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On the Product Knapsack Problem

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Abstract

Given a set of items, each characterized by a profit and a weight, we study the problem of maximizing the product of the profits of the selected items, while respecting a given capacity. To the best of our knowledge this is the first manuscript that studies this variant of the knapsack problem which we call Product Knapsack Problem (PKP). We show that PKP is weakly NP-hard. We propose and implement a Dynamic Programming algorithm and different Mixed Integer Linear and Nonlinear Programming formulations for the PKP. Finally, we present an extensive computational study on a large set of benchmark instances derived from the literature.

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Acknowledgements

The authors would like to thank two anonymous referees for their helpful comments and Cecilia Bruni for her linguistic assistance.

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Authors and Affiliations

  1. LIX CNRS (UMR7161), École Polytechnique, Palaiseau, France

    Claudia D’Ambrosio

  2. PSL, Université Paris Dauphine, LAMSADE, Paris, France

    Fabio Furini

  3. DEI, University of Bologna, Bologna, Italy

    Michele Monaci

  4. LIPN, Paris 13, Villetaneuse, France

    Emiliano Traversi

Authors
  1. Claudia D’Ambrosio
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  2. Fabio Furini
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  3. Michele Monaci
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  4. Emiliano Traversi
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Correspondence to Fabio Furini.

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D’Ambrosio, C., Furini, F., Monaci, M. et al. On the Product Knapsack Problem. Optim Lett 12, 691–712 (2018). https://doi.org/10.1007/s11590-017-1227-5

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  • DOI: https://doi.org/10.1007/s11590-017-1227-5

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