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Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic

Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France
Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France
Département opérations et systèmes de dècision, Faculté des sciences de l'administration, Université Laval, Québec, Canada G1K 7P4
Méthodes quantitatives de gestion, École des hautes études commercioles (HEC-Montréal), 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7, Centre interuniversitaire de recherche sur les réseaux d'entreprise la logistique et le transport (CIRRELT)
Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France
christian.prins{at}utt.fr
caroline.prodhon{at}utt.fr
angel.ruiz{at}fas.ulaval.ca
patrick{at}crt.umontreal.ca
roberto.wolfler{at}utt.fr

Most of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system 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. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances.

Key Words: location-routing problem; Lagrangean relaxation; granular tabu search
History: Received: November 2005; revised: June 2006; accepted: November 2006.