Modeling a closed-loop inventory routing problem for returnable transport items under horizontal logistics collaborations and dynamic demand structure

This paper addresses a closed-loop inventory routing problem with multiple suppliers, products, and periods under horizontal collaboration assumptions. Our problem encompasses various decision aspects, including routing, inventory management, product delivery, returnable transport item collection and cleaning. We analyze various logistics collaboration scenarios. The effects of demand dynamicity are also assessed. The problem has been mathematically defined as a Mixed Integer Linear Programming model. A rolling horizon approach and a hybrid heuristic algorithm are proposed for instances that exceed the computational requirements of solving the exact MILP model. The applicability and potential benefits of the MILP model and the proposed solution methodologies are demonstrated through a base case and additional numerical analyses on larger-sized instances and networks. The results show that supplier collaboration significantly reduces routing costs, while customer collaboration reduces inventory costs. Numerical comparisons reveal that the proposed algorithms outperform the MILP model for large-scale problem instances.