A Branch-and-Cut method for the Capacitated Location-Routing Problem

Authors:
José-Manuel Belenguer;Enrique Benavent;Christian Prins;Caroline Prodhon;Roberto Wolfler Calvo
Affiliations:
Dept. d'Estadística i Investigació Operativa, Universitat de València, Spain;Dept. d'Estadística i Investigació Operativa, Universitat de València, Spain;ICD-LOSI (FRE CNRS 2848), Université de Technologie de Troyes, France;ICD-LOSI (FRE CNRS 2848), Université de Technologie de Troyes, France;LIPN (UMR 7030), Université de Paris Nord, France
Venue:
Computers and Operations Research
Year:
2011

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Abstract

Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5-10 potential depots and 20-88 customers, shows that 26 instances with five depots are solved to optimality, including all instances with up to 40 customers and three with 50 customers.