Knapsack problems with position-dependent item weights or profits

Stanisław Gawiejnowicz, Nir Halman, Hans Kellerer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider three new knapsack problems with variable weights or profits of items, where the weight or profit of an item depends on the position of the item in the sequence of items packed in the knapsack. We show how to solve the problems exactly using dynamic programming algorithms with pseudo-polynomial running times and propose fully polynomial-time approximation schemes for their approximate solution.

Original languageEnglish
Pages (from-to)137-156
Number of pages20
JournalAnnals of Operations Research
Issue number1
StatePublished - Jul 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).


  • Approximation schemes
  • Dynamic programming
  • Knapsack problem


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