Multiperiod Bus Timetabling

The timetabling subproblem of bus transit network planning determines the departure times for all trips of the lines along the entire day. Most of the public transport networks consider planning periods identical for all lines. In this study we drop this strong assumption by introducing specific periods for each line, which is more realistic. Thus, we propose the multiperiod synchronization bus timetabling (MSBT) problem, which specifies the departure times of the trips of all lines where each line has its own planning periods along the day, with the objective of optimizing synchronization events: maximize passenger transfers and minimize bus bunching along the network. We propose an integer linear programming formulation for the MSBT problem and analyze the structural properties of this formulation by a constraint propagation methodology. These properties are the basis for different operators that lead to the design of efficient metaheuristics for solving the problem. We empirically obtain high-quality feasible solutions for real size instances and show that by considering a multiperiod approach, synchronization events of trips belonging to different planning periods are not ignored, as it is the case when several single period timetables are merged.