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Tighter bounds for the harmonic bin packing algorithm

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  • Epstein, Leah

Abstract

The harmonic algorithm, defined for online bin packing, partitions items into a fixed number M of classes of similar items, and packs each class independently and greedily in constant time for every packed item. The positive integer M is a parameter of the algorithm. This algorithm had a major role in the development of the online bin packing problem. Tight bounds on its asymptotic approximation ratio were known for M≤7, and for values of M with specific properties. The parametric variant of this algorithm, where item sizes are bounded from above by a certain value, was studied as well. We find tight bounds for many additional cases that were known as open, including the case M=8 for the classic problem.

Suggested Citation

  • Epstein, Leah, 2024. "Tighter bounds for the harmonic bin packing algorithm," European Journal of Operational Research, Elsevier, vol. 316(1), pages 72-84.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:1:p:72-84
    DOI: 10.1016/j.ejor.2024.01.051
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    References listed on IDEAS

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    1. Fleszar, Krzysztof, 2022. "A MILP model and two heuristics for the Bin Packing Problem with Conflicts and Item Fragmentation," European Journal of Operational Research, Elsevier, vol. 303(1), pages 37-53.
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    4. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    5. Békési, József & Dósa, György & Galambos, Gábor, 2022. "A first Fit type algorithm for the coupled task scheduling problem with unit execution time and two exact delays," European Journal of Operational Research, Elsevier, vol. 297(3), pages 844-852.
    6. Ekici, Ali, 2023. "A large neighborhood search algorithm and lower bounds for the variable-Sized bin packing problem with conflicts," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1007-1020.
    7. János Balogh & Leah Epstein & Asaf Levin, 2021. "More on ordered open end bin packing," Journal of Scheduling, Springer, vol. 24(6), pages 589-614, December.
    8. Baldi, Mauro Maria & Manerba, Daniele & Perboli, Guido & Tadei, Roberto, 2019. "A Generalized Bin Packing Problem for parcel delivery in last-mile logistics," European Journal of Operational Research, Elsevier, vol. 274(3), pages 990-999.
    9. Arbib, Claudio & Marinelli, Fabrizio & Pizzuti, Andrea, 2021. "Number of bins and maximum lateness minimization in two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 291(1), pages 101-113.
    10. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    11. Haouari, Mohamed & Mhiri, Mariem, 2024. "Lower and upper bounding procedures for the bin packing problem with concave loading cost," European Journal of Operational Research, Elsevier, vol. 312(1), pages 56-69.
    12. Leah Epstein, 2023. "Parallel solutions for ordinal scheduling with a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-24, August.
    13. 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.
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