An important strategic phase in the planning process of a railway operator is the development of a line plan, i.e., a set of routes (paths) in a network of tracks, operated at a given hourly frequency. We consider a model formulation of the line-planning problem where total operating costs are to be minimized. This model is solved with a branch-and-cut approach, for which we develop a variety of valid inequalities and reduction methods. A computational study of five real-life instances based on examples from Netherlands Railways (NS) is included.
van Hoesel, C. P. M., Goossens, J. H. M., & Kroon, L. G. (2004). A branch-anc-cut approach for solving line planning problems. Transportation Science, 38(3), 379-393. https://doi.org/10.1287/trsc.1030.0051