New lower bounds and Exact method for the m-PVRP

Sandra Ulrich Ngueveu (1, 2) , Christian Prins (3) , Roberto Wolfler Calvo (4)

1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 LOSI - Laboratoire d'Optimisation des Systèmes Industriels
4 LIPN - Laboratoire d'Informatique de Paris-Nord

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.

Mots clés: m-Peripatetic Vehicle Routing Problem; Dual ascent; Column Generation; Branch-and-Cut; Exact Methods; Lower bounds

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Sandra Ulrich Ngueveu, Christian Prins, Roberto Wolfler Calvo. New lower bounds and Exact method for the m-PVRP. Transportation Science, 2013, 47 (1), pp.38-52. ⟨10.1287/trsc.1120.0421⟩. ⟨hal-01163241⟩