This study addresses the issues of unbalanced capacity allocation and rigid train formations in urban metro systems under tidal passenger flow conditions. By integrating temporal–spatial passenger demand with real-time dynamic train formation, we propose a virtual formation optimization method driven by carriage load factors. This method enhances the flexibility of train formation strategies by coordinating virtual coupling and decoupling operations between trains traveling in opposite directions. A mixed-integer linear programming (MILP) model is developed, with train unit allocation and turnover scheduling as the main decision variables. The model aims to minimize total passenger waiting time and system operating costs, while incorporating constraints related to unit allocation, turnover, and passenger assignment. The model can be efficiently solved using commercial solvers such as CPLEX. To evaluate the proposed method, a case study is conducted on a metro line in a major city. Numerical experiments demonstrate that, compared with a fixed 6-car formation scheme, the proposed method reduces total passenger waiting time by approximately 4.2% and operating costs by 11.6%. When compared to a fixed 8-car formation scheme, it achieves a 48.8% reduction in operating costs with only a 4.3% increase in passenger waiting time. These results highlight the potential of the proposed virtual formation strategy to enhance operational efficiency and resource utilization in urban metro systems, offering both practical value and implementation feasibility.
Chen et al. (Sun,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: