Timetable, train formation plan and rolling stock circulation are the key operational issues for efficient railway operation. The three issues are optimized sequentially based on the order of the operational plan. Sequential optimization manner cannot balance the costs of the three stages effectively and could create an infeasible solution for a later stage when the resources are limited. In addition, because of the computational complexity, multiple variable elements, such as the variable running times, variable dwell times and the coupling/decoupling operations, of a transportation system are ignored. This paper focuses on optimizing timetable, train formation plan and rolling stock circulation simultaneously to minimize costs and meet passenger demand. The key to solving the problem is to determine operation times (i.e., arrival times, departure times, running times and dwell times), the formation type of each train service and rolling stock connections (including the turnaround operations and the coupling/decoupling operations) between these train services. Considering the passenger costs and operator costs, a multi-objective mixed-integer nonlinear programming (MINLP) model is proposed to minimize the total passenger waiting time (TWT), the number of rolling stocks (NR), the number of formations (NF) and the number of coupling/decoupling operations (NC) based on a time–space network. The multi-objective MINLP model is further reformulated into a single-objective mixed-integer linear programming (MILP) model by logical linearizing, piecewise linearizing and fuzzy programming. A numerical example is used in which the exact solution of MINLP obtained by the BARON solver is compared with the approximate solution of MILP obtained by the CPLEX solver to verify the effectiveness of the piecewise linearization. Finally, the model is tested on a real-world case study of the Jinshan Line in Shanghai. The CPLEX solver can efficiently produce the approximate solution within a given computation time in acceptable gaps. The results demonstrate that the integrated model can reduce the number of rolling stocks and improve the utilization rate of rolling stocks. Furthermore, the integrated model can effectively resolve the shortage of rolling stocks when only one depot has rolling stocks or the number of available rolling stocks is limited. In addition, considering the multiple variable elements have a significant effect on the improvement of all the objectives and reduce both the passenger costs and the operator costs.

时刻表、编组方案和机车车辆流通是铁路高效运营的关键运营问题。这三个问题根据操作计划的顺序依次优化。顺序优化方式不能有效地平衡三个阶段的成本，并且在资源有限的情况下可能为后期创建不可行的解决方案。此外，由于计算的复杂性，忽略了交通系统的可变运行时间、可变停留时间和耦合/解耦操作等多个可变因素。本文着重于同时优化时刻表、列车编组计划和机车车辆流通，以最大限度地降低成本并满足乘客需求。解决问题的关键是确定操作时间（即到达时间，发车时间、运行时间和停留时间）、每列列车服务的编组类型以及这些列车服务之间的机车车辆连接（包括周转操作和耦合/解耦操作）。考虑乘客成本和运营商成本，提出了一种多目标混合整数非线性规划（MINLP）模型，以最小化总乘客等待时间（TWT）、机车车辆数量（NR）、编队数量（NF）以及基于时空网络的耦合/解耦操作（NC）的数量。通过逻辑线性化、分段线性化和模糊规划，将多目标 MINLP 模型进一步重构为单目标混合整数线性规划 (MILP) 模型。通过算例将BARON求解器得到的MINLP的精确解与CPLEX求解器得到的MILP的近似解进行比较，验证了分段线性化的有效性。最后，该模型在上海金山线的真实案例研究中进行了测试。CPLEX 求解器可以在给定的计算时间内以可接受的间隙有效地生成近似解。结果表明，集成模型可以减少机车车辆数量，提高机车车辆利用率。此外，集成模型可以有效解决只有一个车辆段或可用机车车辆数量有限时的机车车辆短缺问题。此外，