Optimizing a shared freight and passenger high-speed railway system: A multi-commodity flow formulation with Benders decomposition solution approach

This study investigates the potential of a shared freight and passenger high-speed railway system in which different transportation resources are allowed to be shared under different sharing modes. A sharing-carriage mode is proposed and combined with a sharing-train mode to fully exploit the remaining capacity of the existing railway schedule. The manner in which these two sharing modes are jointly involved to utilize the available capacity is investigated and optimized. First, a space–time network is constructed to analyze the distribution of flow for a given train schedule. Subsequently, the influence of integrated transportation upon passenger satisfaction is included by introducing a load-factor-based penalty cost for each train. The model is first formulated as a mixed-integer program that minimizes service and routing costs and then reformulated into a path-based model. A Benders decomposition approach is proposed to decompose the problem into two subproblems. Instead of exploring every possible path for each commodity when solving the Benders subproblem, a column-pool-based approximation approach is proposed to generate feasible solutions. Finally, the proposed approach is tested on two small-scale examples and 12 scenarios from a real-world high-speed railway network. Different train load factors, penalty costs, sharing modes, and commodity volumes are investigated to demonstrate the applicability of integrated transportation. The performance of the algorithm and acceleration techniques is also analyzed.