The demand-dependent optimization of regular train timetables

Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in North-western Italy.