Integrated Optimization of Overnight Train Service Plans for High-Speed Rail Express: Adaptability of Two Typical Maintenance Windows

• Firstly, we have specifically proposed two forms of maintenance window suitable for operating overnight express trains, which is the spatial-segmented maintenance window and temporal-divided maintenance window respectively. • Secondly, a comprehensive optimization model for the high-speed rail express overnight train service plan is developed, taking into account train operation constraints, demand loading constraints, maintenance window scheduling constraints. • Thirdly, by linearizing the models and employing the commercial optimization software GAMS with the CPLEX solver, the global optimal solutions are obtained. Given the rapidly growing demand for high-speed rail (HSR) express services, operating overnight trains emerges as a viable strategy to enhance service quality. The success of organizing overnight trains hinges on coordinating the relationship between express train operation schedules, comprehensive maintenance window plans, and express parcel assignment plans. We have specifically proposed two forms of maintenance windows suitable for operating overnight express trains: the spatial-segmented maintenance window and the temporal-divided maintenance window. The optimization objective is to minimize the delivery time of high-speed rail express demands. Considering several system constraints, such as train operation, maintenance window settings, and parcel dispatching constraints, two comprehensive optimization models for high-speed rail express service plans are constructed under two different maintenance modes. By linearizing the models and employing the commercial optimization software GAMS with the CPLEX solver, the global optimal solutions are obtained. Based on numerical experiments from the Nanjing-Hangzhou high-speed railway corridor, we demonstrate the correctness of the constructed model and the adaptability of the high-speed rail express service plans under the two maintenance window formats. The experimental results indicate that under the temporal-divided maintenance window mode, organizing high-speed rail express trains results in shorter delivery times for express demands, but it cannot ensure the continuity of maintenance operations within the window period. In contrast, organizing high-speed rail express trains under the spatial-segmented maintenance window mode can achieve a balance between express demand services and maintenance operations of the rail line.