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

Maintenance activities on high-speed railway (HSR) facilities are essential for ensuring operational integrity, typically scheduled during the overnight window (0:00-6:00) to avoid disrupting daytime services. This practice, however, conflicts with the operation of overnight trains. To address this issue, this study develops an integrated optimization model for joint train timetabling and maintenance planning. First, we compare two minimum maintenance units (station sections and power supply sections) and justify the selection of the latter based on its superior applicability in practical scenarios. Subsequently, a mixed-integer linear programming model is formulated using linearization techniques, including the Big-M method and binary state variables. The model incorporates three categories of constraints: train operation constraints, maintenance planning constraints, and their interaction constraints. Two objective functions are established for overnight trains and maintenance plans respectively, which are normalized to a [0, 1] scale to address disparities in their numerical magnitudes. After analyzing the computational complexity of solving the model, it is determined that station track constraints will lead to a sharp increase in the number of variables and constraints, prompting the proposal of an efficient solution algorithm that ignores these constraints. A numerical example is constructed using real-world data from the Beijingxi-Guangzhounan HSR line in China, with several experiments conducted to validate the proposed model and optimization method.