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In this paper, we study the sensitivity of the optimum of a max-min combinatorial optimization problem, namely the knapsack sharing problem, 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 method on several problem instances in the literature.

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In this paper, we study the sensitivity of the optimum of the knapsack problem to the perturbation of the profit of a subset of items. We propose a polynomial heuristic in order to establish both lower and upper bound limits of the sensitivity interval. The aim is to stabilize any given optimal solution obtained by applying any exact algorithm. We then evaluate the effectiveness of the proposed solution procedure on an example and a set of randomly generated problem instances.