Optimizing bus bridging services with mode choice in response to urban rail transit emergencies

During urban rail transit (URT) emergencies, stranded passengers may choose to seek alternative modes of transportation instead of waiting in the URT system for the bus bridging service to commence. To tackle this challenge, we present an optimization-based approach focused on identifying promising bus bridging lines and devising efficient services. Specifically, we introduce a candidate line generation (CLG) model designed to identify potential bus bridging lines. This model is akin to solving a k-all pair elementary shortest path problem with resource constraints (k-APESPPRC). We develop an exact algorithm based on the label setting algorithm and Lawler's algorithm to solve this model effectively. Subsequently, our approach allocates limited bus resources to determine line selection, frequency determination, bus deployment, and passenger assignment on the integrated network (i.e., partial URT network and bus network) with the consideration of mode choice. Given the inherent complexity of this problem, we introduce an optimization-based tabu search method (opt-tabu) designed to efficiently solve real-size instances. To demonstrate the effectiveness of our approach, we present a real case study conducted in Hong Kong, showcasing its efficiency and practicality. In summary, this study makes a valuable contribution to the transportation industry by providing a practical and efficient approach to managing URT emergencies, emphasizing the significance of considering mode choice in the context of bus bridging services.