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The knapsack problem: A survey

Author

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  • Harvey M. Salkin
  • Cornelis A. De Kluyver

Abstract

A unifying survey of the literature related to the knapsack problem; that is, maximize \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {v_i x_{i,} } $\end{document}, subject to \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_j {w_i x_i W} $\end{document} and xi ⩾ 0, integer; where vi, wi and W are known integers, and wi (i = 1, 2, …, N) and W are positive. Various uses, including those in group theory and in other integer programming algorithms, as well as applications from the literature, are discussed. Dynamic programming, branch and bound, search enumeration, heuristic methods, and other solution techniques are presented. Computational experience, and extensions of the knapsack problem, such as to the multi‐dimensional case, are also considered.

Suggested Citation

  • Harvey M. Salkin & Cornelis A. De Kluyver, 1975. "The knapsack problem: A survey," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(1), pages 127-144, March.
    • Handle: RePEc:wly:navlog:v:22:y:1975:i:1:p:127-144
    DOI: 10.1002/nav.3800220110
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    Cited by:

    1. Zhou Xu, 2013. "The knapsack problem with a minimum filling constraint," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 56-63, February.
    2. 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.
    3. 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.
    4. Haihao Lu & Luyang Zhang, 2024. "The Power of Linear Programming in Sponsored Listings Ranking: Evidence from Field Experiments," Papers 2403.14862, arXiv.org.
    5. 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.
    6. Zhou, Qing & Hao, Jin-Kao & Wu, Qinghua, 2022. "A hybrid evolutionary search for the generalized quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 296(3), pages 788-803.

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