A Metaheuristic Algorithm for the Location Routing Problem with Heterogeneous Fleet
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Keywords
Location Routing Problem, Heterogeneous Fleet, Granular Tabu Search, Metaheuristic Algorithms.
Abstract
This paper considers the Location-Routing Problem with Heterogeneous Fleet (LRPH), in which the aim is to determine the depots to be opened, the customers to be assigned to each open depot, and the routes to be performed to fulfill the demand of the customers by considering a heterogeneous fleet with different capacities and associated costs. The objective is to minimize the sum of the cost of the open depots, of the used vehicle costs, and of the variable costs related with the distance traveled by the performed routes. In this paper, it is proposed a metaheuristic algorithm based on a granular tabu search to solve the LRPH. Computational experiments on adapted benchmark instances from the literature show that the proposed approach is able to obtain, within short computing times, high quality solutions illustrating its effectiveness.
MSC: 68Qxx; 68W40
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References
[2] G. Nagy and S. Salhi, “Location-routing: Issues, models and methods,” EuropeanJournal of Operational Research, vol. 177, no. 2, pp. 649–672, 2007.57
[3] S. Salhi, A. Imran, and N. A. Wassan, “The multi-depot vehicle routingproblem with heterogeneous vehicle fleet: Formulation and a variable neighborhoodsearch implementation,” Computers & Operations Research, 2013.57
[4] C. Prins, C. Prodhon, A. Ruiz, P. Soriano, and R. W. Calvo, “Solving thecapacitated location-routing problem by a cooperative lagrangean relaxationgranulartabu search heuristic,” Transportation Science, vol. 41, no. 4, pp.470–483, 2007. 57, 59, 61, 70, 71, 73
[5] C. Duhamel, P. Lacomme, C. Prins, and C. Prodhon, “A GRASP × ELSapproach for the capacitated location-routing problem,” Computers & OperationsResearch, vol. 37, no. 11, pp. 1912–1923, 2010. 57
[6] V. F. Yu, S.-W. Lin, W. Lee, and C.-J. Ting, “A simulated annealing heuristicfor the capacitated location routing problem,” Computers & IndustrialEngineering, vol. 58, no. 2, pp. 288–299, 2010. 57
[7] J. Willmer Escobar, R. Linfati, and P. Toth, “A two-phase hybrid heuristicalgorithm for the capacitated location-routing problem,” Computers &Operations Research, vol. 40, no. 1, pp. 70–79, 2013. 57, 68
[8] J. H. Bookbinder and K. E. Reece, “Vehicle routing considerations in distributionsystem design,” European Journal of Operational Research, vol. 37,no. 2, pp. 204–213, 1988. 58
[9] S. Salhi and M. Fraser, “An integrated heuristic approach for the combinedlocation vehicle fleet mix problem,” Studies in Locational Analysis, vol. 8,pp. 3–21, 1996. 58, 59
[10] T.-H. Wu, C. Low, and J.-W. Bai, “Heuristic solutions to multi-depotlocation-routing problems,” Computers & Operations Research, vol. 29,no. 10, pp. 1393–1415, 2002. 58
[11] D. Ambrosino and M. Grazia Scutellà, “Distribution network design: Newproblems and related models,” European Journal of Operational Research,vol. 165, no. 3, pp. 610–624, 2005. 58
[12] H. Gunnarsson, M. Rönnqvist, and D. Carlsson, “A combined terminal locationand ship routing problem,” Journal of the Operational Research Society,vol. 57, no. 8, pp. 928–938, 2005. 58
[13] M. T. C. S. JIS, Computers and intractability A Guide to the Theory ofNP-Completeness. WH Freeman and Company, 1979. 58
[14] G. Laporte, “The vehicle routing problem: An overview of exact and approximatealgorithms,” European Journal of Operational Research, vol. 59, no. 3,pp. 345–358, 1992. 61
[15] P. Toth and D. Vigo, The vehicle routing problem. Siam, 2002, vol. 9. 61
[16] C. H. Papadimitriou and K. Steiglitz, Combinatorial optimization: algorithmsand complexity. Courier Dover Publications, 1998. 61
[17] P. Toth and D. Vigo, “The granular tabu search and its application to thevehicle-routing problem,” INFORMS Journal on Computing, vol. 15, no. 4,pp. 333–346, 2003. 62, 65
[18] C. Blum and A. Roli, “Metaheuristics in combinatorial optimization: Overviewand conceptual comparison,” ACM Computing Surveys (CSUR), vol. 35,no. 3, pp. 268–308, 2003. 62
[19] S. Lin and B. W. Kernighan, “An effective heuristic algorithm for thetraveling-salesman problem,” Operations research, vol. 21, no. 2, pp. 498–516, 1973. 64
[20] K. Helsgaun, “An effective implementation of the lin–kernighan traveling salesmanheuristic,” European Journal of Operational Research, vol. 126, no. 1,pp. 106–130, 2000. 64
[21] J. Barceló and J. Casanovas, “A heuristic lagrangean algorithm for the capacitatedplant location problem,” European Journal of Operational Research,vol. 15, no. 2, pp. 212–226, 1984. 64
[22] J. G. Klincewicz and H. Luss, “A lagrangian relaxation heuristic for capacitatedfacility location with single-source constraints,” Journal of the OperationalResearch Society, pp. 495–500, 1986. 64
[23] M. Gendreau, A. Hertz, and G. Laporte, “A tabu search heuristic for thevehicle routing problem,” Management science, vol. 40, no. 10, pp. 1276–1290, 1994. 67
[24] É. Taillard, “Parallel iterative search methods for vehicle routing problems,”Networks, vol. 23, no. 8, pp. 661–673, 1993. 67
[25] B. Golden, A. Assad, L. Levy, and F. Gheysens, “The fleet size and mixvehicle routing problem,” Computers & Operations Research, vol. 11, no. 1,pp. 49–66, 1984. 69, 70
[26] N. Christofides and J. E. Beasley, “A tree search algorithm for the p-medianproblem,” European Journal of Operational Research, vol. 10, no. 2, pp. 196–204, 1982. 70, 73
[27] S. P. Coy, B. L. Golden, G. C. Runger, and E. A. Wasil, “Using experimentaldesign to find effective parameter settings for heuristics,” Journal of Heuristics,vol. 7, no. 1, pp. 77–97, 2001. 71