Developing an integrated model of hierarchical hub location and inventory control for perishable products in urban and rural areas: a case study in food supply chain

Optimizing facility location and inventory management in food supply chains is essential for reducing costs, preventing spoilage of perishable products, and ensuring equitable food distribution across rural and urban districts. To deal with this issue, this paper proposes a comprehensive model for the integrated optimization of facility location and inventory management within a three-tier hierarchical hub network architecture. The network topology is a complete-star-star structure, with fully interconnected central hub nodes at the highest level. The intermediate and lowest tiers consist of star-shaped subnetworks, where end nodes, including manufacturers, connect to non-central hubs. Given the NP-complete nature of the problem, we propose a hybrid algorithm combining an exact solution with a meta-heuristic genetic algorithm. These algorithms are implemented in GAMS and MATLAB software. Sensitivity analysis is conducted on the model's parameters. The results show that decreasing the costs of establishing the hub by more than 75% increases the number of median hubs. Production quantity and inventory levels remain steady with cost variations up to −50%, but decrease with production cost increases up to 50%, where inventory levels drop to zero.