Optimizing public transport transfers by integrating timetable coordination and vehicle scheduling

Transfer optimization in public transport (PT) networks can be achieved through coordinated timetabling and vehicle scheduling. Traditionally, the coordinated timetabling problem is solved first before proceeding to the vehicle scheduling problem. The integration of these two problems can help further reduce the total operation cost and improve the level of service, especially when timetables of different PT lines are well-coordinated at transfer stations. This work addresses the integrated PT timetable coordination and vehicle scheduling problem while ensuring that each PT line is dispatched with an even headway. We first separately formulate two integer linear programming models for the timetable coordination and vehicle scheduling problems. Next, the two models are integrated into a bi-objective integer linear programming model for the integrated timetable coordination and vehicle scheduling problem. For small size PT networks, the model can be solved by using an ɛ-constraint method, together with off-the-shelf optimization solvers. For large-size problems, two constraint-reduction procedures are developed to reduce the number of redundant constraints so as to reduce the computation complexity and improve the solution process. Finally, the models and solution method are applied to a numerical example and a real-world bus rapid transit (BRT) network in Chengdu, China. Computation results show that the solution generated by the sequential optimization approach is usually dominated by the Pareto-optimal solutions generated by the integrated optimization approach. Our findings suggest that it is not a wise decision to use the solution generated by the sequential optimization approach or the solution with the minimum fleet size generated by the integrated optimization approach. For practical implementation, it is recommended to choose the solution that has a fleet size of one more vehicle than the minimum fleet size.