Cross-border multi-level warehouse network optimization: Modeling and application based on mixed-integer linear programming

• MILP model cuts cross-border warehouse costs by 20.7%. • Integrates costs, lead times, and multi-level synergies. • Outperforms heuristics by >8% with faster, stable solving. • Robust optima in 15/16 perturbations on real data. With the rapid development of global trade and cross-border e-commerce, optimizing cross-border multi-level warehouse networks has become a critical challenge to enhance supply chain efficiency and reduce operational costs. Traditional logistics planning methods struggle to address complex multi-level network structures, heterogeneous big data, and multi-dimensional influencing factors. This study proposes a mixed-integer linear programming model based on real-world operational requirements to optimize the layout of cross-border multi-level warehouse networks. The model integrates transportation costs, warehousing costs, tariff costs, and service lead time as key considerations. Through the incorporation of heuristic constraints and relaxation strategies, the model significantly improves computational efficiency and stability. Experimental results using real data from a cross-border e-commerce enterprise demonstrate that compared to existing solutions, the MILP model reduces total costs by 20.7%, outperforms heuristic algorithms by more than 8%, achieves faster computational speed, and maintains stable results. Furthermore, in 16 perturbation experiments, the model retained optimal solutions in 15 instances, showcasing strong robustness. This research provides critical theoretical and practical guidance for the scientific planning of cross-border logistics networks.