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The Ordered Open-End Bin-Packing Problem

Author

Listed:
  • Jian Yang

    (Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102)

  • Joseph Y.-T. Leung

    (Department of Computer Science, New Jersey Institute of Technology, Newark, New Jersey 07102)

Abstract

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin's level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst-case analysis, pieces of size 1 play distinct roles and render the analysis more difficult with their presence. We give lower bounds for the performance ratio of any online algorithm for cases both with and without the 1-pieces, and in the case without the 1-pieces, identify an online algorithm whose worst-case performance ratio is less than 2 and an offline algorithm with good worst-case performance. In the average-case analysis, assuming that pieces are independently and uniformly drawn from [0, 1], we find the optimal asymptotic average ratio of the number of occupied bins over the number of pieces. We also introduce other online algorithms and conduct simulation study on the average-case performances of all the proposed algorithms.

Suggested Citation

  • Jian Yang & Joseph Y.-T. Leung, 2003. "The Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 51(5), pages 759-770, October.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:5:p:759-770
    DOI: 10.1287/opre.51.5.759.16753
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    References listed on IDEAS

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    1. Csirik, J. & Frenk, J.B.G. & Galambos, G. & Rinnooy Kan, A.H.G., 1991. "Probabilistic analysis of algorithms for dual bin packing problems," Econometric Institute Research Papers 11733, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

    1. Leah Epstein, 2019. "A lower bound for online rectangle packing," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 846-866, October.
    2. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "An asymptotic approximation scheme for the concave cost bin packing problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 582-586, December.
    3. Alberto Ceselli & Giovanni Righini, 2008. "An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem," Operations Research, INFORMS, vol. 56(2), pages 425-436, April.
    4. 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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