The hierarchical multimodal hub location problem for cross-border logistics networks considering multiple capacity levels, congestion and economies of scale

The continuous growth of international container trade calls for logistics networks that seamlessly connect cross-border, domestic, and local transport services. In the design of these networks with various hubs and modes of transport, the consideration of both economies of scale for multimodal transport and congestion is essential since they can significantly impact the location of the hubs and their size. Thereby, in this paper, we study these features within a multimodal hub location problem for international trade that considers a hierarchy in the network structure. We develop a mixed-integer linear programming formulation, minimizing infrastructural, operational, and congestion costs. A hybrid adaptive variable neighborhood search algorithm with tailored operators and speed-up strategies is proposed to solve large-scale instances. Numerical experiments are conducted for China's New Western Land-Sea Corridor case and provide new managerial insights for designing hierarchical, multi-modal, cross-border logistics networks.