Incorporating multimodal coordination into timetabling optimization of the last trains in an urban railway network

Urban rail transit (URT) provides efficient and low-cost services for passengers. It is a common issue for operators to coordinate the last trains of a URT network. This paper discusses three models in a progressive fashion to optimize the last train timetable incorporating multimodal coordination. The first model maximizes the transferability at transfer stations without the distinction of the stations. The second model, based on a refined classification of stations and lines, optimizes the transferability at transfer stations between different transport modes. The third model maximizes the multimodal coordination taking into account the space-time distribution of the arrivals and departures of the connecting modes. These models are formulated as mixed-integer linear programming by linearization techniques for finding the optimal timetable solutions. The proposed models are tested in the Beijing URT network connecting three railway stations and two airport terminals. The numerical results indicate that the proposed models can effectively improve the coordination among the last trains within the URT network and between the URT and the connecting modes.