An Exact Method for Optimal Inventory Management of Perishable Multi-item Systems with Backorders

Efficient inventory management is especially challenging in systems dealing with multiple perishable items and variable supplier conditions. This study developed a Mixed-Integer Linear Programming model to address the inventory management of perishable and multi-item systems with the possibility of backorders. The model incorporates deterministic demand, supplier-specific lead times, fixed shelf life, and cost components related to ordering, holding, safety stock, and delayed fulfillment. The main contribution lies in integrating perishability and backordering into a unified framework that supports strategic decisions on order timing, quantities, and joint replenishment, while ensuring service level compliance and minimizing total costs. Additionally, by integrating perishability constraints, this model contributes to reducing waste and minimizing the environmental impact associated with product expiration. The model’s applicability was demonstrated through a real case study in the raw materials supply sector to validate its practical relevance and performance, achieving a 0.09% optimality gap within 15 minutes, highlighting its effectiveness for cost-efficient and sustainable decision-making in complex inventory environments.