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Hierarchical location-allocation models for congested systems

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Abstract

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and their locations that will cover a given region with a distance or time standard. The second model is cast as a Maximal Covering Location formulation. A heuristic procedure is then presented together with computational experience. Finally, some extensions of these models that address other types of spatial configurations are offered.

Suggested Citation

  • Vladimir Marianov & Daniel Serra, 2000. "Hierarchical location-allocation models for congested systems," Economics Working Papers 425, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:425
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    References listed on IDEAS

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    1. Marianov, Vladimir & ReVelle, Charles, 1996. "The Queueing Maximal availability location problem: A model for the siting of emergency vehicles," European Journal of Operational Research, Elsevier, vol. 93(1), pages 110-120, August.
    2. Batta, Rajan, 1989. "A queueing-location model with expected service time dependent queueing disciplines," European Journal of Operational Research, Elsevier, vol. 39(2), pages 192-205, March.
    3. Marianov, Vladimir & Revelle, Charles, 1994. "The queuing probabilistic location set covering problem and some extensions," Socio-Economic Planning Sciences, Elsevier, vol. 28(3), pages 167-178.
    4. Daniel Serra, 1996. "The Coherent Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 75(1), pages 79-101, January.
    5. Serra, Daniel & Marianov, Vladimir & ReVelle, Charles, 1992. "The maximum-capture hierarchical location problem," European Journal of Operational Research, Elsevier, vol. 62(3), pages 363-371, November.
    6. Vladimir Marianov & Daniel Serra, 1994. "Probabilistic maximal covering location models for congested systems," Economics Working Papers 70, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Daniel Serra & Charles Revelle, 1992. "The PQ-Median problem: Location and districting of hierarchical facilities. Part I," Economics Working Papers 12, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Daniel Serra & Charles Revelle, 1992. "The PQ-Median problem: Location and districting of hierarchical facilities. Part II: Heuristic solution methods," Economics Working Papers 13, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Berman, Oded & Mandowsky, Ronald R., 1986. "Location-allocation on congested networks," European Journal of Operational Research, Elsevier, vol. 26(2), pages 238-250, August.
    10. ReVelle, Charles, 1993. "Facility siting and integer-friendly programming," European Journal of Operational Research, Elsevier, vol. 65(2), pages 147-158, March.
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    Citations

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    Cited by:

    1. Jayaraman, Vaidyanathan & Gupta, Rakesh & Pirkul, Hasan, 2003. "Selecting hierarchical facilities in a service-operations environment," European Journal of Operational Research, Elsevier, vol. 147(3), pages 613-628, June.
    2. Boffey, Brian & Galvao, Roberto & Espejo, Luis, 2007. "A review of congestion models in the location of facilities with immobile servers," European Journal of Operational Research, Elsevier, vol. 178(3), pages 643-662, May.
    3. repec:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_jors.2008.172 is not listed on IDEAS
    4. Daniel Serra, 2003. "Location of multiple server common service centers or public facilities for minimizing general congestion and travel cost functions," Economics Working Papers 658, Department of Economics and Business, Universitat Pompeu Fabra.
    5. repec:pal:jorsoc:v:60:y:2009:i:5:d:10.1057_palgrave.jors.2602606 is not listed on IDEAS
    6. Vardar, Cem & Gel, Esma S. & Fowler, John W., 2007. "A framework for evaluating remote diagnostics investment decisions for semiconductor equipment suppliers," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1411-1426, August.
    7. Soo-Haeng Cho & Hoon Jang & Taesik Lee & John Turner, 2014. "Simultaneous Location of Trauma Centers and Helicopters for Emergency Medical Service Planning," Operations Research, INFORMS, vol. 62(4), pages 751-771, August.
    8. repec:pal:jorsoc:v:56:y:2005:i:2:d:10.1057_palgrave.jors.2601898 is not listed on IDEAS
    9. Alexandris, George & Giannikos, Ioannis, 2010. "A new model for maximal coverage exploiting GIS capabilities," European Journal of Operational Research, Elsevier, vol. 202(2), pages 328-338, April.
    10. repec:eee:ejores:v:265:y:2018:i:3:p:1013-1032 is not listed on IDEAS
    11. repec:pal:jorsoc:v:68:y:2017:i:9:d:10.1057_s41274-017-0240-5 is not listed on IDEAS
    12. repec:pal:jorsoc:v:61:y:2010:i:6:d:10.1057_jors.2009.12 is not listed on IDEAS
    13. Shariat-Mohaymany, Afshin & Babaei, Mohsen & Moadi, Saeed & Amiripour, Sayyed Mahdi, 2012. "Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads," European Journal of Operational Research, Elsevier, vol. 221(1), pages 263-272.
    14. Robert Cromley & Dean Hanink, 2008. "Population growth and the development of a central place system," Journal of Geographical Systems, Springer, vol. 10(4), pages 383-405, December.
    15. Daniel Serra & Francisco Silva, 2002. "Locating emergency services with priority rules: The priority queuing covering location problem," Economics Working Papers 642, Department of Economics and Business, Universitat Pompeu Fabra, revised May 2008.
    16. Galvao, Roberto D. & Acosta Espejo, Luis Gonzalo & Boffey, Brian & Yates, Derek, 2006. "Load balancing and capacity constraints in a hierarchical location model," European Journal of Operational Research, Elsevier, vol. 172(2), pages 631-646, July.

    More about this item

    Keywords

    Hierarchical location; congestion; queueing;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R53 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Regional Government Analysis - - - Public Facility Location Analysis; Public Investment and Capital Stock

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