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

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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.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, GeorgiaTech, USA

    Ricardo Fukasawa

  2. Instituto de Informática, Universidade Federal de Goiás, Brazil

    Humberto Longo

  3. Department of Accounting, Finance and Logistics, Aarhus School of Business, Denmark

    Jens Lysgaard

  4. Departamento de Informática, PUC Rio de Janeiro, Brazil

    Marcus Poggi de Aragão & Marcelo Reis

  5. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Brazil

    Eduardo Uchoa

  6. Department of Computer Science, Princeton University, USA

    Renato F. Werneck

Authors
  1. Ricardo Fukasawa
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  2. Humberto Longo
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  3. Jens Lysgaard
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  4. Marcus Poggi de Aragão
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  5. Marcelo Reis
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  6. Eduardo Uchoa
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  7. Renato F. Werneck
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Correspondence to Ricardo Fukasawa.

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Fukasawa, R., Longo, H., Lysgaard, J. et al. Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem. Math. Program. 106, 491–511 (2006). https://doi.org/10.1007/s10107-005-0644-x

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  • DOI: https://doi.org/10.1007/s10107-005-0644-x

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