IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v73y2011i1p19-27.html
   My bibliography  Save this article

On generalized balanced optimization problems

Author

Listed:
  • Lara Turner
  • Abraham Punnen
  • Yash Aneja
  • Horst Hamacher

Abstract

In the generalized balanced optimization problem (GBaOP) the objective value $${\max_{e \in S}{|c(e)-k\max(S)|}}$$ is minimized over all feasible subsets S of E = {1, . . . , m}. We show that the algorithm proposed in Punnen and Aneja (Oper Res Lett 32:27–30, 2004 ) can be modified to ensure that the resulting solution is indeed optimal. This modification is attained at the expense of increased worst-case complexity, but still maintains polynomial solvability of various special cases that are of general interest. In particular, we show that GBaOP can be solved in polynomial time if an associated bottleneck problem can be solved in polynomial time. For the solution of this bottleneck problem, we propose two alternative approaches. Copyright Springer-Verlag 2011

Suggested Citation

  • Lara Turner & Abraham Punnen & Yash Aneja & Horst Hamacher, 2011. "On generalized balanced optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 19-27, February.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:1:p:19-27
    DOI: 10.1007/s00186-010-0331-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-010-0331-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-010-0331-4?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. Jon Lee, 1992. "On Constrained Bottleneck Extrema," Operations Research, INFORMS, vol. 40(4), pages 813-814, August.
    2. O. Berman & D. Einav & G. Handler, 1990. "The Constrained Bottleneck Problem in Networks," Operations Research, INFORMS, vol. 38(1), pages 178-181, February.
    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. Elena Fernández & Justo Puerto & Antonio Rodríguez-Chía, 2013. "On discrete optimization with ordering," Annals of Operations Research, Springer, vol. 207(1), pages 83-96, August.

    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. Arora, Shalini & Puri, M. C., 1998. "A variant of time minimizing assignment problem," European Journal of Operational Research, Elsevier, vol. 110(2), pages 314-325, October.
    2. de Lima Pinto, Leizer & Bornstein, Cláudio Thomás & Maculan, Nelson, 2009. "The tricriterion shortest path problem with at least two bottleneck objective functions," European Journal of Operational Research, Elsevier, vol. 198(2), pages 387-391, October.
    3. Y. Wang & H. Yan & C. Sriskandarajah, 1996. "The weighted sum of split and diameter clustering," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 231-248, September.
    4. Patrick J. Andersen & Charl J. Ras, 2020. "Degree bounded bottleneck spanning trees in three dimensions," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 457-491, February.

    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:mathme:v:73:y:2011:i:1:p:19-27. 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.