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A New Formulation Approach for Location-Routing Problems

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  • Hunkar Toyoglu

    ()

  • Oya Karasan
  • Bahar Kara
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    Abstract

    A Location-Routing Problem (LRP) combines two difficult problems, facility location and vehicle routing, and as such it is inherently hard to solve. In this paper, we propose a different formulation approach than the common arc-based product-flow (Arc-BPF) approach in the literature. We associate product amounts to the nodes of the network resulting in a node-based product-flow (Node-BPF) formulation. Our main objective is to develop LRP models with fewer constraints and variables, which can be solved more efficiently. To introduce the proposed approach, we reformulate a complex four-index Arc-BPF LRP model from the literature as a three-index Node-BPF model, which computationally outperforms the former. We then introduce a heuristic method. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s11067-011-9170-y
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    Article provided by Springer in its journal Networks and Spatial Economics.

    Volume (Year): 12 (2012)
    Issue (Month): 4 (December)
    Pages: 635-659

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    Handle: RePEc:kap:netspa:v:12:y:2012:i:4:p:635-659
    Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=106607

    Keywords: Location-routing problem; Mixed integer linear programming; Logistics; Network design;

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    1. Hansen, P. H. & Hegedahl, B. & Hjortkjaer, S. & Obel, B., 1994. "A heuristic solution to the warehouse location-routing problem," European Journal of Operational Research, Elsevier, vol. 76(1), pages 111-127, July.
    2. Perl, Jossef & Daskin, Mark S., 1985. "A warehouse location-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 19(5), pages 381-396, October.
    3. Burcin Bozkaya & Seda Yanik & Selim Balcisoy, 2010. "A GIS-Based Optimization Framework for Competitive Multi-Facility Location-Routing Problem," Networks and Spatial Economics, Springer, vol. 10(3), pages 297-320, September.
    4. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    5. Ambrosino, Daniela & Grazia Scutella, Maria, 2005. "Distribution network design: New problems and related models," European Journal of Operational Research, Elsevier, vol. 165(3), pages 610-624, September.
    6. Laporte, Gilbert & Nobert, Yves, 1981. "An exact algorithm for minimizing routing and operating costs in depot location," European Journal of Operational Research, Elsevier, vol. 6(2), pages 224-226, February.
    7. Nambiar, Jay M. & Gelders, Ludo F. & Van Wassenhove, Luk N., 1989. "Plant location and vehicle routing in the Malaysian rubber smallholder sector: A case study," European Journal of Operational Research, Elsevier, vol. 38(1), pages 14-26, January.
    8. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2011. "A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery," European Journal of Operational Research, Elsevier, vol. 211(2), pages 318-332, June.
    9. Yi, Wei & Ozdamar, Linet, 2007. "A dynamic logistics coordination model for evacuation and support in disaster response activities," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1177-1193, June.
    10. 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.
    11. 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.
    12. 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.
    13. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
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    Cited by:

    1. Jane Lin & Qin Chen & Kazuya Kawamura, 2016. "Sustainability SI: Logistics Cost and Environmental Impact Analyses of Urban Delivery Consolidation Strategies," Networks and Spatial Economics, Springer, vol. 16(1), pages 227-253, March.
    2. Paul Berglund & Changhyun Kwon, 2014. "Robust Facility Location Problem for Hazardous Waste Transportation," Networks and Spatial Economics, Springer, vol. 14(1), pages 91-116, March.
    3. Antonio Palacio & B. Adenso-Díaz & Sebastián Lozano & Salvador Furió, 2016. "Bicriteria Optimization Model for Locating Maritime Container Depots: Application to the Port of Valencia," Networks and Spatial Economics, Springer, vol. 16(1), pages 331-348, March.
    4. Junlong Zhang & William Lam & Bi Chen, 2013. "A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service," Networks and Spatial Economics, Springer, vol. 13(4), pages 471-496, December.

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