Resilience enhancement of multi-modal public transportation system via electric bus network redesign

The multi-modal public transportation system incorporating the electric bus network and the metro network plays a crucial role in meeting the daily transportation demands in urban areas. However, the inadequate connectivity between the electric bus network and the metro network has resulted in poor resilience of the multi-modal public transportation system. When disruptions occur at metro links or metro stations, stranded passengers cannot be rapidly evacuated through bus lines. Therefore, operators need to redesign the multi-modal public transportation system to enhance the integration between the electric bus network and the metro network. Since it is challenging to modify the fixed metro network, we thus focus on introducing redesign plans for the electric bus network, enabling the multi-modal public transportation system to exhibit the desired resilience in scenarios of disruptions. This paper proposes a two-level framework integrating electric bus network redesign at the tactical level and resource deployment at the planning level. For the redesign problem at the tactical level, this paper designs a tailored branch-and-price algorithm to generate high-quality redesign solutions for the electric bus network. For the resource deployment problem at the planning level, this paper determines the locations of charging facilities and the number of electric buses based on the redesigned electric bus network, considering uncertain passenger demands and metro capacities. We propose a two-layer robust optimization model for the resource deployment problem and develop a tailored column-and-constraint generation algorithm to solve it. Finally, this paper tests the performance of the developed models and algorithms on a set of instances in Beijing. The impact of the uncertainty budget, the number of electric buses, bus capacity, and charging time of electric buses on the system performance is discussed.