Sensitivity analysis of the knapsack sharing problem: Perturbation of the weight of an item

In this paper, we study the sensitivity analysis of the optimum of the knapsack sharing problem (KSP) to the perturbation of the weight of an arbitrary item. We determine the interval limits of the weight of each perturbed item using a heuristic approach which reduces the original problem to a series of single knapsack problems. A perturbed item belongs either to an optimal class or to a non-optimal class. We evaluate the performance of the proposed heuristic on a set of problem instances of the literature. Encouraging results are obtained.