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Approximation Algorithms for Capacitated Location Routing

Author

Listed:
  • Tobias Harks

    (School of Business and Economics, Maastricht University, 6200 MD, The Netherlands)

  • Felix G König

    (TomTom International BV, 12435 Berlin, Germany)

  • Jannik Matuschke

    (Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany)

Abstract

An approximation algorithm for an optimization problem runs in polynomial time for all instances and is guaranteed to deliver solutions with bounded optimality gap. We derive such algorithms for different variants of capacitated location routing , an important generalization of vehicle routing where the cost of opening the depots from which vehicles operate is taken into account. Our results originate from combining algorithms and lower bounds for different relaxations of the original problem; along with location routing we also obtain approximation algorithms for multidepot capacitated vehicle routing by this framework. Moreover, we extend our results to further generalizations of both problems, including a prize-collecting variant, a group version, and a variant where cross-docking is allowed. We finally present a computational study of our approximation algorithm for capacitated location routing on benchmark instances and large-scale randomly generated instances. Our study reveals that the quality of the computed solutions is much closer to optimality than the provable approximation factor.

Suggested Citation

  • Tobias Harks & Felix G König & Jannik Matuschke, 2013. "Approximation Algorithms for Capacitated Location Routing," Transportation Science, INFORMS, vol. 47(1), pages 3-22, February.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:1:p:3-22
    DOI: 10.1287/trsc.1120.0423
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    References listed on IDEAS

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    1. Barreto, Sergio & Ferreira, Carlos & Paixao, Jose & Santos, Beatriz Sousa, 2007. "Using clustering analysis in a capacitated location-routing problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 968-977, June.
    2. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    3. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms," Transportation Science, INFORMS, vol. 39(1), pages 104-118, February.
    4. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    5. 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.
    6. Chung-Lun Li & David Simchi-Levi, 1990. "Worst-Case Analysis of Heuristics for Multidepot Capacitated Vehicle Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 64-73, February.
    7. Haimovich, M. & Kan, R. & Stougie, L., 1988. "Analysis Of Heuristics For Vehicle Routing Problems," Papers ae_1-88, Universiteit Amsterdam - Institute of Actuarial Sciences and Econometrics.
    8. R. Ravi & Amitabh Sinha, 2006. "Approximation Algorithms for Problems Combining Facility Location and Network Design," Operations Research, INFORMS, vol. 54(1), pages 73-81, February.
    9. Roberto Baldacci & Paolo Toth & Daniele Vigo, 2010. "Exact algorithms for routing problems under vehicle capacity constraints," Annals of Operations Research, Springer, vol. 175(1), pages 213-245, March.
    10. Liu, Jiyin & Li, Chung-Lun & Chan, Chun-Yan, 2003. "Mixed truck delivery systems with both hub-and-spoke and direct shipment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 39(4), pages 325-339, July.
    11. M Wen & J Larsen & J Clausen & J-F Cordeau & G Laporte, 2009. "Vehicle routing with cross-docking," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1708-1718, December.
    12. 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.
    13. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    14. J-F Cordeau & M Gendreau & G Laporte & J-Y Potvin & F Semet, 2002. "A guide to vehicle routing heuristics," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(5), pages 512-522, May.
    15. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
    16. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    17. 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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