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Continuous Facility Location with Backbone Network Costs

Author

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  • John Gunnar Carlsson

    (Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

  • Fan Jia

    (Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

Abstract

We consider a continuous facility location problem in which our objective is to minimize the weighted sum of three costs: (1) fixed costs from installing the facilities, (2) backbone network costs incurred from connecting the facilities to each other, and (3) transportation costs incurred from providing services from the facilities to the service region. We first analyze the limiting behavior of this model and derive the two asymptotically optimal configurations of facilities: one of these configurations is the well studied honeycomb heuristic , and the other is an Archimedean spiral. We then give a fast constant-factor approximation algorithm for finding the placement of a set of facilities in any convex polygon that minimizes the sum of the three aforementioned costs.

Suggested Citation

  • John Gunnar Carlsson & Fan Jia, 2015. "Continuous Facility Location with Backbone Network Costs," Transportation Science, INFORMS, vol. 49(3), pages 433-451, August.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:3:p:433-451
    DOI: 10.1287/trsc.2013.0511
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    References listed on IDEAS

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    1. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    2. Gérard P. Cachon, 2014. "Retail Store Density and the Cost of Greenhouse Gas Emissions," Management Science, INFORMS, vol. 60(8), pages 1907-1925, August.
    3. James F. Campbell, 1993. "One-to-Many Distribution with Transshipments: An Analytic Model," Transportation Science, INFORMS, vol. 27(4), pages 330-340, November.
    4. Melkote, Sanjay & Daskin, Mark S., 2001. "An integrated model of facility location and transportation network design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(6), pages 515-538, July.
    5. Miranda, Pablo A. & Garrido, Rodrigo A., 2004. "Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 40(3), pages 183-207, May.
    6. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.
    7. 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.
    8. John Gunnar Carlsson & Fan Jia & Ying Li, 2014. "An Approximation Algorithm for the Continuous k -Medians Problem in a Convex Polygon," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 280-289, May.
    9. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    10. Newell, Gordon F. & Daganzo, Carlos F., 1986. "Design of multiple-vehicle delivery tours--I a ring-radial network," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 345-363, October.
    11. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    12. Dimitris J. Bertsimas & David Simchi-Levi, 1996. "A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty," Operations Research, INFORMS, vol. 44(2), pages 286-304, April.
    13. van Bergeijk,Peter A. G. & Brakman,Steven (ed.), 2010. "The Gravity Model in International Trade," Cambridge Books, Cambridge University Press, number 9780521196154.
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