Multiperiod alternative service optimization responding to joint disruptions in multimodal transit systems

Besides disruptions within individual bus or metro transit systems, joint disruptions can occur in multimodal transit systems, which are typically more prolonged and extensive. This paper focuses on joint metro station closures and road disruptions over an entire day, divided into several time periods with various passenger demands and bus travel times. In response, alternative metro services are scheduled to skip the closed stations, while affected bus routes are adapted to provide alternative bus services. We simultaneously optimize adaptive bus routes, vehicle frequencies, and passenger demand assignment to develop multiperiod alternative metro and bus services. Notably, alternative service optimization within each time period is integrated to maintain bus link consistency, enhancing service reliability and passenger travel satisfaction. A novel discount-based strategy is introduced to balance bus link consistency with alternative service effectiveness. For the studied problem, we develop an integer non-linear programming model based on the set of candidate passenger paths, aiming to minimize total passenger and operation costs with discounts. Afterwards, to efficiently generate passenger paths and solve the model, we propose an innovative link-sequence-based column generation with station clustering. In our column generation, we iteratively solve an aggregated restricted master problem and simpler pricing subproblems to first generate passengers' link sequences, which are subsequently expanded to passenger paths by solving a series of tailored expansion models. Additionally, a priority-based rule is incorporated into column generation to avoid generating duplicate link sequences. A station clustering procedure is developed to reduce the problem size of column generation, further improving computational efficiency. Finally, we validate our methodology using mid-and large-scale instances in Beijing, as well as performing comparative and sensitivity analyses.