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.

@en

In recent years, the highly fragmented multimodal transport offer in several countries has required the integration of these services by logistics service integrators (LSIs). The challenge for LSIs is to set up multimodal transport corridors that can respond efficiently to the heterogeneous demand of shippers and that are cost- and price-competitive against other transport solutions. We develop a bi-level programming model to assess the corridor's pricing and the service network design simultaneously. In the upper level, the model maximizes the profit of the LSI by designing the service network and implementing shipment-based pricing for paths adapted to the heterogeneous demand for transport services. In the lower level, the total cost of shippers in the network who choose services according to their preferences is minimized. We solve the model using reformulation and linearization techniques. Computational experiments based on the real-world case of the New Western Land-Sea Corridor in China are conducted to demonstrate the proposed model and to draw managerial insights. The results show that the shipment-based pricing strategy is beneficial for the LSI to obtain profit increases when considering the shippers’ heterogeneous preferences on time and reliability. The results also revealed that the service design and pricing decisions of the LSI are not only related to operational costs but also depend on the competitors’ offers in the market. Moreover, the impact of the level of frequency discretization, waiting time cost, the penalty cost for not fully utilized services, and the generalized cost of the no-purchase option on the decisions of the LSI are also investigated in the sensitivity analysis.@en