On solving multi-type line planning problems

An important strategic element in the planning process of a railway operator is the development of a line plan, i.e. a set of routes (paths) on the network of tracks, operated at a given hourly frequency. The models described in the literature have thus far considered only lines that halt at all stations along their route. In this paper we introduce several models for solving line planning problems in which lines can have di®erent halting patterns. Correctness and equivalence proofs for these models are given, as well as an evaluation using several real life instances.