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Mathematical Methods of Operations Research

, Volume 59, Issue 2, pp 205–220 | Cite as

A fast algorithm for near cost optimal line plans

  • Michael R. Bussieck
  • Thomas Lindner
  • Marco E. LübbeckeEmail author
Article

Abstract.

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.

Keywords

Integer programming Nonlinear integer programming Cutting planes Public transport Line planning 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Michael R. Bussieck
    • 1
  • Thomas Lindner
    • 2
  • Marco E. Lübbecke
    • 3
    Email author
  1. 1.GAMS Development CorporationNWWashington DC
  2. 2.Siemens Transportation SystemsBraunschweigGermany
  3. 3.Technische Universität BerlinInstitut für MathematikBerlinGermany

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