IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i2p516-525.html
   My bibliography  Save this article

The variable radius covering problem

Author

Listed:
  • Berman, Oded
  • Drezner, Zvi
  • Krass, Dmitry
  • Wesolowsky, George O.

Abstract

In this paper we propose a covering problem where the covering radius of a facility is controlled by the decision-maker; the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance (i.e., it costs more to establish a facility with a greater covering radius). The problem is to cover all demand points at a minimum cost by finding optimal number, locations and coverage radii for the facilities. Both, the planar and discrete versions of the model are considered. Heuristic approaches are suggested for solving large problems in the plane. These methods were tested on a set of planar problems. Mathematical programming formulations are proposed for the discrete problem, and a solution approach is suggested and tested.

Suggested Citation

  • Berman, Oded & Drezner, Zvi & Krass, Dmitry & Wesolowsky, George O., 2009. "The variable radius covering problem," European Journal of Operational Research, Elsevier, vol. 196(2), pages 516-525, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:516-525
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00338-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mark S. Daskin, 1983. "A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution," Transportation Science, INFORMS, vol. 17(1), pages 48-70, February.
    2. Berman, Oded, 1994. "The p maximal cover - p partial center problem on networks," European Journal of Operational Research, Elsevier, vol. 72(2), pages 432-442, January.
    3. Rajan Batta & June M. Dolan & Nirup N. Krishnamurthy, 1989. "The Maximal Expected Covering Location Problem: Revisited," Transportation Science, INFORMS, vol. 23(4), pages 277-287, November.
    4. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    5. Mark S. Daskin & Edmund H. Stern, 1981. "A Hierarchical Objective Set Covering Model for Emergency Medical Service Vehicle Deployment," Transportation Science, INFORMS, vol. 15(2), pages 137-152, May.
    6. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Watson-Gandy, C. D. T., 1982. "Heuristic procedures for the m-partial cover problem on a plane," European Journal of Operational Research, Elsevier, vol. 11(2), pages 149-157, October.
    8. 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.
    9. Plastria, Frank & Carrizosa, Emilio, 1999. "Undesirable facility location with minimal covering objectives," European Journal of Operational Research, Elsevier, vol. 119(1), pages 158-180, November.
    10. Drezner, Zvi, 1986. "The p-cover problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 312-313, August.
    11. Fernandez, Jose & Pelegri'n, Blas & Plastria, Frank & Toth, Boglarka, 2007. "Solving a Huff-like competitive location and design model for profit maximization in the plane," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1274-1287, June.
    12. Emilio Carrizosa & Frank Plastria, 1998. "Polynomial algorithms for parametric minquantile and maxcovering planar location problems with locational constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 179-194, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Karatas, Mumtaz & Eriskin, Levent, 2023. "Linear and piecewise linear formulations for a hierarchical facility location and sizing problem," Omega, Elsevier, vol. 118(C).
    2. Murali, Pavankumar & Ordóñez, Fernando & Dessouky, Maged M., 2012. "Facility location under demand uncertainty: Response to a large-scale bio-terror attack," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 78-87.
    3. John Gunnar Carlsson & Raghuveer Devulapalli, 2013. "Dividing a Territory Among Several Facilities," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 730-742, November.
    4. Karatas, Mumtaz, 2017. "A multi-objective facility location problem in the presence of variable gradual coverage performance and cooperative cover," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1040-1051.
    5. Blanco, Víctor & Gázquez, Ricardo & Saldanha-da-Gama, Francisco, 2023. "Multi-type maximal covering location problems: Hybridizing discrete and continuous problems," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1040-1054.
    6. Ran Wei & Alan Murray & Rajan Batta, 2014. "A bounding-based solution approach for the continuous arc covering problem," Journal of Geographical Systems, Springer, vol. 16(2), pages 161-182, April.
    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. Vicencio-Medina, Salvador J. & Rios-Solis, Yasmin A. & Ibarra-Rojas, Omar Jorge & Cid-Garcia, Nestor M. & Rios-Solis, Leonardo, 2023. "The maximal covering location problem with accessibility indicators and mobile units," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    2. Karatas, Mumtaz, 2017. "A multi-objective facility location problem in the presence of variable gradual coverage performance and cooperative cover," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1040-1051.
    3. 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).
    4. 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.
    5. Boffey, Brian & Galvao, Roberto & Espejo, Luis, 2007. "A review of congestion models in the location of facilities with immobile servers," European Journal of Operational Research, Elsevier, vol. 178(3), pages 643-662, May.
    6. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    7. Su, Qiang & Luo, Qinyi & Huang, Samuel H., 2015. "Cost-effective analyses for emergency medical services deployment: A case study in Shanghai," International Journal of Production Economics, Elsevier, vol. 163(C), pages 112-123.
    8. Shariat-Mohaymany, Afshin & Babaei, Mohsen & Moadi, Saeed & Amiripour, Sayyed Mahdi, 2012. "Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads," European Journal of Operational Research, Elsevier, vol. 221(1), pages 263-272.
    9. Bélanger, V. & Lanzarone, E. & Nicoletta, V. & Ruiz, A. & Soriano, P., 2020. "A recursive simulation-optimization framework for the ambulance location and dispatching problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 713-725.
    10. Sunarin Chanta & Maria Mayorga & Laura McLay, 2014. "Improving emergency service in rural areas: a bi-objective covering location model for EMS systems," Annals of Operations Research, Springer, vol. 221(1), pages 133-159, October.
    11. Jenkins, Phillip R. & Lunday, Brian J. & Robbins, Matthew J., 2020. "Robust, multi-objective optimization for the military medical evacuation location-allocation problem," Omega, Elsevier, vol. 97(C).
    12. Brotcorne, Luce & Laporte, Gilbert & Semet, Frederic, 2003. "Ambulance location and relocation models," European Journal of Operational Research, Elsevier, vol. 147(3), pages 451-463, June.
    13. Sardar Ansari & Laura Albert McLay & Maria E. Mayorga, 2017. "A Maximum Expected Covering Problem for District Design," Transportation Science, INFORMS, vol. 51(1), pages 376-390, February.
    14. 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).
    15. 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.
    16. M Gendreau & G Laporte & F Semet, 2006. "The maximal expected coverage relocation problem for emergency vehicles," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 22-28, January.
    17. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    18. KC, Kiran & Corcoran, Jonathan & Chhetri, Prem, 2020. "Measuring the spatial accessibility to fire stations using enhanced floating catchment method," Socio-Economic Planning Sciences, Elsevier, vol. 69(C).
    19. Sun Hoon Kim & Young Hoon Lee, 2016. "Iterative optimization algorithm with parameter estimation for the ambulance location problem," Health Care Management Science, Springer, vol. 19(4), pages 362-382, December.
    20. Beraldi, P. & Bruni, M.E., 2009. "A probabilistic model applied to emergency service vehicle location," European Journal of Operational Research, Elsevier, vol. 196(1), pages 323-331, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:516-525. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.