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Knapsack problems with position-dependent item weights or profits

Author

Listed:
  • Stanisław Gawiejnowicz

    (Adam Mickiewicz University Poznań)

  • Nir Halman

    (Bar-Ilan University)

  • Hans Kellerer

    (Universität Graz)

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.

Suggested Citation

  • Stanisław Gawiejnowicz & Nir Halman & Hans Kellerer, 2023. "Knapsack problems with position-dependent item weights or profits," Annals of Operations Research, Springer, vol. 326(1), pages 137-156, July.
    • Handle: RePEc:spr:annopr:v:326:y:2023:i:1:d:10.1007_s10479-023-05265-x
    DOI: 10.1007/s10479-023-05265-x
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    References listed on IDEAS

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    1. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
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    Cited by:

    1. Vijay Mohan & Peyman Khezr, 2024. "Blockchains, MEV and the knapsack problem: a primer," Papers 2403.19077, arXiv.org.

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