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Sensitivity analysis of the knapsack sharing problem: perturbation of the profit

Author

Listed:
  • Tarik Belgacem

    (Centre d'Economie de la Sorbonne)

  • Mhand Hifi

    (LaRIA et Centre d'Economie de la Sorbonne)

Abstract

In this paper, we study the sensitivity of the optimum of a max-min combinatorial optimization problem, namely the Knapsack Sharing Problem (KSP), to the perturbation of the profit of an arbitrary item. We mainly establish the interval limits of each perturbed item by applying a reduction of the original problem into a series of single knapsack problems. We propose a solution procedure in order to establish these interval limits. The principle of the method is to stabilize the optimal solution in the perturbed problem, following two cases: (i) when the item belongs to an optimal class, and (ii) when the item belongs to a non optimal class. We also consider either the problem admits a unique or multiple optimal classes. Finally, we evaluate the effectiveness of the proposed solution procedure on several problem instances of the literature

Suggested Citation

  • Tarik Belgacem & Mhand Hifi, 2007. "Sensitivity analysis of the knapsack sharing problem: perturbation of the profit," Documents de travail du Centre d'Economie de la Sorbonne b07064, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b07064
    DOI: 10.1111/j.1475-3995.2007.00619.x
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    More about this item

    Keywords

    Sensitivity analysis; knapsack sharing; max-min; combinatorial optimization; optimality;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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