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Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm

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  • Stefanie Kosuch
  • Abdel Lisser

Abstract

In this paper we study and solve two different variants of static knapsack problems with random weights: The stochastic knapsack problem with simple recourse as well as the stochastic knapsack problem with probabilistic constraint. Special interest is given to the corresponding continuous problems and three different problem solving methods are presented. The resolution of the continuous problems allows to provide upper bounds in a branch-and-bound framework in order to solve the original problems. Numerical results on a dataset from the literature as well as a set of randomly generated instances are given. Copyright Springer Science+Business Media, LLC 2010

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  • 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.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:77-93:10.1007/s10479-009-0577-5
    DOI: 10.1007/s10479-009-0577-5
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    References listed on IDEAS

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    6. Martello, Silvano & Toth, Paolo, 1977. "An upper bound for the zero-one knapsack problem and a branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 1(3), pages 169-175, May.
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    Cited by:

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    2. Aslan, Ayse & Ursavas, Evrim & Romeijnders, Ward, 2023. "A Precedence Constrained Knapsack Problem with Uncertain Item Weights for Personalized Learning Systems," Omega, Elsevier, vol. 115(C).
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    4. Shuang Chen & Joseph Geunes, 2013. "Optimal allocation of stock levels and stochastic customer demands to a capacitated resource," Annals of Operations Research, Springer, vol. 203(1), pages 33-54, March.

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