A Multimodal Multicommodity Network Equilibrium Model with Service Capacity and Bottleneck Congestion for China-Europe Containerized Freight Flows

As a traditional way for transporting containerized cargoes, international liner shipping has long played a dominant role in the China-Europe freight transportation market. In recent years, China Railway Express has offered a new and competitive freight transportation option, contributing to a significant increase in the trade volume by rail between China and Europe. With the goal of providing a holistic computational tool that can predict and analyze the spatial distribution of containerized freight flows and suggest strategic transportation infrastructure and service expansion options, this paper develops and implements a multimodal multicommodity freight transportation network equilibrium model, based on a newly constructed supernetwork integrating international liner shipping lines, international freight rail services, and international and domestic highway networks in relevant countries. The combined transportation mode-route choice behavior of individual shippers is characterized by the widely used multinomial logit model, where the values of time of different commodity categories are included in its utility functions. The congestion effects arising from bottleneck facilities along liner shipping and freight rail lines (i.e., seaports, water channels, and break-of-gauge stations) are first captured by queueing models and then approximated by polynomial delay functions, while the accommodation capacity of individual service lines is explicitly embedded into the model as hard constraints. This supernetwork equilibrium model is tackled by a subgradient algorithm in the Lagrangian relaxation framework embedding a disaggregate simplicial decomposition algorithm. Computational experiments are conducted with a multi-layer, hetero-structure set of supply and demand data collected from multiple data repositories, government agencies, freight carriers, and research papers and reports. The preliminary results exhibit the computational performance of the solution procedure and reveal the variation of congestion levels of bottleneck facilities, queueing delays of saturated service lines, and competitiveness conditions between liner shipping and freight rail services under different monthly demand patterns