Integrated Line Planning and Timetable Scheduling for Railways Considering the Dynamics and Uncertainty of Passenger Demand

Scheduling plans catering to dynamic and complex passenger demands have drawn recent attention. Given dynamic demand, there is an urgent need to explore methods for extracting valid data from vast amounts of information and achieving flexible, robust parametric control of scheduling to boost transportation resource utilization efficiency. This paper proposes a deep learning technique to construct uncertainty sets using first- and second-order moment information of passenger demand. Based on previous research under deterministic demands, a distributional robust optimization model for integrated line plan and timetable scheduling is established. Unlike other robust optimization models, the distributional robust one can better utilize the information in uncertain data. To handle the ensuing mixed integer semidefinite programming problem, a generalized benders decomposition algorithm post-linearization is presented, which decomposes the model for iterative solving. Notably, the proposed model attains an average demand satisfaction rate 10.19% higher than the deterministic demand model, reduces train usage by 9, and lifts the average full load rate by 19.05% compared to the strongly robust model. It can flexibly select parameters for diverse demand scenarios and decision-making objectives, offering theoretical support for planning under uncertain passenger demands.