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An Enumeration Algorithm for Knapsack Problems

Author

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  • A. Victor Cabot

    (Indiana University, Bloomington, Indiana)

Abstract

Enumeration techniques have been shown to be successful for solving integer linear programming problems. The purpose of this paper is to apply the enumeration philosophy to the classical knapsack problem; it shows that this approach applies quite naturally to this type of integer linear program when combined with the Fourier-Motzkin elimination method for solving linear inequalities. Some computational results are reported.

Suggested Citation

  • A. Victor Cabot, 1970. "An Enumeration Algorithm for Knapsack Problems," Operations Research, INFORMS, vol. 18(2), pages 306-311, April.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:2:p:306-311
    DOI: 10.1287/opre.18.2.306
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    Citations

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    Cited by:

    1. Y-J Seong & Y-G G & M-K Kang & C-W Kang, 2004. "An improved branch and bound algorithm for a strongly correlated unbounded knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(5), pages 547-552, May.
    2. Leonardo Boncinelli & Alessio Muscillo & Paolo Pin, 2022. "Efficiency and Stability in a Process of Teams Formation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1101-1129, December.
    3. Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    4. Hasan Pirkul, 1987. "A heuristic solution procedure for the multiconstraint zero‐one knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 161-172, April.
    5. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    6. Becker, Henrique & Buriol, Luciana S., 2019. "An empirical analysis of exact algorithms for the unbounded knapsack problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 84-99.
    7. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    8. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    9. Chia‐Shin Chung & Ming S. Hung & Walter O. Rom, 1988. "A hard knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 85-98, February.

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