Mathematical Analysis and an Exact Solution Combined with Preprocessing Method for Resynchronizing of Bus Timetable Problem

Bus timetabling is a subproblem of bus network planning, and it determines departure time of each trip of lines to make vehicles from different lines synchronously arrive at transfer stations. Due to the well-designed coordination of bus timetables, passengers can make a smooth transfer without waiting a long time for connecting buses. This paper addresses the planning level of resynchronizing of bus timetable problem allowing modifications to initial timetable. Timetable modifications consist of shifts in the departure times and headways. A single-objective mixed-integer programming model is proposed for this problem to maximize the number of total transferring passengers benefiting from smooth transfers. We analyze the mathematical properties of this model, and then a preprocessing method is designed to reduce the solution space of the proposed model. The numerical results show that the reduced model is effectively solved by branch and bound algorithm, and the preprocessing method has the potential to be applied for large-scale bus networks.