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The gradual covering problem

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  • Zvi Drezner
  • George O. Wesolowsky
  • Tammy Drezner

Abstract

In this paper we investigate the gradual covering problem. Within a certain distance from the facility the demand point is fully covered, and beyond another specified distance the demand point is not covered. Between these two given distances the coverage is linear in the distance from the facility. This formulation can be converted to the Weber problem by imposing a special structure on its cost function. The cost is zero (negligible) up to a certain minimum distance, and it is a constant beyond a certain maximum distance. Between these two extreme distances the cost is linear in the distance. The problem is analyzed and a branch and bound procedure is proposed for its solution. Computational results are presented. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:6:p:841-855
    DOI: 10.1002/nav.20030
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    References listed on IDEAS

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    1. 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.
    2. Tammy Drezner & Zvi Drezner, 2004. "Finding the optimal solution to the Huff based competitive location model," Computational Management Science, Springer, vol. 1(2), pages 193-208, July.
    3. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    4. 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.
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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. Fadda, Edoardo & Manerba, Daniele & Tadei, Roberto, 2024. "How to locate services optimizing redundancy: A comparative analysis of K-Covering Facility Location models," Socio-Economic Planning Sciences, Elsevier, vol. 94(C).
    3. 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.
    4. 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.
    5. Tanaka, Ken-ichi & Furuta, Takehiro & Toriumi, Shigeki, 2019. "Railway flow interception location model: Model development and case study of Tokyo metropolitan railway network," Operations Research Perspectives, Elsevier, vol. 6(C).
    6. Karatas, Mumtaz & Eriskin, Levent, 2023. "Linear and piecewise linear formulations for a hierarchical facility location and sizing problem," Omega, Elsevier, vol. 118(C).
    7. T Drezner & Z Drezner & P Kalczynski, 2011. "A cover-based competitive location model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 100-113, January.
    8. Narjes Sabeghi & Hamed Reza Tareghian, 2020. "Using the generalized maximum covering location model to control a project’s progress," Computational Management Science, Springer, vol. 17(1), pages 1-21, January.
    9. Ibarra-Rojas, O.J. & Ozuna, L. & López-Piñón, D., 2020. "The maximal covering location problem with accessibility indicators," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    10. Tony H. Grubesic & Timothy C. Matisziw & Alan T. Murray, 2011. "Market Coverage and Service Quality in Digital Subscriber Lines Infrastructure Planning," International Regional Science Review, , vol. 34(3), pages 368-390, July.
    11. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    12. Taymaz, S. & Iyigun, C. & Bayindir, Z.P. & Dellaert, N.P., 2020. "A healthcare facility location problem for a multi-disease, multi-service environment under risk aversion," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    13. 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.
    14. Wang, Wei & Wu, Shining & Wang, Shuaian & Zhen, Lu & Qu, Xiaobo, 2021. "Emergency facility location problems in logistics: Status and perspectives," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    15. Eda Yücel & F. Sibel Salman & Burçin Bozkaya & Cemre Gökalp, 2020. "A data-driven optimization framework for routing mobile medical facilities," Annals of Operations Research, Springer, vol. 291(1), pages 1077-1102, August.
    16. Dianne Villicaña-Cervantes & Omar J. Ibarra-Rojas, 2024. "Accessible location of mobile labs for COVID-19 testing," Health Care Management Science, Springer, vol. 27(1), pages 1-19, March.
    17. Mehdi Ansari & Juan S. Borrero & Leonardo Lozano, 2023. "Robust Minimum-Cost Flow Problems Under Multiple Ripple Effect Disruptions," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 83-103, January.
    18. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    19. 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.
    20. 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.
    21. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.

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