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

  • Authors:

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

  • Affiliations:

  • School of Industrial and Systems Engineering, GeorgiaTech, USA;Instituto de Informática, Universidade Federal de Goiás, Brazil;Department of Accounting, Finance and Logistics, Aarhus School of Business, Denmark;Departamento de Informática, PUC Rio de Janeiro, Brazil;Departamento de Informática, PUC Rio de Janeiro, Brazil;Departamento de Engenharia de Produção, Universidade Federal Fluminense;Department of Computer Science, Princeton University, Brazil, USA

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2006

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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.