Title: Inverse Fractional Knapsack Problem with Profits and Costs Modification,
Abstract: We address in this paper the problem of modifying both profits and costs of a
fractional knapsack problem optimally such that a prespecified solution becomes
an optimal solution with prespect to new parameters. This problem is called the
inverse fractional knapsack problem. Concerning the $l_1$-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 $l_\infty$-norm.