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High Multiplicity Scheduling with Switching Costs for Few Products

  • Michaël Gabay
  • Alexander Grigoriev
  • Vincent J. C. Kreuzen
  • Tim Oosterwijk
Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

We study several variants of the single machine capacitated lot sizing problem with sequence-dependent setup costs and product-dependent inventory costs. Here we are given one machine and \(n \ge 1\) types of products that need to be scheduled. Each product is associated with a constant demand rate \(d_i\), production rate \(p_i\) and inventory costs per unit \(h_i\). When the machine switches from producing product i to product j, setup costs \(s_{i,j}\) are incurred. The goal is to minimize the total costs subject to the condition that all demands are satisfied and no backlogs are allowed. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding “normal” counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products.

References

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    Brauner, N., Crama, Y., Grigoriev, A., Van De Klundert, J.: A framework for the complexity of high-multiplicity scheduling problems. J. Comb. Optim. 9(3), 313–323 (2005)CrossRefGoogle Scholar
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    Goyal, S.K.: Scheduling a multi-product single machine system. J. Oper. Res. Soc. 24(2), 261–269 (1973)CrossRefGoogle Scholar
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    Madigan, J.G.: Scheduling a multi-product single machine system for an infinite planning period. Manag. Sci. 14(11), 713–719 (1968)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire G-SCOPGrenobleFrance
  2. 2.School of Business and EconomicsMaastricht UniversityMaastrichtNetherlands

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