Optimisation of High-Speed Railway Freight Transport Service Plan in Inter-Modal Transport Based on Extended Time-Space Network

The air-rail inter-modal transport is a feasible choice to enlarge the freight service scope of high-speed railway. Essentially, optimising the service plan for high-speed rail express under inter-modal mainly involves determining the train and flight trips, and space-time route selections for each batch of express shipment from the origin to the destination. We construct an extended space-time network to capture the transport and transfer space-time attributes of the serviced express shipments. A multi-commodity flow model is then established with a series of practical constraints. The Lagrangian relaxation algorithm is designed to decompose the original problem into a shortest path problem of a single-batch express shipment in a multi-dimensional network. The sub-problem is solved by the dynamic programming method, and a heuristic algorithm based on sub-gradient sorting is designed to ensure the feasibility of the dual solutions. In order to compare the performance of the traditional solver method with that of the LR algorithm, a nonlinear mixed-integer programming model was constructed in the appendix and solved by using the DICOPT solver. Taking the Shanghai-Kunming corridor as an example, the experimental results demonstrate that the LR algorithm can obtain high-quality solutions within a relatively short time, while the traditional solver method has certain limitations. Furthermore, the inter-modal transport is validated with a significant advantage in expanding the service scope of express demand. The research results are of great theoretical significance for the rational allocation of transportation resources and enhancement of the quality and efficiency of high-speed rail express services.