Routing in Line Planning for Public Transport

The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a network such that a given demand can be satisfied. There are two objectives. Passengers want to minimize travel times, the transport company wishes to minimize operating costs. We investigate three variants of a multi-commodity flow model for line planning that differ with respect to passenger routings. The first model allows arbitrary routings, the second only unsplittable routings, and the third only shortest path routings with respect to the network. We compare these models theoretically and computationally on data for the city of Potsdam.