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

• Published in: Transportation science Vol. 41; no. 4; pp. 470 - 483
• Main Authors: Prins, Christian, Prodhon, Caroline, Ruiz, Angel, Soriano, Patrick, Wolfler Calvo, Roberto
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.11.2007; Transportation Science & Logistic Society of the Institute for Operations Research and Management Sciences; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Automobile industry; Automobiles; Computer Science; Costs; Customers; Distribution planning; Diversification; Exact sciences and technology; Fixed costs; Forecasts and trends; Global telecommunication system; granular tabu search; Granularity; Ground, air and sea transportation, marine construction; Heuristic; Heuristics; Iterative solutions; Lagrange equations; Lagrangean relaxation; Linear programming; location-routing problem; Logistics; Mathematical methods; Mathematical models; Methods; Operations Research; Performance evaluation; Routing; Services; Studies; Tabu search; Total costs; Transport economics; Transportation; Transportation planning, management and economics; Traveling salesman problem; Vehicle capacity; Vehicles; United States; Heuristics; Lagrangean relaxation; Routing; location-routing problem; granular tabu search; Result; Relaxation; Tabu search; Problem solving; Localization; Mathematical model; Computing method; Logistics
• ISSN: 0041-1655; 1526-5447
• DOI: 10.1287/trsc.1060.0187

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.