Robust optimization model for closed-loop supply chain planning under reverse logistics flow and demand uncertainty

Awareness of environmental pollution, interest in recycling, and the importance of closed-loop supply chain management are all on the rise. In a closed-loop supply chain, production planning is influenced by uncertainty not only from customers’ demand, but also from collectors due to difficulties in the reverse logistics flow. Therefore, it is important to develop a robust closed-loop supply chain model to respond to uncertainty from reverse logistics. In this study, we develop a deterministic mixed-integer optimization model and robust counterparts to cope with the uncertainty of recycled products and customer demand in the fashion industry. We show that a robust counterpart with a budget of uncertainty is equivalent to a robust counterpart with a box uncertainty under special conditions. To avoid the conservatism of a robust solution, an alternative optimization problem is developed to take advantage of the budget of uncertainty. To verify the performance of the proposed model, numerical experiments are conducted. The simulation results show the proposed model responds robustly to uncertainty and is superior to a deterministic model and other robust counterparts.