IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v330y2026i3p733-744.html

The Weber problem with demand uniformly generated in discs

Author

Listed:
  • Kalczynski, Pawel
  • Brimberg, Jack
  • Drezner, Zvi

Abstract

We propose a Disc-Weber (DW) problem in which demand is represented as discs rather than points. We show exact formulations of the new model, study its properties, and propose a very close approximation. The new DW problem is strictly convex, and its analytical continuous derivative exists for the entire domain when all areas (radii) are positive. Therefore, unlike the original Weber problem, it lacks non-continuous derivatives at fixed points. We solve several illustrative examples to global optimality using the exact and approximate formulations. Our analysis and experiments show that the original point-based Weber formulation underestimates the objective function when area demand is present. Furthermore, the optimal solution for point and disc representations of demand can be substantially different. We also show that the DW problem approximation results are virtually identical to its exact formulation.

Suggested Citation

  • Kalczynski, Pawel & Brimberg, Jack & Drezner, Zvi, 2026. "The Weber problem with demand uniformly generated in discs," European Journal of Operational Research, Elsevier, vol. 330(3), pages 733-744.
    • Handle: RePEc:eee:ejores:v:330:y:2026:i:3:p:733-744
    DOI: 10.1016/j.ejor.2025.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725008070
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.10.006?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Zvi Drezner & A. J. Goldman, 1991. "On the Set of Optimal Points to the Weber Problem," Transportation Science, INFORMS, vol. 25(1), pages 3-8, February.
    2. David L. Huff, 1966. "A Programmed Solution for Approximating an Optimum Retail Location," Land Economics, University of Wisconsin Press, vol. 42(3), pages 293-303.
    3. Jack Brimberg & Zvi Drezner, 2025. "Less is more: adjusting convergence of Cooper’s algorithm in the continuous location-allocation problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 76(8), pages 1599-1611, August.
    4. Richard L. Church, 2019. "Understanding the Weber Location Paradigm," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Contributions to Location Analysis, chapter 0, pages 69-88, Springer.
    5. Drezner, Tammy & Drezner, Zvi, 2007. "The gravity p-median model," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1239-1251, June.
    6. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    7. Carling, Kenneth & Håkansson, Johan, 2013. "A compelling argument for the gravity p-median model," European Journal of Operational Research, Elsevier, vol. 226(3), pages 658-660.
    8. Carling, Kenneth & Han, Mengjie & Håkansson, Johan & Rebreyend, Pascal, 2015. "Testing the gravity p-median model empirically," Operations Research Perspectives, Elsevier, vol. 2(C), pages 124-132.
    9. Leon Cooper, 1963. "Location-Allocation Problems," Operations Research, INFORMS, vol. 11(3), pages 331-343, June.
    10. 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.
    11. Zvi Drezner & Taly Dawn Drezner, 2020. "Biologically Inspired Parent Selection in Genetic Algorithms," Annals of Operations Research, Springer, vol. 287(1), pages 161-183, April.
    12. J. Brimberg & S. Salhi, 2019. "A General Framework for Local Search Applied to the Continuous p-Median Problem," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Contributions to Location Analysis, chapter 0, pages 89-108, Springer.
    13. Sean Harris & Ronald Mcgarvey & Andreas Thorsen & Maggie Thorsen, 2024. "Inferred attractiveness gravity-based models for estimating realized access at rural hospitals," Post-Print hal-04836421, HAL.
    14. Mark S. Daskin & Kayse Lee Maass, 2015. "The p-Median Problem," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 21-45, Springer.
    15. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    16. 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.
    17. Pawel Kalczynski & Zvi Drezner, 2025. "Further Analysis of the Weber Problem," Networks and Spatial Economics, Springer, vol. 25(2), pages 513-532, June.
    18. 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.
    19. İ K Altınel & N Aras & K C Özkısacık, 2011. "Variable neighbourhood search heuristics for the probabilistic multi-source Weber problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1813-1826, October.
    20. Jack Brimberg & Andrea Maier & Anita Schöbel, 2021. "When closest is not always the best: The distributed p-median problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(1), pages 200-216, January.
    21. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    22. İ K Altınel & N Aras & K C Özkısacık, 2011. "Variable neighbourhood search heuristics for the probabilistic multi-source Weber problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1813-1826, October.
    23. Jack Brimberg & John M. Hodgson, 2011. "Heuristics for Location Models," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 335-355, Springer.
    24. Carrizosa, E. & Munoz-Marquez, M. & Puerto, J., 1998. "The Weber problem with regional demand," European Journal of Operational Research, Elsevier, vol. 104(2), pages 358-365, January.
    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. Richard L. Church & Zvi Drezner & Pawel Kalczynski, 2023. "Extensions to the planar p-median problem," Annals of Operations Research, Springer, vol. 326(1), pages 115-135, July.
    2. 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.
    3. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    4. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    5. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.
    6. Pawel Kalczynski & Zvi Drezner, 2025. "Further Analysis of the Weber Problem," Networks and Spatial Economics, Springer, vol. 25(2), pages 513-532, June.
    7. Gökhan Altay & M. Hakan Akyüz & Temel Öncan, 2023. "Solving a minisum single facility location problem in three regions with different norms," Annals of Operations Research, Springer, vol. 321(1), pages 1-37, February.
    8. 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.
    9. Jing Yao & Alan T. Murray, 2014. "Serving regional demand in facility location," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 643-662, August.
    10. Carling, Kenneth & Han, Mengjie & Håkansson, Johan & Rebreyend, Pascal, 2015. "Testing the gravity p-median model empirically," Operations Research Perspectives, Elsevier, vol. 2(C), pages 124-132.
    11. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2025. "On the probability that the optimal solution of the Weber location problem is at a demand point," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 102(2), pages 229-244, December.
    12. Pawel Kalczynski & Zvi Drezner, 2021. "The obnoxious facilities planar p-median problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 577-593, June.
    13. Jean-Paul Arnaout & John Khoury, 2022. "Adaptation of WO to the Euclidean location-allocation with unknown number of facilities," Annals of Operations Research, Springer, vol. 315(1), pages 57-72, August.
    14. N Aras & K C Özkısacık & İ K Altınel, 2006. "Solving the uncapacitated multi-facility Weber problem by vector quantization and self-organizing maps," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 82-93, January.
    15. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    16. Zvi Drezner & Taly Dawn Drezner, 2020. "Biologically Inspired Parent Selection in Genetic Algorithms," Annals of Operations Research, Springer, vol. 287(1), pages 161-183, April.
    17. Tammy Drezner & Zvi Drezner & Dawit Zerom, 2023. "The Obnoxious Competitive Facility Location Model," Networks and Spatial Economics, Springer, vol. 23(4), pages 885-903, December.
    18. Tao Zhuolin & Zheng Qingjing & Kong Hui, 2018. "A Modified Gravity p-Median Model for Optimizing Facility Locations," Journal of Systems Science and Information, De Gruyter, vol. 6(5), pages 421-434, October.
    19. 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.
    20. N Aras & M Orbay & I K Altinel, 2008. "Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 64-79, January.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:330:y:2026:i:3:p:733-744. 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.