Joint optimization of bus scheduling and seat allocation for reservation-based travel

Reservation -based travel is an effective method for managing passenger demand during public health emergency. It helps limit the number of passengers boarding at each bus stop, thereby reducing the risk of infectious disease transmission among passengers. This study proposes a joint optimization method for bus scheduling and seat allocation with the consideration of travel time stochasticity based on the reservation -based travel, in which different buses with various capacities are put into operations to satisfy the uneven passenger demand in different periods. To characterize the problem mathematically, a mixed -integer nonlinear programming model is formulated to simultaneously minimize the passenger waiting cost and operating costs of the bus system. This model is further reformulated equivalently into a mixed -integer linear programming model via the linearization method. An effective heuristic algorithm is designed to find highquality solution for the proposed model. Finally, two sets of numerical examples, including a small-scale example and a large-scale example based on the Beijing bus line 6, are conducted to validate the performance of the proposed method. The experimental results demonstrate that the proposed method can effectively reduce operation costs and satisfy passenger demand during different periods.