Non-cyclic train timetabling and comparability graphs

We consider the customary formulation of non-cyclic train timetabling, calling for a maximum-profit collection of compatible paths in a suitable graph. The associated ILP models look for a maximum-weight clique in a (n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models, propose some new stronger ones, all having the essential property that both the separation and the column generation can be carried out efficiently, and report the computational results on highly-congested instances.