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On Multi-product Lot-Sizing and Scheduling with Multi-machine Technologies

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Operations Research Proceedings 2014

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

We consider a problem of multi-product lot-sizing and scheduling where each product can be produced by a family of alternative multi-machine technologies. Multi-machine technologies require one or more machine at the same time. A sequence dependent setup time is needed between different technologies. The criterion is to minimize the makespan. Preemptive and non-preemptive versions of the problem are studied. We formulate mixed integer linear programming models based on a continuous time representation for both versions of the problem. Using these models, the polynomially solvable cases of the problem are found. It is proved that the problem without setup times is strongly NP-hard if there is only one product, and each technology occupies at most three machines. Besides that, problem cannot be approximated within a practically relevant factor of the optimum in polynomial time, if P \(\ne \) NP.

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Acknowledgments

This research have been supported by the RFBR Grants 12-01-00122 and 13-01-00862.

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Authors and Affiliations

  1. Omsk Branch of Sobolev Institute of Mathematics SB RAS, 13 Pevtsov Str., 644099, Omsk, Russia

    Anton V. Eremeev

  2. Omsk Law Academy, 12 Korolenko Str., 644010, Omsk, Russia

    Julia V. Kovalenko

Authors
  1. Anton V. Eremeev
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  2. Julia V. Kovalenko
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Corresponding authors

Correspondence to Anton V. Eremeev or Julia V. Kovalenko .

Editor information

Editors and Affiliations

  1. Operations Research, RWTH Aachen University, Aachen, Germany

    Marco Lübbecke

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    Arie Koster

  3. RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Peter Letmathe

  4. E.ON Energy Research Center, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Reinhard Madlener

  5. Management Science, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Britta Peis

  6. Chair of Operations Management, RWTH Aachen University, Aachen, Germany

    Grit Walther

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Eremeev, A.V., Kovalenko, J.V. (2016). On Multi-product Lot-Sizing and Scheduling with Multi-machine Technologies. In: Lübbecke, M., Koster, A., Letmathe, P., Madlener, R., Peis, B., Walther, G. (eds) Operations Research Proceedings 2014. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-28697-6_42

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