Optimization of Bus Bridging Strategy for Two Bus Types during Planned Metro Disruptions

When planned metro disruptions occur, the connectivity of the metro network is severely reduced, impacting the travel of a large number of commuters. The duration of planned metro disruptions varies from a few days to several weeks. To ensure the quality of public transportation services during this period, we propose a bus bridging strategy to address the travel issues of disrupted passengers. This paper introduces a mathematical model for the timetable and bus scheduling of bus bridging when a section of a metro line is planned for disruption, considering two types of buses. In this model, regular buses transfer disrupted passengers whose original destinations are on the disrupted metro section, whereas shuttle buses transfer disrupted passengers whose destinations are on the normal metro line. The model takes into account the impact of metro disruptions on the original passengers of regular buses and aims to minimize passenger transfer waiting time and congestion disutility. The model is solved using a commercial solver and is validated with the case study of Beijing Bus No. 16 and a hypothetical metro line. The results demonstrate that metro disruptions have a significant negative impact on the transfer waiting time and congestion disutility of regular buses. However, the timetable generated by the model effectively mitigates this impact. Additionally, the shuttle bus scheduling solutions generated by the model are not unique, and a specific schedule can be determined based on the shuttle bus costs and service quality. Both the crowding threshold of buses and the maximum number of pickups can reduce the congestion disutility of shuttle buses, but the impact of the crowding threshold is more significant.