IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v13y1967i9p723-735.html
   My bibliography  Save this article

A Branch and Bound Algorithm for the Knapsack Problem

Author

Listed:
  • Peter J. Kolesar

    (Columbia University)

Abstract

A branch and bound algorithm for solution of the "knapsack problem," max \sum v i x i where \sum w i x i \leqq W and x i - 0, 1, is presented which can obtain either optimal or approximate solutions. Some characteristics of the algorithm are discussed and computational experience is presented. Problems involving 50 items from which approximately 25 items were loaded were solved in an average of 0.07 minutes each by a coded version of this algorithm for the IBM 7094 computer.

Suggested Citation

  • Peter J. Kolesar, 1967. "A Branch and Bound Algorithm for the Knapsack Problem," Management Science, INFORMS, vol. 13(9), pages 723-735, May.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:9:p:723-735
    DOI: 10.1287/mnsc.13.9.723
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.13.9.723
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.13.9.723?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
    ---><---

    Citations

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


    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    3. Audrey Cerqueus & Xavier Gandibleux & Anthony Przybylski & Frédéric Saubion, 2017. "On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem," Journal of Heuristics, Springer, vol. 23(5), pages 285-319, October.
    4. Debels, D. & Vanhoucke, M., 2006. "A finite capacity production scheduling procedure for a belgian steel company," Vlerick Leuven Gent Management School Working Paper Series 2006-41, Vlerick Leuven Gent Management School.
    5. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    6. Evgenii Burashnikov, 2024. "Branch-and-Bound and Dynamic Programming Approaches for the Knapsack Problem," SN Operations Research Forum, Springer, vol. 5(4), pages 1-19, December.
    7. Stefanie Kosuch & Abdel Lisser, 2010. "Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm," Annals of Operations Research, Springer, vol. 176(1), pages 77-93, April.

    More about this item

    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:inm:ormnsc:v:13:y:1967:i:9:p:723-735. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.