The knapsack problem with scheduled items

We consider a new variant of the knapsack problem, where the contribution of each item on total profit is determined by its position in the knapsack via a specific function. While in the classic version this function could be considered a constant, we study two non-monotone convex functions motived by several real applications. We propose a binary linear programming (BLP) model and a polynomial time algorithm, called Greedy. Computational experiments are carried out, discussing practical and theoretical aspects of the problem resolution.