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A Branch and Bound Algorithm for the Knapsack Problem

Author

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  • Peter J. Kolesar

    (Columbia University)

Abstract

A branch and bound algorithm for solution of the "knapsack problem," max \sum v i x i where \sum w i x i \leqq W and x i - 0, 1, is presented which can obtain either optimal or approximate solutions. Some characteristics of the algorithm are discussed and computational experience is presented. Problems involving 50 items from which approximately 25 items were loaded were solved in an average of 0.07 minutes each by a coded version of this algorithm for the IBM 7094 computer.

Suggested Citation

  • Peter J. Kolesar, 1967. "A Branch and Bound Algorithm for the Knapsack Problem," Management Science, INFORMS, vol. 13(9), pages 723-735, May.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:9:p:723-735
    DOI: 10.1287/mnsc.13.9.723
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    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    3. Audrey Cerqueus & Xavier Gandibleux & Anthony Przybylski & Frédéric Saubion, 2017. "On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem," Journal of Heuristics, Springer, vol. 23(5), pages 285-319, October.
    4. Debels, D. & Vanhoucke, M., 2006. "A finite capacity production scheduling procedure for a belgian steel company," Vlerick Leuven Gent Management School Working Paper Series 2006-41, Vlerick Leuven Gent Management School.
    5. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    6. Stefanie Kosuch & Abdel Lisser, 2010. "Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm," Annals of Operations Research, Springer, vol. 176(1), pages 77-93, April.

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