Proactive-adaptive public transport planning: bus network redesign for urban rail disruptions

Accessibility, understood as the extent to which opportunities can be reached within a specified travel-time threshold, constitutes a central benefit of public transport systems.Although Urban Rail Transit (URT) plays a pivotal role in ensuring such accessibility, its inherent susceptibility to disruptions disproportionately affects suburban regions where alternative travel options are scarce.Existing disruption management strategies, however, often fall short: rigid proactive measures offer limited operational flexibility, whereas purely reactive responses are typically inefficient in restoring accessibility once disruptions occur.To address these limitations, this paper introduces a novel two-stage stochastic optimization framework that couples proactive infrastructure investment with adaptive operational adjustments.The first stage identifies flexible network enhancements to be implemented in advance, while the second stage optimizes bus operations dynamically in response to disruption scenarios, thereby enhancing the resilience of the overall transport system.Empirical results from a stylized case study reveal that, relative to conventional replacement strategies, the proposed framework consistently achieves higher accessibility restoration across diverse disruption scenarios.Notably, the approach not only secures substantial accessibility gains and preserves access to opportunities but also maintains at least 66.7% path similarity with original bus routes, ensuring operational feasibility and practical implementability.