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Replacing continuous demand with discrete demand in a competitive location model

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  • Tammy Drezner
  • Zvi Drezner

Abstract

Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous‐demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models. © 1997 John Wiley & Sons, Inc.

Suggested Citation

  • Tammy Drezner & Zvi Drezner, 1997. "Replacing continuous demand with discrete demand in a competitive location model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 81-95, February.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:1:p:81-95
    DOI: 10.1002/(SICI)1520-6750(199702)44:13.0.CO;2-I
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    References listed on IDEAS

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    1. Z. Drezner & G. O. Weslowsky, 1980. "Optimal location of a facility relative to area demands," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(2), pages 199-206, June.
    2. Zvi Drezner, 1986. "Location of regional facilities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 523-529, August.
    3. G. O. Wesolowsky & R. F. Love, 1971. "Location of facilities with rectangular distances among point and area destinations," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(1), pages 83-90, March.
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    Cited by:

    1. F. Javier Otamendi & David García-Heredia, 2015. "Isochrones as Indicators of the Influence of Traffic in Public Health: A Visual Simulation Application in Ávila, Spain," IJERPH, MDPI, vol. 12(10), pages 1-21, October.
    2. Ran Wei, 2016. "Coverage Location Models," International Regional Science Review, , vol. 39(1), pages 48-76, January.
    3. Matisziw, Timothy C. & Murray, Alan T., 2009. "Siting a facility in continuous space to maximize coverage of a region," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 131-139, June.
    4. Jing Yao & Alan T. Murray, 2014. "Serving regional demand in facility location," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 643-662, August.
    5. Ran Wei & Alan Murray, 2015. "Spatial uncertainty in harvest scheduling," Annals of Operations Research, Springer, vol. 232(1), pages 275-289, September.
    6. Zvi Drezner, 2009. "On the convergence of the generalized Weiszfeld algorithm," Annals of Operations Research, Springer, vol. 167(1), pages 327-336, March.
    7. H Küçükaydın & N Aras & İ K Altınel, 2011. "A discrete competitive facility location model with variable attractiveness," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1726-1741, September.
    8. H. A. Eiselt & Vladimir Marianov, 2020. "Stability of utility functions and apportionment rules in location models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 772-792, October.
    9. Hai Yang & S. C. Wong, 2000. "A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality," Transportation Science, INFORMS, vol. 34(2), pages 216-227, May.
    10. Haase, Knut & Hoppe, Mirko, 2008. "Standortplanung unter Wettbewerb - Teil 1: Grundlagen," Discussion Papers 2/2008, Technische Universität Dresden, "Friedrich List" Faculty of Transport and Traffic Sciences, Institute of Transport and Economics.

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