IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v28y1980i6p1412-1423.html
   My bibliography  Save this article

The Linear Multiple Choice Knapsack Problem

Author

Listed:
  • Eitan Zemel

    (Northwestern University, Evanston, Illinois)

Abstract

A fast algorithm is presented for the linear programming relaxation of the Multiple Choice Knapsack Problem. If N is the total number of variables and J and J max denote the total number of multiple choice variables and the cardinality of the largest multiple choice set, respectively, the running time of the algorithm is then bounded by 0( J log J max ) + 0( N ). Under certain conditions it is possible to reduce this bound to 0( N ) steps on the average. Possible further improvements are also discussed.

Suggested Citation

  • Eitan Zemel, 1980. "The Linear Multiple Choice Knapsack Problem," Operations Research, INFORMS, vol. 28(6), pages 1412-1423, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1412-1423
    DOI: 10.1287/opre.28.6.1412
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.28.6.1412
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.28.6.1412?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. Tue R. L. Christensen & Kim Allan Andersen & Andreas Klose, 2013. "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, INFORMS, vol. 47(3), pages 428-438, August.
    2. Bagchi, Ansuman & Bhattacharyya, Nalinaksha & Chakravarti, Nilotpal, 1996. "LP relaxation of the two dimensional knapsack problem with box and GUB constraints," European Journal of Operational Research, Elsevier, vol. 89(3), pages 609-617, March.
    3. Walter, Rico & Schulze, Philipp & Scholl, Armin, 2021. "SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 295(3), pages 857-873.
    4. Vijay Aggarwal & Narsingh Deo & Dilip Sarkar, 1992. "The knapsack problem with disjoint multiple‐choice constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 213-227, March.
    5. Wilbaut, Christophe & Todosijevic, Raca & Hanafi, Saïd & Fréville, Arnaud, 2023. "Heuristic and exact reduction procedures to solve the discounted 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 304(3), pages 901-911.
    6. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.
    7. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    8. Boysen, Nils & Fliedner, Malte, 2008. "A versatile algorithm for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 39-56, January.
    9. Schulze, Philipp & Scholl, Armin & Walter, Rico, 2024. "R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines," European Journal of Operational Research, Elsevier, vol. 312(1), pages 38-55.
    10. Endre Boros & Noam Goldberg & Paul Kantor & Jonathan Word, 2011. "Optimal sequential inspection policies," Annals of Operations Research, Springer, vol. 187(1), pages 89-119, July.

    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:28:y:1980:i:6:p:1412-1423. 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.