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Bin‐packing problem with concave costs of bin utilization

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  • Chung‐Lun Li
  • Zhi‐Long Chen

Abstract

We consider a generalized one‐dimensional bin‐packing model where the cost of a bin is a nondecreasing concave function of the utilization of the bin. Four popular heuristics from the literature of the classical bin‐packing problem are studied: First Fit (FF), Best Fit (BF), First Fit Decreasing (FFD), and Best Fit Decreasing (BFD). We analyze their worst‐case performances when they are applied to our model. The absolute worst‐case performance ratio of FF and BF is shown to be exactly 2, and that of FFD and BFD is shown to be exactly 1.5. Computational experiments are also conducted to test the performance of these heuristics. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:4:p:298-308
    DOI: 10.1002/nav.20142
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    1. Scholl, Armin & Klein, Robert & Jürgens, Christian, 1996. "BISON : a fast hybrid procedure for exactly solving the one-dimensional bin packing problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 49135, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Argote, L. & Epple, D., 1990. "Learning Curves In Manufacturing," GSIA Working Papers 89-90-02, Carnegie Mellon University, Tepper School of Business.
    3. J.M. Valério de Carvalho, 1999. "Exact solution of bin‐packing problems using column generation and branch‐and‐bound," Annals of Operations Research, Springer, vol. 86(0), pages 629-659, January.
    4. Shoshana Anily & Julien Bramel & David Simchi-Levi, 1994. "Worst-Case Analysis of Heuristics for the Bin Packing Problem with General Cost Structures," Operations Research, INFORMS, vol. 42(2), pages 287-298, April.
    5. Ronald J. Ebert, 1976. "Aggregate Planning with Learning Curve Productivity," Management Science, INFORMS, vol. 23(2), pages 171-182, October.
    6. A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1982. "Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 30(5), pages 1018-1022, October.
    7. A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1985. "Consecutive Optimizers for a Partitioning Problem with Applications to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 33(4), pages 820-834, August.
    8. S. Anily & A. Federgruen, 1991. "Structured Partitioning Problems," Operations Research, INFORMS, vol. 39(1), pages 130-149, February.
    9. Shmuel Gal & Boris Klots, 1995. "Optimal Partitioning Which Maximizes the Sum of the Weighted Averages," Operations Research, INFORMS, vol. 43(3), pages 500-508, June.
    10. Kang, Jangha & Park, Sungsoo, 2003. "Algorithms for the variable sized bin packing problem," European Journal of Operational Research, Elsevier, vol. 147(2), pages 365-372, June.
    11. 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.
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    4. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).

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