Inverse Fractional Knapsack Problem with Profits and Costs Modification

We address in this paper the problem of modifying both profits and costs of a fractional knapsack problem optimally such that a prespectified solution becomes an optimal solution with prespect to new parameters. This problem is called the inverse fractional knapsack problem. Concerning the l1-norm, we first prove that the problem is NP -hard. The problem can be however solved in quadratic time if we only modify profit parameters. Additionally, we develop a quadratic-time algorithm that solves the inverse fractional knapsack problem under l∞-norm.