A fast algorithm for near cost optimal line plans

We consider the design of line plans in public transport at a minimal total cost. Both, linear and nonlinear integer programming are adequate and intuitive modeling approaches for this problem. We present a heuristic variable fixing procedure which builds on problem knowledge from both techniques. We derive and compare lower bounds from different linearizations in order to assess the quality of our solutions. The involved integer linear programs are strengthened by means of problem specific valid inequalities. Computational results with practical data from the Dutch Railways indicate that our algorithm gives excellent solutions within minutes of computation time.