Robust train carriage planning for mixed transportation of passengers and uncertain freights in a high-speed railway network

Mixed transportation of passengers and freights is an effective strategy for reducing environmental pollution and improving the service level of railway systems. This study addresses the problem of robust train composition and carriage arrangement for the mixed transportation of passengers and freights in a high-speed railway (HSR) network. Specifically, a network-based robust optimization (RO) model is introduced to address the uncertainty in freight demand while considering deterministic passenger demand. The model utilizes space–time network representations to characterize the movements of passengers and freights. To account for various potential scenarios, a polyhedral uncertainty set is integrated into the model. Moreover, we develop a novel exact algorithm called B-C&CG, which utilizes the strengths of Benders decomposition for solving the deterministic passenger sub-problem and the strengths of column-and-constraint generation (C&CG) for solving the robust freight sub-problem. This provides an efficient solution to the RO model formulated for our problem. The objective is to optimize the train operating cost, passenger generalized travel cost, and the worst-case freight travel cost simultaneously. Additionally, a series of numerical experiments based on the real-world instance in a HSR network are conducted to verify the effectiveness of the developed B-C&CG algorithm and the advantages of the proposed RO model. The results demonstrate that (i) the newly developed algorithm outperforms both the Benders decomposition algorithm and the hybrid algorithm (B-BC&CG) in terms of computing time, where the latter differs from B-C&CG by using both Benders decomposition and C&CG to handle the robust freight sub-problem; (ii) the degree of conservatism can be controlled by altering parameters related to uncertain freight demand; (iii) the proposed RO model can improve the worst-case solutions under polyhedral uncertainty set, compared to nominal and stochastic programming models.