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

Author

Listed:
  • Christian Prins

    (Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France)

  • Caroline Prodhon

    (Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France)

  • Angel Ruiz

    (Département opérations et systèmes de dècision, Faculté des sciences de l'administration, Université Laval, Québec, Canada G1K 7P4)

  • Patrick Soriano

    (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))

  • Roberto Wolfler Calvo

    (Institute Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, BP 2060, 10010 Troyes Cedex, France)

Abstract

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.

Suggested Citation

  • Christian Prins & Caroline Prodhon & Angel Ruiz & Patrick Soriano & Roberto Wolfler Calvo, 2007. "Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic," Transportation Science, INFORMS, vol. 41(4), pages 470-483, November.
    • Handle: RePEc:inm:ortrsc:v:41:y:2007:i:4:p:470-483
    DOI: 10.1287/trsc.1060.0187
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    References listed on IDEAS

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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    2. Salhi, Said & Rand, Graham K., 1989. "The effect of ignoring routes when locating depots," European Journal of Operational Research, Elsevier, vol. 39(2), pages 150-156, March.
    3. Srivastava, R, 1993. "Alternate solution procedures for the location-routing problem," Omega, Elsevier, vol. 21(4), pages 497-506, July.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    6. Cortinhal, Maria Joao & Captivo, Maria Eugenia, 2003. "Upper and lower bounds for the single source capacitated location problem," European Journal of Operational Research, Elsevier, vol. 151(2), pages 333-351, December.
    7. Paolo Toth & Daniele Vigo, 2003. "The Granular Tabu Search and Its Application to the Vehicle-Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 333-346, November.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    9. Mina, Hokey & Jayaraman, Vaidyanathan & Srivastava, Rajesh, 1998. "Combined location-routing problems: A synthesis and future research directions," European Journal of Operational Research, Elsevier, vol. 108(1), pages 1-15, July.
    10. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    11. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 383-399, March.
    12. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    13. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    14. Laporte, Gilbert & Louveaux, Francois & Mercure, Helene, 1989. "Models and exact solutions for a class of stochastic location-routing problems," European Journal of Operational Research, Elsevier, vol. 39(1), pages 71-78, March.
    15. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    16. Tuzun, Dilek & Burke, Laura I., 1999. "A two-phase tabu search approach to the location routing problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 87-99, July.
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