Mathematical Programming

, Volume 106, Issue 3, pp 491–511 | Cite as

Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem

  • Ricardo Fukasawa
  • Humberto Longo
  • Jens Lysgaard
  • Marcus Poggi de Aragão
  • Marcelo Reis
  • Eduardo Uchoa
  • Renato F. Werneck
Article

Abstract

The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and capacity constraints. This is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods. The resulting branch-and-cut-and-price algorithm can solve to optimality all instances from the literature with up to 135 vertices. This more than doubles the size of the instances that can be consistently solved.

Mathematics Subject Classification (2000)

20E28 20G40 20C20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ricardo Fukasawa
    • 1
  • Humberto Longo
    • 2
  • Jens Lysgaard
    • 3
  • Marcus Poggi de Aragão
    • 4
  • Marcelo Reis
    • 4
  • Eduardo Uchoa
    • 5
  • Renato F. Werneck
    • 6
  1. 1.School of Industrial and Systems EngineeringGeorgiaTechUSA
  2. 2.Instituto de InformáticaUniversidade Federal de GoiásBrazil
  3. 3.Department of Accounting, Finance and LogisticsAarhus School of BusinessDenmark
  4. 4.Departamento de InformáticaPUC Rio de JaneiroBrazil
  5. 5.Departamento de Engenharia de ProduçãoUniversidade Federal FluminenseBrazil
  6. 6.Department of Computer SciencePrinceton UniversityUSA

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