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Directional approach to gradual cover: the continuous case

Author

Listed:
  • Tammy Drezner

    (California State University-Fullerton)

  • Zvi Drezner

    (California State University-Fullerton)

  • Pawel Kalczynski

    (California State University-Fullerton)

Abstract

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. 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”. Contrary to all gradual cover models, the joint cover depends on the facilities’ directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:18:y:2021:i:1:d:10.1007_s10287-020-00378-1
    DOI: 10.1007/s10287-020-00378-1
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    References listed on IDEAS

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    1. P. Hansen & J. Perreur & J.-F. Thisse, 1980. "Technical Note—Location Theory, Dominance, and Convexity: Some Further Results," Operations Research, INFORMS, vol. 28(5), pages 1241-1250, October.
    2. Zakir Hussain Ahmed, 2016. "Experimental analysis of crossover and mutation operators on the quadratic assignment problem," Annals of Operations Research, Springer, vol. 247(2), pages 833-851, December.
    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. Leon Cooper, 1963. "Location-Allocation Problems," Operations Research, INFORMS, vol. 11(3), pages 331-343, June.
    5. Oded Berman & David Simchi-Levi, 1990. "Technical Note—Conditional Location Problems on Networks," Transportation Science, INFORMS, vol. 24(1), pages 77-78, February.
    6. 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.
    7. 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.
    8. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    9. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    10. 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.
    11. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    12. 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.
    13. 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.
    14. 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.
    15. Osman Alp & Erhan Erkut & Zvi Drezner, 2003. "An Efficient Genetic Algorithm for the p-Median Problem," Annals of Operations Research, Springer, vol. 122(1), pages 21-42, September.
    16. Włodzimierz Ogryczak & Mariusz Zawadzki, 2002. "Conditional Median: A Parametric Solution Concept for Location Problems," Annals of Operations Research, Springer, vol. 110(1), pages 167-181, February.
    17. Zvi Drezner, 2003. "A New Genetic Algorithm for the Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 320-330, August.
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