Joint Optimization of Fair Facility Allocation and Robust Inventory Management for Perishable Consumer Products

Perishable consumer products like food, cosmetics, and household chemicals face challenges in supply chain management due to limited shelf life and uncertainties in demand and transportation. To address some of these issues, this work proposes a robust optimization framework for jointly optimizing facility allocation and inventory management. The framework determines optimal locations for distribution centers and their assigned customers, as well as inventory policies that minimize the total costs related to transportation, distribution, and storage under uncertain demand in a robust setting. Specifically, we develop a two-stage mixed-integer linear programming (MILP) model is that incorporates First-In-First-Out (FIFO) inventory policy to reduce spoilage. The bilinear FIFO constraints are linearized to improve computational efficiency. Social equity is integrated by defining a fairness index and incorporating it in facility allocation. Demand uncertainty is tackled using a robust optimization approach with affine demand functions to handle multiple scenarios. The model is solved using row and column generation techniques for scalability. Overall, this robust optimization framework is expected to enhance supply chain resilience, reduce waste, and improve cost-effectiveness in managing perishable products.