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A Lower Bound for the Weighted Completion Time Variance Problem

Author

Listed:
  • Rabia Nessah

    (IÉSEG School of Management, (LEM-CNRS))

  • Chengbin Chu

    (Laboratoire Génie Industriel, École Centrale Paris)

Abstract

We consider a single machine scheduling problem to minimize the weighted completion time variance. This problem is known to be NP-hard in the strong sense. We propose a lower bound based on splitting of jobs and the Viswanathkumar and Srinivasan procedure and a heuristic. The test on more than 2000 instances shows that this lower bound is very tight.

Suggested Citation

  • Rabia Nessah & Chengbin Chu, 2008. "A Lower Bound for the Weighted Completion Time Variance Problem," Working Papers 2008-ECO-16, IESEG School of Management, revised May 2010.
    • Handle: RePEc:ies:wpaper:e200816
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    File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=904328991_2008-ECO-16_Nessah_Chu.pdf
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    References listed on IDEAS

    as
    1. Cai, X., 1995. "Minimization of agreeably weighted variance in single machine systems," European Journal of Operational Research, Elsevier, vol. 85(3), pages 576-592, September.
    2. Uttarayan Bagchi & Robert S. Sullivan & Yih-Long Chang, 1987. "Minimizing Mean Squared Deviation of Completion Times About a Common Due Date," Management Science, INFORMS, vol. 33(7), pages 894-906, July.
    3. T. Badics & E. Boros, 1998. "Minimization of Half-Products," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 649-660, August.
    4. Cai, X., 1996. "V-shape property for job sequences that minimize the expected completion time variance," European Journal of Operational Research, Elsevier, vol. 91(1), pages 118-123, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Pereira, Jordi & Vásquez, Óscar C., 2017. "The single machine weighted mean squared deviation problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 515-529.
    2. Koulamas, Christos & Kyparisis, George J., 2023. "Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 608-616.
    3. Nasini, Stefano & Nessah, Rabia, 2024. "Time-flexible min completion time variance in a single machine by quadratic programming," European Journal of Operational Research, Elsevier, vol. 312(2), pages 427-444.
    4. Nasini, Stefano & Nessah, Rabia, 2022. "A multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications," International Journal of Production Economics, Elsevier, vol. 251(C).
    5. Nasini, Stefano & Nessah, Rabia, 2021. "An almost exact solution to the min completion time variance in a single machine," European Journal of Operational Research, Elsevier, vol. 294(2), pages 427-441.

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