Integrated optimization of demand-driven timetable, train formation plan and rolling stock circulation with variable running times and dwell times

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.