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More on ordered open end bin packing

Author

Listed:
  • János Balogh

    (University of Szeged)

  • Leah Epstein

    (University of Haifa)

  • Asaf Levin

    (The Technion)

Abstract

We consider the Ordered Open End Bin Packing problem. Items of sizes in (0, 1] are presented one by one, to be assigned to bins in this order. An item can be assigned to any bin for which the current total size is strictly below 1. This means also that the bin can be overloaded by its last packed item. We improve lower and upper bounds on the asymptotic competitive ratio in the online case. Specifically, we design the first algorithm whose asymptotic competitive ratio is strictly below 2, and its value is close to the lower bound. This is in contrast to the best possible absolute competitive ratio, which is equal to 2. We also study the offline problem where the sequence of items is known in advance, while items are still assigned to bins based on their order in the sequence. For this scenario, we design an asymptotic polynomial time approximation scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:6:d:10.1007_s10951-021-00709-3
    DOI: 10.1007/s10951-021-00709-3
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    References listed on IDEAS

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    1. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    2. Leah Epstein, 2009. "On online bin packing with LIB constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 780-786, December.
    3. Leah Epstein, 2019. "A lower bound for online rectangle packing," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 846-866, October.
    4. 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.
    5. Jian Yang & Joseph Y.-T. Leung, 2003. "The Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 51(5), pages 759-770, October.
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