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Technical Note—The Multiperiod Knapsack Problem

Author

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  • Bruce H. Faaland

    (University of Washington, Seattle, Washington)

Abstract

In the multiperiod knapsack problem the decision maker faces a horizon of m periods. Associated with each period are a number of types of items, each with a value and weight. Subject to the requirement that the cumulative capacity of the knapsack in each period i cannot be exceeded by items chosen in periods 1, …, i , the decision maker chooses the most valuable knapsack possible. A branch and bound algorithm exploits the special structure of the multiperiod knapsack problem by calculating bounds by the direct solution of linear programs with m constraints in 0( m ) operations. Computational experience is reported on problems ranging in size up to 200 constraints and 1,000 general integer variables.

Suggested Citation

  • Bruce H. Faaland, 1981. "Technical Note—The Multiperiod Knapsack Problem," Operations Research, INFORMS, vol. 29(3), pages 612-616, June.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:3:p:612-616
    DOI: 10.1287/opre.29.3.612
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    Cited by:

    1. Gasparini, Gaia & Brunelli, Matteo & Chiriac, Marius Dan, 2022. "Multi-period portfolio decision analysis: A case study in the infrastructure management sector," Operations Research Perspectives, Elsevier, vol. 9(C).
    2. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "The Fixed-Charge Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 578-596, November.
    3. Faramroze G. Engineer & Kevin C. Furman & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "A Branch-Price-and-Cut Algorithm for Single-Product Maritime Inventory Routing," Operations Research, INFORMS, vol. 60(1), pages 106-122, February.
    4. Kameng Nip & Zhenbo Wang, 2019. "On the approximability of the two-phase knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1155-1179, November.
    5. Brunelli, Matteo & Corrente, Salvatore, 2024. "Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral," Omega, Elsevier, vol. 126(C).
    6. Edward Y H Lin & Chung-Min Wu, 2004. "The multiple-choice multi-period knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 187-197, February.

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