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An exact decomposition algorithm for the generalized knapsack sharing problem

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  • Dahmani, Isma
  • Hifi, Mhand
  • Wu, Lei

Abstract

This paper presents an exact algorithm for solving the knapsack sharing problem with common items. In literature, this problem is also denominated the Generalized Knapsack Sharing Problem (GKSP). The GKSP is NP-hard because it lays on the 0–1 knapsack problem and the knapsack sharing problem. The proposed exact method is based on a rigorous decomposition technique which leads to an intense simplification of the solution procedure for the GKSP. Furthermore, in order to accelerate the procedure for finding the optimum solution, an upper bound and several reduction strategies are considered. Computational results on two sets of benchmark instances from literature show that the proposed method outperforms the other approaches in most instances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:761-774
    DOI: 10.1016/j.ejor.2016.02.009
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    References listed on IDEAS

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    1. Raidl, Günther R., 2015. "Decomposition based hybrid metaheuristics," European Journal of Operational Research, Elsevier, vol. 244(1), pages 66-76.
    2. 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.
    3. Yamada, Takeo & Futakawa, Mayumi & Kataoka, Seiji, 1998. "Some exact algorithms for the knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 177-183, April.
    4. Rooderkerk, Robert P. & van Heerde, Harald J., 2016. "Robust optimization of the 0–1 knapsack problem: Balancing risk and return in assortment optimization," European Journal of Operational Research, Elsevier, vol. 250(3), pages 842-854.
    5. Silvano Martello & Paolo Toth, 1984. "A Mixture of Dynamic Programming and Branch-and-Bound for the Subset-Sum Problem," Management Science, INFORMS, vol. 30(6), pages 765-771, June.
    6. Mhand Hifi & Slim Sadfi, 2002. "The Knapsack Sharing Problem: An Exact Algorithm," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 35-54, March.
    7. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
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    Cited by:

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