Line Planning at Scale: Models, Methods, and Insights

Abstract

Line planning, the problem of deciding which lines to operate and at what frequency, is a fundamental step in public transport planning. To accurately model passenger routing, the problem is traditionally defined on a change-and-go network (CGN), which captures transfers between lines exactly. However, this network grows large quickly and is hard to solve at scale. We compare the CGN against three more compact models, differing with respect to how transfers are approximated, and characterize how they relate in terms of solution quality and modeling accuracy. We develop state-of-the-art solution methods tailored to each model, and evaluate all four across 972 instances based on the Dutch and Swiss railway networks. Contrary to the CGN's canonical status, we find that it is competitive only on small or easy instances and often fails to find any feasible solution on large networks. Instead, a compact direct connection model performs best overall, finding the best solution on over 83% of instances. Our results indicate that carefully designed approximations, rather than exact transfer modeling, are the more promising foundation for large-scale line planning.