A data-driven optimization approach for the integrated train scheduling and maintenance planning in high-speed railways

In railway systems, preventive maintenance plans are essential for ensuring the safety of train operations. However, these tasks are often subject to various disturbances (e.g., bad weather), leading to unpredictable deviations between planned and actual maintenance durations, which can further disrupt train schedules. Unlike most studies that assume constant maintenance durations, this paper introduces a data-driven, two-stage distributionally robust optimization (DRO) model for jointly optimizing train scheduling and maintenance planning. In the first stage, we determine the initial train schedule and maintenance plan. In the second stage, we allow for slight adjustments to train departure and arrival times at each station to accommodate disturbances affecting maintenance tasks. Our objective is to minimize both the expected travel time of trains and the deviation from the planned schedule under worst-case scenarios for maintenance disturbances. To capture the uncertainty of maintenance disturbances, we construct an ambiguity set using historical data and the Wasserstein metric. We show that the proposed two-stage DRO model, formulated over the Wasserstein ambiguity set, can be reformulated into an efficiently solvable equivalent form. Finally, we apply our model to a real-world case study of the Beijing–Guangzhou high-speed railway and compare it with traditional stochastic programming methods, including sample average approximation and robust optimization. The results highlight the efficiency of our approach and provide valuable insights for railway management.