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Preprint 43-2003

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

A Fast Algorithm for Near Cost Optimal Line Plans
Appears in Math. Meth. Oper. Res.
primary: 90C10 Integer programming
secondary: 90C30 Nonlinear programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90B06 Transportation, logistics
Integer programming, non-linear integer programming, cutting planes, public transport, line planning
We consider the design of line plans in public transport at a minimal total cost. Both, linear and non-linear 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.
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