A relation between the knapsack and group knapsack problems Original Research Article

In this paper, we investigate a relation between the equality constrained Knapsack and Group Knapsack problems. This relation concerns the periodicity of optimal solutions of the Knapsack problem. We study the smallest integer b∗ such that for every b⩾b∗, the Knapsack problem of size b is equivalent to the Group Knapsack problem. The results can be regarded as generalizations of some well-known results on the Frobenius problem of Number Theory. Two examples are provided to illustrate our results.