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An Efficient Algorithm for the 0-1 Knapsack Problem

Author

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  • Robert M. Nauss

    (University of Missouri-St. Louis)

Abstract

In this note we present an efficient algorithm for the 0-1 knapsack problem and announce the availability of a callable FORTRAN subroutine which solves this problem. Computational results show that 50 variable problems can be solved in an average of 4 milliseconds and 200 variable problems in an average of 7 milliseconds on an IBM 360/91.

Suggested Citation

  • Robert M. Nauss, 1976. "An Efficient Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 23(1), pages 27-31, September.
    • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:1:p:27-31
    DOI: 10.1287/mnsc.23.1.27
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    Citations

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    Cited by:

    1. LeBlanc, Larry J. & Shtub, Avraham & Anandalingam, G., 1999. "Formulating and solving production planning problems," European Journal of Operational Research, Elsevier, vol. 112(1), pages 54-80, January.
    2. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    3. Michel Vasquez & Jin-Kao Hao, 2003. "Upper Bounds for the SPOT 5 Daily Photograph Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 7(1), pages 87-103, March.
    4. Chu, Chi-Leung & Leon, V. Jorge, 2008. "Single-vendor multi-buyer inventory coordination under private information," European Journal of Operational Research, Elsevier, vol. 191(2), pages 485-503, December.
    5. Noriyoshi Sukegawa & Yoshitsugu Yamamoto & Liyuan Zhang, 2013. "Lagrangian relaxation and pegging test for the clique partitioning problem," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 363-391, December.
    6. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    7. June S. Park & Byung Ha Lim & Youngho Lee, 1998. "A Lagrangian Dual-Based Branch-and-Bound Algorithm for the Generalized Multi-Assignment Problem," Management Science, INFORMS, vol. 44(12-Part-2), pages 271-282, December.
    8. Zhenbo Wang & Wenxun Xing, 2009. "A successive approximation algorithm for the multiple knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 347-366, May.
    9. R M Nauss, 2004. "The elastic generalized assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1333-1341, December.

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