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New Lower Bounds and Exact Method for the m -PVRP

Author

Listed:
  • Sandra Ulrich Ngueveu

    (CNRS, LAAS, F-31400 Toulouse, France; and Univerité de Toulouse, INP, LAAS, F-31400 Toulouse, France)

  • Christian Prins

    (ICD-LOSI (UMR 6279), Université de Technologie de Troyes, 10010 Troyes Cedex, France)

  • Roberto Wolfler Calvo

    (LIPN (UMR 7030), Université de Paris-Nord, 93430 Villetaneuse, France)

Abstract

This paper presents new lower bounding procedures and an exact method for the m -peripatetic vehicle routing problem ( m -PVRP) based on polyhedral and column generation approaches. The branch-and-cut algorithms use three types of valid cuts on the edge-based formulation. The column-generation-based lower bounding procedure is applied on the dual set partitioning formulation and is composed of dual heuristics that estimate good dual variable values and therefore high lower bounds. Computational results on instances from the literature show that these new lower bounds reach on average 97.5% to 99% of the best known upper bounds and optimality is proven for a third of the instances.

Suggested Citation

  • Sandra Ulrich Ngueveu & Christian Prins & Roberto Wolfler Calvo, 2013. "New Lower Bounds and Exact Method for the m -PVRP," Transportation Science, INFORMS, vol. 47(1), pages 38-52, February.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:1:p:38-52
    DOI: 10.1287/trsc.1120.0421
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    References listed on IDEAS

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    1. Araque, J. & Hall, L. & Magnanti, T., 1990. "Capacitated trees, capacitated routing, and associated polyhedra," LIDAM Discussion Papers CORE 1990061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    3. A N Letchford & J Lysgaard & R W Eglese, 2007. "A branch-and-cut algorithm for the capacitated open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1642-1651, December.
    4. Araque, J., 1990. "Lots of combs of different sizes for vehicle routing," LIDAM Discussion Papers CORE 1990074, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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