-product, single-period CLSC network is proposed under uncertain conditions. A single-objective mixed-integer linear programming (MILP) model is formulated to minimize the total system cost. The model addresses strategic, tactical, and operational decisions, including facility location, allocation quantities, return levels, recovery rates, and overall network configuration. To effectively manage uncertainty, robust optimization techniques are employed by integrating possibilistic and probabilistic programming approaches. The validity of the proposed model is demonstrated through numerical examples and a case study. Findings: The results provide optimal decisions regarding network configuration, material flows, recovery operations, and cost minimization. The findings indicate that the proposed CLSC model adopts a cost-efficient strategy by preserving the core capacity of the forward supply chain while integrating a centralized reverse logistics (RL) structure. Operational efficiency is achieved through strategic facility location decisions, enabling a balance between cost reduction and system performance. Moreover, the results confirm that the implementation of a CLSC enhances resource utilization and environmental sustainability while maintaining economic feasibility. Originality/Value: This study contributes to the literature by presenting a comprehensive leagile CLSC model that simultaneously considers uncertainty and CE objectives. The proposed framework offers practical insights for decision-makers seeking to design costeffective and environmentally sustainable CLSCs.