Alternative service network design for bus systems responding to time-varying road disruptions

In practice, road disruptions occur frequently, interrupting multiple bus routes at the same time and causing widespread passenger delays. Typically, these disrupted roads are repaired sequentially and then gradually put into service. In response to such time-varying road disruptions, this paper aims to assist bus operators in developing effective alternative service networks for passengers. The proposed approach involves the joint optimization of service-based route adjustments, bus timetables, and passenger assignment to minimize the total passenger cost and weighted bus operation time. Specifically, a novel service-based adjustment strategy is introduced to flexibly adapt each bus service to time-varying road disruptions. An integer programming model is built for the studied problem based on the set of passengers’ time-space itineraries. To efficiently generate these time-space itineraries and solve models for large-scale problems, this paper develops a hierarchical solution framework. The framework consists of three key parts: (1) a column generation procedure to iteratively explore passengers’ spatial paths; (2) a customized extension algorithm to extend these spatial paths to time-space itineraries; and (3) a tailored adaptive large neighbourhood search heuristic to solve the final itinerary-based model. After that, the overall methodology is tested with both an illustrative example and a real-world example in Beijing. Experimental results show that our methodology produces a high-performance solution with only 7.3% of unserved passengers. Besides, compared to the two benchmark adjustment strategies, our service-based adjustment strategy reduces the average itinerary cost for all passengers by 27.0% and 43.3%, respectively.