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Online bin packing with (1,1) and (2, $$R$$ R ) bins

Author

Listed:
  • Jing Chen

    (Kyoto University)

  • Xin Han

    (Dalian University of Technology)

  • Kazuo Iwama

    (Kyoto University)

  • Hing-Fung Ting

    (The University of Hong Kong)

Abstract

We study a variant of online bin packing problem, in which there are two types of bins: $$(1,1)$$ ( 1 , 1 ) and $$(2,R)$$ ( 2 , R ) , i.e., unit size bin with cost 1 and size 2 bin with cost $$R > 1$$ R > 1 , the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. When $$R > 3$$ R > 3 , the offline version of this problem is equivalent to the classical bin packing problem. In this paper, we focus on the case $$ R \le 3$$ R ≤ 3 , and propose online algorithms and obtain lower bounds for the problem.

Suggested Citation

  • Jing Chen & Xin Han & Kazuo Iwama & Hing-Fung Ting, 2015. "Online bin packing with (1,1) and (2, $$R$$ R ) bins," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 276-298, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9749-6
    DOI: 10.1007/s10878-014-9749-6
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    References listed on IDEAS

    as
    1. Yong Zhang & Francis Y. L. Chin & Hing-Fung Ting & Xin Han, 2013. "Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 223-236, August.
    2. János Balogh & József Békési & Gábor Galambos & Gerhard Reinelt, 2014. "On-line bin packing with restricted repacking," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 115-131, January.
    3. János Balogh & József Békési, 2013. "Semi-on-line bin packing: a short overview and a new lower bound," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 685-698, December.
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