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

In: Operations Research Proceedings 2014

Author

Listed:
  • Anton V. Eremeev

    (Omsk Branch of Sobolev Institute of Mathematics SB RAS)

  • Julia V. Kovalenko

    (Omsk Law Academy)

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.

Suggested Citation

  • Anton V. Eremeev & Julia V. Kovalenko, 2016. "On Multi-product Lot-Sizing and Scheduling with Multi-machine Technologies," Operations Research Proceedings, in: Marco Lübbecke & Arie Koster & Peter Letmathe & Reinhard Madlener & Britta Peis & Grit Walther (ed.), Operations Research Proceedings 2014, edition 1, pages 301-306, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-28697-6_42
    DOI: 10.1007/978-3-319-28697-6_42
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