IDEAS home Printed from
   My bibliography  Save this article

The maximum dispersion problem


  • Fernández, Elena
  • Kalcsics, Jörg
  • Nickel, Stefan


In the maximum dispersion problem, a given set of objects has to be partitioned into a number of groups. Each object has a non-negative weight and each group has a target weight, which may be different for each group. In addition to meeting the target weight of each group, all objects assigned to the same group should be as dispersed as possible with respect to some distance measure between pairs of objects. Potential applications for this problem come from such diverse fields as the problem of creating study groups or the design of waste collection systems. We develop and compare two different (mixed-) integer linear programming formulations for the problem. We also study a specific relaxation that enables us to derive tight bounds that improve the effectiveness of the formulations. Thereby, we obtain an upper bound by finding in an auxiliary graph subsets of given size with minimal diameter. A lower bound is derived based on the relation of the optimal solution of the relaxation to the chromatic number of a series of auxiliary graphs. Finally, we propose an exact solution scheme for the maximum dispersion problem and present extensive computational experiments to assess its efficiency.

Suggested Citation

  • Fernández, Elena & Kalcsics, Jörg & Nickel, Stefan, 2013. "The maximum dispersion problem," Omega, Elsevier, vol. 41(4), pages 721-730.
  • Handle: RePEc:eee:jomega:v:41:y:2013:i:4:p:721-730
    DOI: 10.1016/

    Download full text from publisher

    File URL:
    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

    1. Martí, Rafael & Gallego, Micael & Duarte, Abraham, 2010. "A branch and bound algorithm for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 36-44, January.
    2. Jörg Kalcsics & Stefan Nickel & Michael Schröder, 2005. "Towards a unified territorial design approach — Applications, algorithms and GIS integration," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-56, June.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
    2. Nickel, Stefan & Velten, Sebastian, 2017. "Optimization problems with flexible objectives: A general modeling approach and applications," European Journal of Operational Research, Elsevier, vol. 258(1), pages 79-88.


    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:jomega:v:41:y:2013:i:4:p:721-730. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.