4OR

, Volume 9, Issue 1, pp 49–82 | Cite as

A column generation algorithm for the vehicle routing problem with soft time windows

  • Federico Liberatore
  • Giovanni Righini
  • Matteo Salani
Research Paper

Abstract

The Vehicle Routing Problem with Time Windows consists of computing a minimum cost set of routes for a fleet of vehicles of limited capacity visiting a given set of customers with known demand, with the additional constraint that each customer must be visited in a specified time window. We consider the case in which time window constraints are relaxed into “soft” constraints, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. We present a branch-and-price algorithm which is the first exact optimization algorithm for this problem.

Keywords

Vehicle routing problem Soft time windows Column generation Branch-and-price Combinatorial optimization 

MSC classification (2000)

90C27 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Federico Liberatore
    • 1
    • 3
  • Giovanni Righini
    • 1
  • Matteo Salani
    • 2
    • 4
  1. 1.Dipartimento di Tecnologie dell’InformazioneUniversità degli Studi di MilanoCremaItaly
  2. 2.TRANSP-OR, École Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Kent Business SchoolUniversity of KentCanterbury, KentUK
  4. 4.IDSIA, Istituto Dalle Molle di Studi sull’Intelligenza ArtificialeManno-LuganoSwitzerland

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