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

Abstract

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.

Sensitivity analysis of the setup knapsack problem to perturbation of arbitrary profits or weights

“…(), an adaptive algorithm has been described in order to reach the set of all interval limits, especially when perturbing either the profit or weight. Among other problems related to the knapsack family, Belgacem and Hifi (,b,c) tackled the sensitivity analysis of the classical knapsack and the sharing problems in which the perturbation was related either to the profit or weight of an item (and a subset of items) by considering the cases of single and multiple optimal solutions.…”