The Complexity of the 0/1 Multi-knapsack Problem

In this paper complexity of the 0/1 multi-knapsack problem is discussed. First we prove that the corresponding decision problem is NP-complete in the strong sense. For any fixed numberk of knapsacks, the problem is only NP-complete in the ordinary sense, but not NP-complete in the strong sense. Then, we prove that the 0/1 multi-knapsack optimization problem is NP-equivalent by using Turing reduction.