Train Scheduling Optimization for Mixed Passenger and Freight Transportation on an Urban Rail Line

The urban rail transit system, traditionally focused on passenger transport, is now also emerging as a potential solution to the increasing demands of urban freight transport on the road, by using its surplus capacity for freight transport during off-peak hours. A key challenge is the planning of rail trains considering the demand from both passengers and freight. In this context, we adopt an empirical study to investigate the train scheduling problem with mixed passenger and freight transportation, which involves determining the optimal train timetable, flexible carriage allocation, and rolling stock circulation plan to accommodate both passenger and freight demands. Considering the time-invariant freight transportation demand and time-varying passenger transportation demand, we formulated a mixed integer linear programming model, which optimizes the departure/arrival times of trains, the flexible carriage allocation for passenger and freight, and the rolling stock circulation, to minimize the remaining number of passengers and freight in a metro system. We conduct numerical experiments based on the real-world data from Beijing Metro Line 1. The numerical results show that adding freight services will not have a significant impact on passenger service quality. We also analyze the impacts of freight demand quantity on passenger service quality to provide valuable insights and inspiration for tactical decision-making of rail managers.