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Bin covering with a general profit function: approximability results

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  • Attila Benkő
  • György Dósa
  • Zsolt Tuza

Abstract

In the recent paper (Benkő et al. 2010 ) we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a “good and fast” packing or covering. In the present paper we investigate the offline case. For the analysis, a novel view on “offline optimum” is introduced, which appears to be relevant concerning all problems where a final solution is ordering-dependent. We prove that if the item sizes are not allowed to be arbitrarily close to zero, then an optimal offline solution can be found in polynomial time. On the other hand, for unrestricted problem instances, no polynomial-time algorithm can achieve an asymptotic approximation ratio better than 6/7 if $$P\ne NP$$ . Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Attila Benkő & György Dósa & Zsolt Tuza, 2013. "Bin covering with a general profit function: approximability results," 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 805-816, December.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:4:p:805-816
    DOI: 10.1007/s10100-012-0269-0
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    References listed on IDEAS

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    1. Zhong, Weiya & Dosa, Gyorgy & Tan, Zhiyi, 2007. "On the machine scheduling problem with job delivery coordination," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1057-1072, November.
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    Cited by:

    1. Gyula Abraham & Peter Auer & Gyorgy Dosa & Tibor Dulai & Zsolt Tuza & Agnes Werner-Stark, 2023. "The bin covering with delivery problem, extended investigations for the online case," 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. 31(1), pages 21-47, March.

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