## Metric Inequalities for Routings on Direct Connections with Application in Line Planning

Please always quote using this URN: urn:nbn:de:0297-zib-53507
• We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows. The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers.

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