Integrated capacity allocation and timetable coordination for multimodal railway networks

Modern transportation systems are moving towards shared mobility with diverse demands, and resource aggregation and coordination among different transport modes have become more and more significant. In this study, we investigate the integrated train capacity allocation and timetable coordination for multimodal railway networks to release the congestion of transfer hubs between metro and mainline rail networks. We consider that a part of vehicles can be dynamically allocated to some metro trains to increase their capacity to take more passengers at transfer hubs alighting from mainline rail trains. We formulate this problem into a mixed-integer linear programming (MILP) model, which simultaneously generates the coordinated timetables of both metro and mainline rail trains, as well as the train capacity allocation strategy in the network. The objectives are to minimize the passenger travel time, passenger transfer time at the hubs and the operational costs for rail managers. To tackle computational challenges in real-world instances, we develop an exact branch-and-cut solution algorithm to generate (near-)optimal solutions more efficiently. In our algorithm, we propose five sets of valid inequalities that are dynamically added to the model to strengthen the linear relaxation bounds at each node. We also design a customized branching strategy in the search tree by imposing branching on the key decision variables regarding the train sequences at transfer stations. Real-world case studies based on the operational data of a realistic multimodal railway network in Beijing are conducted to verify the effectiveness of our approach. The results demonstrate that our branch-and-cut-based approach outperforms commercial solvers regarding solution quality and computational efficiency. Compared to the current non-coordinated train timetable in practice, our approach by flexibly allocation train capacities can reduce the passenger transfer waiting time by over 40%. • We address the integrated train capacity allocation and timetable coordination for multimodal railway networks. • A mixed-integer linear programming model is proposed to optimize the schedules of railway and metro trains. • We develop an exact branch-and-cut algorithm to generate high quality solutions. • The effectiveness of the proposed approaches is verified by the numerical experiments.