Timetable optimization for a moving block system

We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model can solve reasonably sized instances with up to a hundred trains to optimality. •A general train timetabling problem formulation for fixed and moving block systems with flexible routing.•A multi-layer graph approach using velocity expansion to model the problem.•A branch-and-cut algorithm to solve the model formulation.•A computational study and comparison for realistic data for a corridor in Germany.