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The Knapsack Sharing Problem: An Exact Algorithm

Author

Listed:
  • Mhand Hifi

    (Université de Paris 1 Panthéon-Sorbonne
    PRiSM, Université de Versailles St-Quentin-en-Yvelines)

  • Slim Sadfi

    (Université de Paris 1 Panthéon-Sorbonne
    Université de Paris XI)

Abstract

In this paper, we propose an exact algorithm for the knapsack sharing problem. The proposed algorithm seems quite efficient in the sense that it solves quickly some large problem instances. The problem is decomposed into a series of single constraint knapsack problems; and by applying the dynamic programming and another strategy, we solve optimally the original problem. The performance of the exact algorithm is evaluated on a set of medium and large problem instances (a total of 240 problem instances). This algorithm is parallelizable and this is one of its important feature.

Suggested Citation

  • Mhand Hifi & Slim Sadfi, 2002. "The Knapsack Sharing Problem: An Exact Algorithm," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 35-54, March.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:1:d:10.1023_a:1013385216761
    DOI: 10.1023/A:1013385216761
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    References listed on IDEAS

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    1. Christopher S. Tang, 1988. "A Max-Min Allocation Problem: Its Solutions and Applications," Operations Research, INFORMS, vol. 36(2), pages 359-367, April.
    2. Luss, Hanan, 1992. "Minimax resource allocation problems: Optimization and parametric analysis," European Journal of Operational Research, Elsevier, vol. 60(1), pages 76-86, July.
    3. Hifi, M. & Zissimopoulos, V., 1996. "A recursive exact algorithm for weighted two-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 91(3), pages 553-564, June.
    4. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    5. J. Randall Brown, 1979. "The Knapsack Sharing Problem," Operations Research, INFORMS, vol. 27(2), pages 341-355, April.
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    Cited by:

    1. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    2. Dahmani, Isma & Hifi, Mhand & Wu, Lei, 2016. "An exact decomposition algorithm for the generalized knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 252(3), pages 761-774.

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