Integrated optimization for high-speed railway express system with multiple modes

High-speed railway (HSR) express, as an emerging transport option in the logistics industry, provides sufficient transport resources to satisfy the demands for large-scale, high value-added, and customized logistics requirements. Unlike conventional transport options, the HSR express is capable of using multiple modes (i.e., piggybacking, reserved-coach, and freight trains modes) to efficiently convey freights to a broad variety of locations. Based on the operational characteristics of various HSR express modes, this study takes into consideration of integrated optimization problems, such as whether high-speed trains of various HSR express modes can transport the freights of specific types, the amounts of freights transported by each HSR express mode, and the arrangement of capacity resources of each mode. This study establishes a stochastic mixed integer programming model with the goal of maximizing the net profit of the HSR express system and designs a heuristic solution approach to solve the model efficiently. To verify the validity of the proposed model and algorithm, a large number of numerical experiments and a real-world case are conducted. Based on the extensive experiments, this study provides railway companies potentially with useful insights for developing the HSR express with various modes.