Bus bridging service optimisation for urban rail transit disruption under uncertainty

In this study, we consider the operational problem of an urban rail transit (URT)-bus bridging service system considering the uncertainty of passengers, and formulate the problem as a two-stage stochastic programming model. In the first stage, optimal travel paths are determined to minimise in-vehicle time and transfer times. In the second stage, the assignment of passenger flow is decided to minimise the system load. To efficiently solve this model, we develop a binary particle swarm optimisation algorithm and validate its effectiveness using numerical experiments. We analyze two case studies based on Shanghai Metro. The results demonstrate that the URT-bus bridging service system achieves improvements in weighted in-vehicle and transfer times by 14.04% to 17.30%, and in system load by 11.85% to 23.83%, compared to the performance of only standard bus bridging lines. A further analysis on travel paths shows that approximately 30% of the passengers are diverted by longer paths.