Approaches to a real-world Train Timetabling Problem in a railway node

The problem was studied for a research project funded by Rete Ferroviaria Italiana (RFI), the main Italian railway Infrastructure Manager, who also provided us with real-world instances. We present an Integer Linear Programming (ILP) model for the problem, which adapts previous ILP models from the literature to deal with the case of a railway node. The Linear Programming (LP) relaxation of the model is used to derive a dual bound. In addition, we propose an iterative heuristic algorithm that is able to obtain good solutions to real-world instances with up to 1500 trains in short computing times. The proposed algorithm is also used to evaluate the capacity saturation of the railway nodes.