An Efficient Method for Facility Location with Multiple Products and Heterogeneous Warehouse Capacities

In today's business environment, companies must balance cost efficiency with customer satisfaction through effective supply chain network design. The Facility Location Problem (FLP) addresses this challenge, but becomes computationally intractable for large-scale instances involving multiple product categories and heterogeneous warehouse sizes. To address these limitations, we propose a mathematical model and an efficient solution approach that substantially reduces computational time while preserving optimal facility location decisions. The proposed method integrates relaxation techniques to improve computational efficiency, jointly determining warehouse locations, capacities, and product assignments under storage constraints. Unlike classical LP-based relaxation methods and LP-guided variable selection approaches used in capacitated and step-cost FLPs, our approach exploits the structural properties of warehouse–product interactions, enabling tractable solutions without compromising modeling fidelity. A European case study demonstrates that the proposed approach significantly reduces computational time without loss of accuracy. This research provides a practical decision-support tool for enhancing supply chain resilience and efficiency.