Line Planning and Connectivity

The line planning problem in public transport deals with the construction of a system of lines that is both attractive for the passengers and of low costs for the operator. In general, the computed line system should be connected, i.e., for each two stations there have to be a path that is covered by the lines. This subproblem is a generalization of the well-known Steiner tree problem; we call it the Steiner connectivity problem. We show in this talk that important results on the Steiner tree polytope can be carried over to the SCP case. Furthermore, we generalize the famous relation between undirected and directed Steiner tree formulations.