IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v50y1999i1p9-16.html
   My bibliography  Save this article

A note on the complexity of the transportation problem with a permutable demand vector

Author

Listed:
  • Mihály Hujter
  • Bettina Klinz
  • Gerhard J. Woeginger

Abstract

In this note we investigate the computational complexity of the transportation problem with a permutable demand vector, TP-PD for short. In the TP-PD, the goal is to permute the elements of the given integer demand vector b=(b 1 ,…,b n ) in order to minimize the overall transportation costs. Meusel and Burkard [6] recently proved that the TP-PD is strongly NP-hard. In their NP-hardness reduction, the used demand values b j , j=1,…,n, are large integers. In this note we show that the TP-PD remains strongly NP-hard even for the case where b j ∈{0,3} for j=1,…,n. As a positive result, we show that the TP-PD becomes strongly polynomial time solvable if b j ∈{0,1,2} holds for j=1,…,n. This result can be extended to the case where b j ∈{κ,κ+1,κ+2} for an integer κ. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Mihály Hujter & Bettina Klinz & Gerhard J. Woeginger, 1999. "A note on the complexity of the transportation problem with a permutable demand vector," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(1), pages 9-16, August.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:1:p:9-16
    DOI: 10.1007/PL00020923
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/PL00020923
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/PL00020923?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.

    Citations

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


    Cited by:

    1. Mihály Hujter, 2010. "Some good characterization results relating to the Kőnig–Egerváry theorem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(1), pages 37-45, 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:mathme:v:50:y:1999:i:1:p:9-16. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.