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The binary knapsack problem with qualitative levels

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  • Schäfer, Luca E.
  • Dietz, Tobias
  • Barbati, Maria
  • Figueira, José Rui
  • Greco, Salvatore
  • Ruzika, Stefan

Abstract

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

Suggested Citation

  • Schäfer, Luca E. & Dietz, Tobias & Barbati, Maria & Figueira, José Rui & Greco, Salvatore & Ruzika, Stefan, 2021. "The binary knapsack problem with qualitative levels," European Journal of Operational Research, Elsevier, vol. 289(2), pages 508-514.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:2:p:508-514
    DOI: 10.1016/j.ejor.2020.07.040
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    References listed on IDEAS

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    1. Schäfer, Luca E. & Dietz, Tobias & Fröhlich, Nicolas & Ruzika, Stefan & Figueira, José R., 2020. "Shortest paths with ordinal weights," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1160-1170.
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    Cited by:

    1. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.

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