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

Tarik Belgacem () and Mhand Hifi ()
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Tarik Belgacem: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique
Mhand Hifi: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UPJV - Université de Picardie Jules Verne

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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.

Keywords: Sensitivity analysis; knapsack sharing; max-min; combinatorial optimization; optimality; Analyse de sensibilité; partage équitable; optimisation combinatoire; programmation dynamique. (search for similar items in EconPapers)
Date: 2007-11
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Published in 2007

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00188334

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