Abstract: We address a variant of the continuous knapsack problem, where capacities regarding costs of items are given into account. We prove that the problem is NP-complete although the classical continuous knapsack problem is solvable in linear time. For the case that there exists exactly one capacity for all items, we solve the corresponding problem in O(n log n) time, where n is the number of items.

Key words: Knapsack problem, Complexity, Capacity, Polynomially solvable