IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v25y2017i2d10.1007_s11750-016-0435-y.html
   My bibliography  Save this article

Locating a minisum annulus: a new partial coverage distance model

Author

Listed:
  • Loay Alkhalifa

    (The Royal Military College of Canada)

  • Jack Brimberg

    (The Royal Military College of Canada)

Abstract

The problem is to find the best location in the plane of a minisum annulus with fixed width using a partial coverage distance model. Using the concept of partial coverage distance, those demand points within the area of the annulus are served at no cost, while for ‘uncovered’ demand points there will be additional costs proportional to their distances to the annulus. The objective of the problem is to locate the annulus such that the sum of distances from the uncovered demand points to the annulus (covering area) is minimized. The distance is measured by the Euclidean norm. We discuss the case where the radius of the inner circle of the annulus is variable, and prove that at least two demand points must be on the boundary of any optimal annulus. An algorithm to solve the problem is derived based on this result.

Suggested Citation

  • Loay Alkhalifa & Jack Brimberg, 2017. "Locating a minisum annulus: a new partial coverage distance model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 373-393, July.
    • Handle: RePEc:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0435-y
    DOI: 10.1007/s11750-016-0435-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-016-0435-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11750-016-0435-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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. 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.
    3. Zvi Drezner & Jack Brimberg, 2014. "Fitting concentric circles to measurements," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 119-133, February.
    4. Emanuel Melachrinoudis, 2011. "The Location of Undesirable Facilities," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 207-239, Springer.
    Full references (including those not matched with items on IDEAS)

    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. T Drezner & Z Drezner, 2008. "Lost demand in a competitive environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 362-371, March.
    2. J. Redondo & J. Fernández & I. García & P. Ortigosa, 2009. "A robust and efficient algorithm for planar competitive location problems," Annals of Operations Research, Springer, vol. 167(1), pages 87-105, March.
    3. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    4. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2016. "New local searches for solving the multi-source Weber problem," Annals of Operations Research, Springer, vol. 246(1), pages 181-203, November.
    5. Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.
    6. Daniel Scholz, 2013. "Geometric branch-and-bound methods for constrained global optimization problems," Journal of Global Optimization, Springer, vol. 57(3), pages 771-782, November.
    7. 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.
    8. Drezner, Tammy & Drezner, Zvi & Hulliger, Beat, 2014. "The Quintile Share Ratio in location analysis," European Journal of Operational Research, Elsevier, vol. 238(1), pages 166-174.
    9. Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    10. Tammy Drezner & Zvi Drezner, 2011. "A note on equity across groups in facility location," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 705-711, October.
    11. 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.
    12. Daniel Scholz, 2012. "Theoretical rate of convergence for interval inclusion functions," Journal of Global Optimization, Springer, vol. 53(4), pages 749-767, August.
    13. 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.
    14. Zvi Drezner & Jack Brimberg, 2014. "Fitting concentric circles to measurements," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 119-133, February.
    15. Drezner, Zvi & Drezner, Tammy & Wesolowsky, George O., 2009. "Location with acceleration-deceleration distance," European Journal of Operational Research, Elsevier, vol. 198(1), pages 157-164, October.
    16. Frank Plastria, 2016. "Up- and downgrading the euclidean 1-median problem and knapsack Voronoi diagrams," Annals of Operations Research, Springer, vol. 246(1), pages 227-251, November.
    17. 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.
    18. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    19. Tammy Drezner & Zvi Drezner, 2016. "Sequential location of two facilities: comparing random to optimal location of the first facility," Annals of Operations Research, Springer, vol. 246(1), pages 5-18, November.
    20. Chan He & Yafang Lv & Horst Martini & Senlin Wu, 2023. "A Branch-and-Bound Approach for Estimating Covering Functionals of Convex Bodies," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1036-1055, March.

    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:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-016-0435-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.