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Directional approach to gradual cover: a maximin objective

Author

Listed:
  • Tammy Drezner

    (California State University-Fullerton)

  • Zvi Drezner

    (California State University-Fullerton)

  • Pawel Kalczynski

    (California State University-Fullerton)

Abstract

The objective of original cover location models is to cover demand within a given distance by facilities. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover, and finding the minimum number of facilities required to cover all the demand is referred to as set covering. When the objective is to maximize the minimum cover of demand points, the maximin objective is equivalent to set covering because each demand point is either covered or not. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. Both maximizing total cover and maximizing the minimum cover are useful objectives using the gradual cover measure. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed “directional gradual cover”. The objective is to maximize the minimum cover of demand points. The solution approaches were extensively tested on a case study of covering Orange County, California.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:1:d:10.1007_s10287-019-00353-5
    DOI: 10.1007/s10287-019-00353-5
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    References listed on IDEAS

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    1. 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.
    2. Oded Berman & Zvi Drezner & Dmitry Krass, 2019. "The multiple gradual cover location problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(6), pages 931-940, June.
    3. T Drezner & Z Drezner & S Salhi, 2006. "A multi-objective heuristic approach for the casualty collection points location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 727-734, June.
    4. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    5. Eiselt, H.A. & Marianov, Vladimir, 2009. "Gradual location set covering with service quality," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 121-130, June.
    6. 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.
    7. 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.
    8. Zvi Drezner & George O. Wesolowsky & Tammy Drezner, 2004. "The gradual covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 841-855, September.
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    Cited by:

    1. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2022. "Less is more: discrete starting solutions in the planar p-median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 34-59, April.

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