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Solving the median problem with continuous demand on a network

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  • Rafael Blanquero
  • Emilio Carrizosa

Abstract

Where to locate one or several facilities on a network so as to minimize the expected users-closest facility transportation cost is a problem well studied in the OR literature under the name of median problem. In the median problem users are usually identified with nodes of the network. In many situations, however, such assumption is unrealistic, since users should be better considered to be distributed also along the edges of the transportation network. In this paper we address the median problem with demand distributed along edges and nodes. This leads to a global-optimization problem, which can be solved to optimality by means of a branch-and-bound with DC bounds. Our computational experience shows that the problem is solved in short time even for large instances. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Rafael Blanquero & Emilio Carrizosa, 2013. "Solving the median problem with continuous demand on a network," Computational Optimization and Applications, Springer, vol. 56(3), pages 723-734, December.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:3:p:723-734
    DOI: 10.1007/s10589-013-9574-3
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    3. R. Blanquero & E. Carrizosa, 2000. "Optimization of the Norm of a Vector-Valued DC Function and Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 245-260, November.
    4. Cavalier, Tom M. & Sherali, Hanif D., 1986. "Network location problems with continuous link demands: p-medians on a chain and 2-medians on a tree," European Journal of Operational Research, Elsevier, vol. 23(2), pages 246-255, February.
    5. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
    6. L. G. Mitten, 1970. "Branch-and-Bound Methods: General Formulation and Properties," Operations Research, INFORMS, vol. 18(1), pages 24-34, February.
    7. Paul T. Nkansah & H. T. David, 1986. "Network Median Problems with Continuously Distributed Demand," Transportation Science, INFORMS, vol. 20(3), pages 213-219, August.
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    Cited by:

    1. Blanquero, Rafael & Carrizosa, Emilio & G.-Tóth, Boglárka & Nogales-Gómez, Amaya, 2016. "p-facility Huff location problem on networks," European Journal of Operational Research, Elsevier, vol. 255(1), pages 34-42.
    2. Blanquero, Rafael & Carrizosa, Emilio & G.-Tóth, Boglárka, 2016. "Maximal Covering Location Problems on networks with regional demand," Omega, Elsevier, vol. 64(C), pages 77-85.
    3. Emilio Carrizosa, 2015. "Comments on: Static and dynamic source locations in undirected networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 647-649, October.

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