Joint Rolling Stock and Crew Scheduling with Multi-train Composition in Urban Rail Networks

Rolling stock scheduling and crew scheduling are two fundamental problems that arise in the planning of urban rail operations and that are especially important in the case of flexible operations in real-world networks. These problems are often solved separately and sequentially in different planning stages, resulting in limited options to adjust crew schedules after rolling stock decisions have been made. To better adjust these two decision-making processes and achieve better solutions, this paper studies a joint rolling stock and crew scheduling problem in urban rail networks. A novel optimization model is formulated with the aim of reducing the operational cost of rolling stock units and crew members. In addition, the multi-train composition mode is considered to adequately match different frequency requirements and rolling stock transport capacities. To solve the model, a customized branch-and-price-and-cut solution algorithm is proposed to find the optimal schedule schemes, in which Benders decomposition is used to solve the linear programming relaxation of the path-based reformulation. Two customized column generation methods with label correcting are embedded to solve the master problem and pricing subproblem for generating paths (columns) corresponding to rolling stock units and crew groups, respectively. Finally, a branch-and-bound procedure with several acceleration techniques is proposed to find integer solutions. To demonstrate the computational performance and the robustness of the proposed approaches, a series of numerical experiments are performed in real-world instances of the Beijing urban rail network under different settings. The computational results confirm the high efficiency of the solution methodology and the benefits of the flexible operation schemes based on the solutions found by the proposed methods. Funding: This work was supported by National Natural Science Foundation of China [Grants 72288101, 72322022, 72371015]. The first author sincerely thanks the China Scholarship Council for supporting his visiting PhD program [Grant 202407090173]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2024.0905 .