The binary knapsack problem with qualitative levels

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

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number0
Pages (from-to)508-514
Number of pages7
JournalEuropean Journal of Operational Research
Issue number2
Early online date25 Jul 2020
Publication statusPublished - 1 Mar 2021


  • Computing science
  • Knapsack problem
  • Non-dominance
  • Qualitative levels
  • Dynamic programming


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