A linear programming joint optimization model of over-night train timetabling and maintenance planning on high-speed railway

Maintenance activities on high-speed railway (HSR) facilities, which ensure that HSR remains in good condition, are typically carried out between 0:00 and 6:00 daily to minimize the negative impact on daytime train operations. However, there has been an emerging demand for overnight trains that operate during night, leading to a conflict between overnight train operations and HSR maintenance activities, which makes this problem more challenging than other train scheduling issues. Unlike current literature that simply considers the station section between two consecutive railway stations as the minimum maintenance unit, this study considers the power section between consecutive power substations as minimum maintenance unit, aiming to enhance the practical applicability of the research findings. By applying linearization techniques such as the Big-M method and binary state variables, a mixed-integer linear programming model is formulated to integrate overnight train timetables and maintenance schedules. As for objective functions, in the context of overnight trains, for sunset-departure and sunrise-arrival trains, we formulated an objective function centered on the satisfaction of arrival and departure timings, for super long-distance trains, our focus was on minimizing the total travel time. Regarding the maintenance plan, we put forward two distinct objective functions, which include minimizing the deviation starting time from the pre-set plan and maximizing the maintenance duration for all power sections. Given the variance in numerical scales across these functions, we standardized them to a maximized scale within the [0, 1] interval. Considering that station track constraints can potentially yield a staggering number (up to the million-level) of constraints, we proposed a solution-seeking approach in a timely manner. A numerical example is designed based on real-world data from the Beijingxi-Guangzhounan HSR line in China. Several experiments are conducted to validate the proposed model and optimization method.