Bi-level programming model for multi-modal regional bus timetable and vehicle dispatch with stochastic travel time

Public transit can be interrupted by emergencies, which can prevent vehicles from completing a trip on time, making travel times stochastic variables. In this paper, an uncertain bi-level programming model for multi-modal regional bus timetables and vehicle dispatch is presented by assuming travel times follow normal distribution based on GPS data for automatic bus station system. The lower model studies coordinating the timetables in regional bus transit with multiple modes of transport, by considering transfers between buses and buses, subways, special passenger lines with intersecting routes. The upper model assigns trips from several routes to buses located at different depots to minimize operating costs; some restrictions such as parking capacity are considered in this model. A group of feasible solutions generated by the lower level plan is provided for input into the upper level plan in order to compare their best solutions. The lower and upper solutions are calculated using the Estimation of Distribution Algorithm, which defines the satisfactory degree of the solutions to reduce their search space to find optimal scheme quickly.