Dynamic bus bridging strategy in response to metro disruptions integrated with routing, timetabling and vehicle dispatching

Unplanned metro disruptions always result in severe confusion and delays, while bus bridging can provide a promising resolution by efficient evacuating stranded passengers. This article investigates the dynamic bus bridging problem under metro disruptions to generate the routing, timetabling and vehicle dispatching schemes for bus bridging services in an online fashion. Specifically, we formulate a mixed-integer non-linear programming model for each decision stage, with the objective of minimizing passenger travel times and operational costs. This model focuses on the role of multimodal transportation in improving the overall urban public transportation network's responses to metro disruption emergencies, which involves the utilization of temporary bus bridging services and the spare capacity of unaffected metro lines, passenger transfers and path choices. To address the model complexity, we propose a two-level decomposition approach to split the original problem into the master problem and subproblem. The approach can ensure the optimal solution in finite iterations. To further improve the performance of the solution approach, we design multiple acceleration techniques (i.e., customizing integer cuts supporting parallel computation, solution adjustment, domain reduction for the master problem, warm start and bound contraction for the subproblem) without compromising optimality. Extensive experiments verify that the proposed method can effectively evacuate stranded passengers, improving passenger satisfaction and meanwhile reducing operational costs. The proposed two-level decomposition approach with multiple acceleration techniques demonstrates higher computational efficiency than the common commercial solver and standard two-level decomposition approach, facilitating timely disruption responses. Additionally, according to the computational results, we derive a series of managerial insights for decision-makers.