Coordinated Optimization of Train Timetables and Maintenance Windows for Plateau Railways

The conventional sequential planning of train timetables and maintenance windows cannot fully capture their interactions, particularly on plateau railways where infrastructure maintenance requirements are more demanding. This study develops a coordinated optimization model that jointly determines train arrival and departure times and the timing and duration of segmented rectangular maintenance windows. The model simultaneously minimizes total train travel time and maximizes maintenance-window duration while considering train departure and arrival time windows, section running times, dwell times, train headways, maintenance-window timing requirements, and safety separation between train operations and maintenance activities. A linear weighted-sum method is used to scalarize the bi-objective model, and a Benders-decomposition-based solution method is developed by separating discrete operating-sequence decisions from continuous timing decisions. The method incorporates optimality, feasibility, and conflict cuts to iteratively coordinate the master problem and subproblem. A case study of a certain plateau railway in China, involving 22 passenger trains and 25 section-based maintenance windows, demonstrates the applicability of the proposed approach. Sensitivity analysis reveals a clear trade-off between train operating efficiency and maintenance provision. With a weighting coefficient of λ = 0.8, the algorithm obtains a representative coordinated solution with a total train travel time of 8488.37 min and a maintenance-window duration of 200.64 min, illustrating the trade-off between transport efficiency and maintenance requirements. The proposed framework provides a practical modeling and solution approach for coordinated train timetabling and maintenance-window planning on plateau railways.