A two-stage robust approach for multi-echelon facility location in cross-border logistics under demand uncertainty

Rationally selecting facility locations and allocating resources are significant for improving the accessibility and the coverage of products. Inspired by a real-world scenario in which a Non-Governmental Organization promotes the production and distribution of 3D-printed orthotics in Africa, this study investigates a multi-level robust Facility Location Problem under cross-border transportation in the healthcare context. Unlike existing Facility Location Problem that treat location decisions as static or only allow operational adjustments, we proposed a novel two-stage approach that explicitly addresses temporal structural consistency. The first stage establishes a baseline network using current known demand, while the second stage optimizes under future demand uncertainty with the objective of minimizing both system costs and structural deviations from the initial configuration. This bi-objective framework ensures that the international logistics network maintains efficient demand coverage while avoiding the excessive restructuring costs typically ignored in traditional robust optimization models. Experimental results demonstrate that in medium- and large-scale cases, the proposed hybrid algorithm reduces computation time by over 30% and up to 25% improvement in terms of solution quality compared to benchmark method.