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An asymptotic approximation scheme for the concave cost bin packing problem

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  • Leung, Joseph Y.-T.
  • Li, Chung-Lun

Abstract

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant [epsilon], there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1Â +Â [epsilon].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:582-586
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    References listed on IDEAS

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    1. Crainic, Teodor Gabriel & Perboli, Guido & Pezzuto, Miriam & Tadei, Roberto, 2007. "Computing the asymptotic worst-case of bin packing lower bounds," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1295-1303, December.
    2. 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.
    3. Alves, Claudio & Valerio de Carvalho, J.M., 2007. "Accelerating column generation for variable sized bin-packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1333-1352, December.
    4. 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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    Cited by:

    1. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
    2. Hu, Qian & Zhu, Wenbin & Qin, Hu & Lim, Andrew, 2017. "A branch-and-price algorithm for the two-dimensional vector packing problem with piecewise linear cost function," European Journal of Operational Research, Elsevier, vol. 260(1), pages 70-80.
    3. Haouari, Mohamed & Mhiri, Mariem, 2024. "Lower and upper bounding procedures for the bin packing problem with concave loading cost," European Journal of Operational Research, Elsevier, vol. 312(1), pages 56-69.
    4. Hu, Qian & Wei, Lijun & Lim, Andrew, 2018. "The two-dimensional vector packing problem with general costs," Omega, Elsevier, vol. 74(C), pages 59-69.
    5. Wang, Ting & Hu, Qian & Lim, Andrew, 2022. "An exact algorithm for two-dimensional vector packing problem with volumetric weight and general costs," European Journal of Operational Research, Elsevier, vol. 300(1), pages 20-34.
    6. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).

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