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Production scheduling with history‐dependent setup times

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  • Kangbok Lee
  • Lei Lei
  • Michael Pinedo

Abstract

We consider a parallel‐machine scheduling problem with jobs that require setups. The duration of a setup does not depend only on the job just completed but on a number of preceding jobs. These setup times are referred to as history‐dependent. Such a scheduling problem is often encountered in the food processing industry as well as in other process industries. In our model, we consider two types of setup times—a regular setup time and a major setup time that becomes necessary after several “hard‐to‐clean” jobs have been processed on the same machine. We consider multiple objectives, including facility utilization, flexibility, number of major setups, and tardiness. We solve several special cases assuming predetermined job sequences and propose strongly polynomial time algorithms to determine the optimal timing of the major setups for given job sequences. We also extend our analysis to develop pseudopolynomial time algorithms for cases with additional objectives, including the total weighted completion time, the total weighted tardiness, and the weighted number of tardy jobs. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Suggested Citation

  • Kangbok Lee & Lei Lei & Michael Pinedo, 2012. "Production scheduling with history‐dependent setup times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 58-68, February.
    • Handle: RePEc:wly:navres:v:59:y:2012:i:1:p:58-68
    DOI: 10.1002/nav.21472
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    References listed on IDEAS

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    1. Mika, Marek & Waligora, Grzegorz & Weglarz, Jan, 2008. "Tabu search for multi-mode resource-constrained project scheduling with schedule-dependent setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1238-1250, June.
    2. Janiak, Adam & Kovalyov, Mikhail Y. & Portmann, Marie-Claude, 2005. "Single machine group scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 162(1), pages 112-121, April.
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    4. C. Ng & T. Cheng & Adam Janiak & Mikhail Kovalyov, 2005. "Group Scheduling with Controllable Setup and Processing Times: Minimizing Total Weighted Completion Time," Annals of Operations Research, Springer, vol. 133(1), pages 163-174, January.
    5. Drexl, Andreas & Nissen, Rudiger & Patterson, James H. & Salewski, Frank, 2000. "ProGen/[pi]x - An instance generator for resource-constrained project scheduling problems with partially renewable resources and further extensions," European Journal of Operational Research, Elsevier, vol. 125(1), pages 59-72, August.
    6. Koulamas, Christos & Kyparisis, George J., 2008. "Single-machine scheduling problems with past-sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1045-1049, June.
    7. Allahverdi, Ali & Soroush, H.M., 2008. "The significance of reducing setup times/setup costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 978-984, June.
    8. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    9. Kats, Vladimir & Lei, Lei & Levner, Eugene, 2008. "Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1196-1211, June.
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    Cited by:

    1. Davood Golmohammadi & S. Afshin Mansouri, 2015. "Complexity and workload considerations in product mix decisions under the theory of constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 357-369, August.

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