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Bin packing problem with scenarios

Author

Listed:
  • Attila Bódis

    (University of Szeged)

  • János Balogh

    (University of Szeged)

Abstract

Scheduling over scenarios is one of the latest approaches in modelling scheduling problems including uncertainty. However, to the best of our knowledge, scenarios have never been applied to the bin packing problem, so here we introduce the bin packing problem with scenarios. In this model, we have a list of items with sizes between 0 and 1, and each item is assigned to one or more scenarios. In reality, the items of only one scenario will occur, but this chosen scenario is unknown at the time of packing, so the algorithms have to examine all scenarios. This means that the items have to be packed into bins such that for any scenario, the total size of the items in this scenario is at most 1 in each bin. The objective of the standard bin packing problem is to minimize the number of bins. Here, we introduce some extensions of the objective function to the scenario based model, and we present our competitive analysis of some online bin packing algorithms adapted to scenarios.

Suggested Citation

  • Attila Bódis & János Balogh, 2019. "Bin packing problem with scenarios," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 377-395, June.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:2:d:10.1007_s10100-018-0574-3
    DOI: 10.1007/s10100-018-0574-3
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    References listed on IDEAS

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    1. Roman Rischke, 2014. "Two-Stage Robust Combinatorial Optimization with Priced Scenarios," Operations Research Proceedings, in: Dennis Huisman & Ilse Louwerse & Albert P.M. Wagelmans (ed.), Operations Research Proceedings 2013, edition 127, pages 377-382, Springer.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    3. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    4. Esteban Feuerstein & Alberto Marchetti-Spaccamela & Frans Schalekamp & René Sitters & Suzanne Ster & Leen Stougie & Anke Zuylen, 2017. "Minimizing worst-case and average-case makespan over scenarios," Journal of Scheduling, Springer, vol. 20(6), pages 545-555, December.
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    Cited by:

    1. Yulle G. F. Borges & Vinícius L. Lima & Flávio K. Miyazawa & Lehilton L. C. Pedrosa & Thiago A. Queiroz & Rafael C. S. Schouery, 2024. "Algorithms for the bin packing problem with scenarios," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-28, November.
    2. Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.

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