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A stochastic gradual cover location problem

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Listed:
  • Tammy Drezner
  • Zvi Drezner
  • Zvi Goldstein

Abstract

Covering models assume that a point is covered if it is within a certain distance from a facility and not covered beyond that distance. In gradual cover models it is assumed that a point is fully covered within a given distance from a facility, then cover gradually declines, and the point is not covered beyond a larger distance. Gradual cover models address the discontinuity in cover which may not be the correct approach in many situations. In the stochastic gradual cover model presented in this article it is assumed that the short and long distances employed in gradual cover models are random variables. This refinement of gradual cover models provides yet a more realistic depiction of actual behavior in many situations. The maximal cover model based on the new concept is analyzed and the single facility location cover problem in the plane is solved. Computational results illustrating the effectiveness of the solution procedures are presented. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Tammy Drezner & Zvi Drezner & Zvi Goldstein, 2010. "A stochastic gradual cover location problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 367-372, June.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:4:p:367-372
    DOI: 10.1002/nav.20410
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    References listed on IDEAS

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    1. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    2. Zvi Drezner & Avram Mehrez & George O. Wesolowsky, 1991. "The Facility Location Problem with Limited Distances," Transportation Science, INFORMS, vol. 25(3), pages 183-187, August.
    3. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    4. White, D. J., 1982. "Dominance and optimal location," European Journal of Operational Research, Elsevier, vol. 9(3), pages 309-308, March.
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    Citations

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    Cited by:

    1. Tammy Drezner & Zvi Drezner, 2019. "Cooperative Cover of Uniform Demand," Networks and Spatial Economics, Springer, vol. 19(3), pages 819-831, September.
    2. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2021. "Directional approach to gradual cover: the continuous case," Computational Management Science, Springer, vol. 18(1), pages 25-47, January.
    3. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2020. "Gradual cover competitive facility location," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 333-354, June.
    4. Bertsimas, Dimitris & Ng, Yeesian, 2019. "Robust and stochastic formulations for ambulance deployment and dispatch," European Journal of Operational Research, Elsevier, vol. 279(2), pages 557-571.
    5. Yıldız, Barış & Olcaytu, Evren & Şen, Ahmet, 2019. "The urban recharging infrastructure design problem with stochastic demands and capacitated charging stations," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 22-44.
    6. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2020. "Directional approach to gradual cover: a maximin objective," Computational Management Science, Springer, vol. 17(1), pages 121-139, January.
    7. Karatas, Mumtaz & Eriskin, Levent, 2021. "The minimal covering location and sizing problem in the presence of gradual cooperative coverage," European Journal of Operational Research, Elsevier, vol. 295(3), pages 838-856.
    8. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2019. "A directional approach to gradual cover," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-93, April.
    9. Shahzad Bhatti & Michael Lim & Ho-Yin Mak, 2015. "Alternative fuel station location model with demand learning," Annals of Operations Research, Springer, vol. 230(1), pages 105-127, July.
    10. Bashiri, Mahdi & Chehrepak, Elaheh & Gomari, Saeed, 2014. "Gradual Covering Location Problem with Stochastic Radius," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 165-186, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.

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