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Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations

Author

Listed:
  • Gyorgy Dosa

    (University of Pannonia)

  • Zsolt Tuza

    (Hungarian Academy of Sciences
    University of Pannonia)

  • Deshi Ye

    (Zhejiang University)

Abstract

The (online) bin packing problem with LIB constraint is stated as follows: The items arrive one by one, and must be packed into unit capacity bins, but a bigger item cannot be packed into a bin which already contains a smaller item. The number of used bins has to be minimized as usually. We show that the absolute performance bound of algorithm First Fit is not worse than 2+1/6≈2.1666 for the problem, improving the previous best upper bound 2.5. Moreover, if the item sizes do not exceed 1/d, then we improve the previous best result 2+1/d to 2+1/d(d+2), for any d≥2. (Both previously best results are due to Epstein, Nav. Res. Logist. 56(8):780–786, 2009.) Furthermore, we define a problem with the generalized LIB constraint, where some incoming items cannot be packed into the bins of some already packed items. The (in)compatibility of the incoming item with the items already packed becomes known only at the arrival of the actual item, and is given by an undirected graph (and, as usual in case of online graph problems, we can see only that part of the graph what already arrived). We show that 3 is an upper bound for this general problem if some natural transitivity constraint is satisfied.

Suggested Citation

  • Gyorgy Dosa & Zsolt Tuza & Deshi Ye, 2013. "Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 416-436, October.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:3:d:10.1007_s10878-011-9408-0
    DOI: 10.1007/s10878-011-9408-0
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    References listed on IDEAS

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    1. Leah Epstein, 2009. "On online bin packing with LIB constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 780-786, December.
    2. Klaus Jansen, 1999. "An Approximation Scheme for Bin Packing with Conflicts," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 363-377, December.
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    Cited by:

    1. Feifeng Zheng & Li Luo & E. Zhang, 2015. "NF-based algorithms for online bin packing with buffer and bounded item size," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 360-369, August.
    2. Perboli, Guido & Brotcorne, Luce & Bruni, Maria Elena & Rosano, Mariangela, 2021. "A new model for Last-Mile Delivery and Satellite Depots management: The impact of the on-demand economy," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    3. Zhu, Dingju, 2016. "Quasi-human seniority-order algorithm for unequal circles packing," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 506-517.
    4. Minghui Zhang & Xin Han & Yan Lan & Hing-Fung Ting, 2017. "Online bin packing problem with buffer and bounded size revisited," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 530-542, February.
    5. 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.

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