Inverse Fractional Knapsack Problem with Profits and Costs Modification

Kien Trung Nguyen; Huynh Duc Quoc

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arXiv · 1704.00145

Inverse Fractional Knapsack Problem with Profits and Costs Modification

Kien Trung Nguyen·Huynh Duc Quoc

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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.

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Kien Trung Nguyen, Huynh Duc Quoc. 2017-04-01. Inverse Fractional Knapsack Problem with Profits and Costs Modification. https://arxiv.org/abs/1704.00145

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