Knapsack problems with position-dependent item weights or profits

Stanisław Gawiejnowicz (), Nir Halman () and Hans Kellerer ()
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Stanisław Gawiejnowicz: Adam Mickiewicz University Poznań
Nir Halman: Bar-Ilan University
Hans Kellerer: Universität Graz

Annals of Operations Research, 2023, vol. 326, issue 1, No 6, 137-156

Abstract: Abstract 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.

Keywords: Knapsack problem; Approximation schemes; Dynamic programming (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-023-05265-x

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