Non-cyclic train timetabling and comparability graphs

We consider the customary formulation of non-cyclic train timetabling, calling for a maximumprofit 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 and propose some new stronger ones, all having the essential property that both separation and column generation can be carried out efficiently. Computational results show that the LP relaxations of the new formulations can lead to notably stronger upper bounds on highly-congested instances.