Omar J. Ibarra-Rojas

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.

Valid inequalities for the synchronization bus timetabling problem

Bus transit network planning is a complex process that is divided into several phases such as: line planning, timetable generation, vehicle scheduling, and crew scheduling. In this work, we address the timetable generation which consists in scheduling the departure times for all trips of each bus line. We focus on the Synchronization Bus Timetabling Problem (SBTP) that favors passenger transfers and avoids congestion of buses at common stops. A Mixed Integer Program (MIP) was proposed in the literature for the SBTP but it fails to solve real bus network instances. We develop in this paper four classes of valid inequalities for this MIP using combinatorial properties of the SBTP on the number of synchronizations. Experimental results show that large instances are solved within few minutes with a relative deviation from the optimal solution that is usually less than 3 percent.