Line planning with equilibrium routing

Planning of lines and frequencies is a well-known problem in public transportation. Passengeroriented approaches to line planning often determine the lines to be established, the corresponding frequencies, and the passenger routing simultaneously. This integration of the planning steps yields better results than stepwise approaches which start with an estimation of the passengers’ paths by traffic-assignment procedures and then establish lines and frequencies accordingly. However, in presence of capacity constraints, integrated approaches aiming at a minimization of the total travel time may find solutions which force some passengers to make long detours. When such a line concept is realized in practice, passengers will most likely not accept such a solution but choose a shortest route among the available ones, leading to a violation of capacity constraints. For this reason, we develop a new integrated line planning model that allows every passenger to choose a shortest route among all available ones. We provide complexity results and an integer programming formulation for this model.