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A Median Location Model with Nonclosest Facility Service

Author

Listed:
  • Jerry R. Weaver

    (University of Alabama, University, Alabama)

  • Richard L. Church

    (University of California, Santa Barbara, California)

Abstract

This paper deals with the location of service facilities on a transportation network where the closest (in distance, time or cost) facility is known not to service some significant portion of demand. The concept of vector assignment of demand nodes to facilities is introduced to account for nonclosest facility service. A generalized formulation of the p-median problem incorporating vector assignment is presented. It is shown that an optimal solution to this vector assignment p-median problem exists which consists entirely of nodes of the graph; however, there may be more than one facility per node. Three different solution procedures are discussed for the vector assignment p-median problem. Computational experiments for three different moderately sized data sets give encouraging results. A locational example is included which gives a comparison of an optimal p-median solution and an optimal p-median solution with vector assignment.

Suggested Citation

  • Jerry R. Weaver & Richard L. Church, 1985. "A Median Location Model with Nonclosest Facility Service," Transportation Science, INFORMS, vol. 19(1), pages 58-74, February.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:1:p:58-74
    DOI: 10.1287/trsc.19.1.58
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    Citations

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    Cited by:

    1. Rolland, Erik & Schilling, David A. & Current, John R., 1997. "An efficient tabu search procedure for the p-Median Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 329-342, January.
    2. Oded Berman & Dmitry Krass & Mozart B. C. Menezes, 2007. "Facility Reliability Issues in Network p -Median Problems: Strategic Centralization and Co-Location Effects," Operations Research, INFORMS, vol. 55(2), pages 332-350, April.
    3. Klibi, Walid & Martel, Alain, 2012. "Modeling approaches for the design of resilient supply networks under disruptions," International Journal of Production Economics, Elsevier, vol. 135(2), pages 882-898.
    4. Karatas, Mumtaz & Yakıcı, Ertan, 2019. "An analysis of p-median location problem: Effects of backup service level and demand assignment policy," European Journal of Operational Research, Elsevier, vol. 272(1), pages 207-218.
    5. Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
    6. Wang, Yu & Luangkesorn, K. Louis & Shuman, Larry, 2012. "Modeling emergency medical response to a mass casualty incident using agent based simulation," Socio-Economic Planning Sciences, Elsevier, vol. 46(4), pages 281-290.
    7. R A Gerrard & R L Church, 1995. "A General Construct for the Zonally Constrained p-Median Problem," Environment and Planning B, , vol. 22(2), pages 213-236, April.
    8. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.
    9. Abareshi, Maryam & Zaferanieh, Mehdi, 2019. "A bi-level capacitated P-median facility location problem with the most likely allocation solution," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 1-20.
    10. Ting L. Lei & Richard L. Church, 2011. "Constructs for Multilevel Closest Assignment in Location Modeling," International Regional Science Review, , vol. 34(3), pages 339-367, July.
    11. Caio Vitor Beojone & Regiane Máximo de Souza & Ana Paula Iannoni, 2021. "An Efficient Exact Hypercube Model with Fully Dedicated Servers," Transportation Science, INFORMS, vol. 55(1), pages 222-237, 1-2.
    12. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
    13. Masashi Miyagawa, 2012. "Joint distribution of distances to the first and the second nearest facilities," Journal of Geographical Systems, Springer, vol. 14(2), pages 209-222, April.
    14. Ting L. Lei & Richard L. Church, 2014. "Vector Assignment Ordered Median Problem," International Regional Science Review, , vol. 37(2), pages 194-224, April.

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