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. These characteristics and the embedded flexibility of the SBTP are crucial for many transit networks in Latin America. A Mixed Integer linear 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 the enhanced MIP yields high quality solutions using small computational times. In particular, instances based on real transit networks are solved within few minutes with a relative deviation from the optimal solution that is usually less than 2%.