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Probabilistic Analysis of Bin Packing Heuristics

Author

Listed:
  • Hoon Liong Ong

    (National University of Singapore, Kent Ridge, Singapore)

  • M. J. Magazine

    (University of Waterloo, Waterloo, Ontario, Canada)

  • T. S. Wee

    (Canadian Pacific, Ltd., Montreal, Quebec, Canada)

Abstract

In this paper we present both a probabilistic and statistical analysis of several bin packing heuristics. With mild conditions on the distribution of problem data, we show that the ratio of the expected number of bins packed for these heuristics to the number of elements converges to some constant. This constant can either be derived analytically or estimated through simulation. We analyze the variance in performance of these heuristics, and we further show that as the number of elements, n , increases, the probability that the number of bins required for these heuristics exceeds any fixed percentage of their expected performance goes to zero.

Suggested Citation

  • Hoon Liong Ong & M. J. Magazine & T. S. Wee, 1984. "Probabilistic Analysis of Bin Packing Heuristics," Operations Research, INFORMS, vol. 32(5), pages 983-998, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:983-998
    DOI: 10.1287/opre.32.5.983
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    Cited by:

    1. Liu, Weimiao & Deng, Tianhu & Li, Jianbin, 2019. "Product packing and stacking under uncertainty: A robust approach," European Journal of Operational Research, Elsevier, vol. 277(3), pages 903-917.
    2. Frenk, J.B.G. & Galambos, G., 1987. "Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem," Econometric Institute Research Papers 11691, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Chung‐Lun Li & Zhi‐Long Chen, 2006. "Bin‐packing problem with concave costs of bin utilization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 298-308, June.

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