Adopting GRASP to solve a novel model for bus timetabling problem with minimum transfer and fruitless waiting times

This paper addresses a variant of bus timetabling problem assuming that travel times changes dynamically over the planning horizon. In addition to minimizing the transfer waiting time, another objective, namely minimizing the fruitless waiting time, is introduced in this paper as a new realistic objective. First, the problem is formulated as a mixed integer linear programming model. Then, since commercial solvers become inefficient to solve moderate and large sized instances of the problem (due to the NP-hardness), a GRASP heuristic algorithm is developed. Computational experiments over a variety of random instances verify the performance of the proposed method

Valid inequalities for the synchronization bus timetabling problem

International audienceBus 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