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A General Algorithm for One-Dimensional Knapsack Problems

Author

Listed:
  • Giorgio P. Ingargiola

    (Temple University, Philadelphia, Pennsylvania)

  • James F. Korsh

    (Temple University, Philadelphia, Pennsylvania)

Abstract

This paper presents a reduction algorithm and a branch-search algorithm that, in sequence, allow the solution of sizeable problems of the form: maximize ∑ i =1 N c i x i , subject to ∑ i =1 N l i x i ≦ s and 0 ≦ x i ≦ b i and integer, 1 ≦ i ≦ N . The reduction algorithm is proportional to N in space and proportional to N ∑ i =1 N b i in time. The branch-search algorithm's space requirement is linear in N . Computational experience with these algorithms is presented.

Suggested Citation

  • Giorgio P. Ingargiola & James F. Korsh, 1977. "A General Algorithm for One-Dimensional Knapsack Problems," Operations Research, INFORMS, vol. 25(5), pages 752-759, October.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:5:p:752-759
    DOI: 10.1287/opre.25.5.752
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    Cited by:

    1. Rong, Aiying & Figueira, José Rui, 2013. "A reduction dynamic programming algorithm for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 231(2), pages 299-313.
    2. David Pisinger, 2000. "A Minimal Algorithm for the Bounded Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 75-82, February.

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