IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v15y1967i1p83-103.html
   My bibliography  Save this article

Methods for the Solution of the Multidimensional 0/1 Knapsack Problem

Author

Listed:
  • H. Martin Weingartner

    (The University of Rochester, Rochester, New York)

  • David N. Ness

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

In the knapsack problem, given the desirability of each of a number of items, one seeks to find that subset which satisfies a constraint on total weight. The multidimensional variant imposes constraints on additional variables of the items; the 0/1 specification means that an item is either taken or not, i.e., multiples of the same item are not considered, except possibly indirectly. Traditionally the one-dimensional knapsack problem is solved by means of dynamic programming. The multidimensional problem is usually reduced to a one-dimensional one by use of Lagrangian Multipliers that, however, do not generally yield the exact solution to the problem posed. Here some new algorithms are developed that are applied within a dynamic programming framework. Additionally, the methods make integral use of an interactive computer system in which the heuristics of the problem solver are applied and changed as the character of the solution process evolves. The problem arises in the context of capital budgeting, but has obvious applications in a variety of other areas. The methods have been employed for solving numerical problems with as many as 105 items, the parameters having been obtained from industrial applications.

Suggested Citation

  • H. Martin Weingartner & David N. Ness, 1967. "Methods for the Solution of the Multidimensional 0/1 Knapsack Problem," Operations Research, INFORMS, vol. 15(1), pages 83-103, February.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:1:p:83-103
    DOI: 10.1287/opre.15.1.83
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.15.1.83
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.15.1.83?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. Yanhong Feng & Hongmei Wang & Zhaoquan Cai & Mingliang Li & Xi Li, 2023. "Hybrid Learning Moth Search Algorithm for Solving Multidimensional Knapsack Problems," Mathematics, MDPI, vol. 11(8), pages 1-28, April.
    2. Silvano Martello & Paolo Toth, 2003. "An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem," Operations Research, INFORMS, vol. 51(5), pages 826-835, October.
    3. Raquel Sanchis & Raúl Poler, 2019. "Enterprise Resilience Assessment—A Quantitative Approach," Sustainability, MDPI, vol. 11(16), pages 1-13, August.
    4. Nils Boysen & Simon Emde & Malte Fliedner, 2016. "The basic train makeup problem in shunting yards," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 207-233, January.
    5. Setzer, Thomas & Blanc, Sebastian M., 2020. "Empirical orthogonal constraint generation for Multidimensional 0/1 Knapsack Problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 58-70.
    6. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    7. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    8. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.

    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:oropre:v:15:y:1967:i:1:p:83-103. 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.