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Lot-size scheduling of a single product on unrelated parallel machines

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Abstract

We study a problem in which at least a given quantity of a single product has to be partitioned into lots, and lots have to be assigned to the unrelated parallel machines for processing so that the maximum machine completion time or the sum of machine completion times is minimized. Machine dependent lower and upper bounds on the lot size are given. The product can be continuously divisible or discrete. We derive optimal polynomial time algorithms for several special cases of the problem. For other cases we provide NP-hardness proofs and demonstrate existence of fully polynomial time approximation schemes.

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Acknowledgements

The research presented in Sect. 2 is supported by the Russian Science Foundation Grant 15-11-10009. Research presented in Sect. 3 is supported by the program of fundamental scientific researches of the SB RAS I.5.1., Project 0314-2016-0019.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia

    Anton V. Eremeev

  2. United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus

    Mikhail Y. Kovalyov

  3. Dostoevsky Omsk State University, Omsk, Russia

    Pavel M. Kuznetsov

Authors
  1. Anton V. Eremeev
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  2. Mikhail Y. Kovalyov
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  3. Pavel M. Kuznetsov
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Correspondence to Anton V. Eremeev.

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Eremeev, A.V., Kovalyov, M.Y. & Kuznetsov, P.M. Lot-size scheduling of a single product on unrelated parallel machines. Optim Lett 14, 557–568 (2020). https://doi.org/10.1007/s11590-018-1307-1

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  • DOI: https://doi.org/10.1007/s11590-018-1307-1

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