Abstract Unplanned disruptions to urban rail systems can result in widespread confusion and severe delays, and running bus bridging service is a common solution. Currently, transit operators usually adopt experience-based response strategy in such a way that spare buses from bus terminals and parking lots are used to run bus bridging services. Such a response approach can be effective when there are spare buses available at nearby terminals/parking lots. However, in case spare buses are not available or enough, it could be beneficial to dispatch running buses from nearby operating bus lines to ensure efficient response while incurring minimal inconvenience to on-board passengers. While this approach could reduce metro users’ delays, it causes extra delays and dissatisfaction to affected bus riders. In this study, we investigate the optimal bus dispatching problem for responding to unplanned disruptions of urban rail transit system with two bus fleet sources: (1) spare buses at terminals and parking lots, and (2) running buses from nearby operating bus lines. To obtain the optimal dispatching scheme, we develop an integer programming model, which achieves a balance between the delays of metro users and that of bus riders. Considering of the high uncertainty of bus headways which could affect the performance of the above deterministic model, we further develop a robust optimization model to obtain more reliable bus dispatching schemes. Case studies based on the data sets in Shanghai are conducted. The results demonstrate that our approach can be carried out in real-time, and employing running buses from operating bus lines shows great potential in reducing affected users’ delays. In addition, the robust model offers a more reliable and competitive solution when the headway varies widely.

Highlights • A bus dispatching problem aiming at unplanned disruptions of the metro is introduced. • Two bus fleet sources including spare buses at terminals and operating buses are considered. • An integer programming model minimizing the delays of affected users is proposed. • A robust optimization model considering the uncertainty of headway is developed. • The proposed method efficiently solves the real problem in a short time.