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A lower bound for weighted completion time variance

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  • R. Nessah

    (LEM - Lille - Economie et Management - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • C. Chu

Abstract

We consider a single machine scheduling problem to minimize the weighted completion time variance. This problem is known to be NP-hard. We propose a heuristic and a lower bound based on job splitting and the Viswanathkumar and Srinivasan procedure. The test on more than 2000 instances shows that this lower bound is very tight and the heuristic yields solutions very close to optimal ones since the gap between the solution given by the heuristic and the lower bound is very small.
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Suggested Citation

  • R. Nessah & C. Chu, 2010. "A lower bound for weighted completion time variance," Post-Print hal-00572982, HAL.
    • Handle: RePEc:hal:journl:hal-00572982
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the Minimization of Completion Time Variance with a Bicriteria Extension," Operations Research, INFORMS, vol. 40(6), pages 1148-1155, December.
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    5. Manna, D. K. & Prasad, V. Rajendra, 1999. "Bounds for the position of the smallest job in completion time variance minimization," European Journal of Operational Research, Elsevier, vol. 114(2), pages 411-419, April.
    6. Mittenthal, John & Raghavachari, M. & Rana, Arif I., 1995. "V- and GG-shaped properties for optimal single machine schedules for a class of non-separable penalty functions," European Journal of Operational Research, Elsevier, vol. 86(2), pages 262-269, October.
    7. 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.
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    10. Cheng, Jinliang & Kubiak, Wieslaw, 2005. "A half-product based approximation scheme for agreeably weighted completion time variance," European Journal of Operational Research, Elsevier, vol. 162(1), pages 45-54, April.
    11. Samuel Eilon & I. G. Chowdhury, 1977. "Minimising Waiting Time Variance in the Single Machine Problem," Management Science, INFORMS, vol. 23(6), pages 567-575, February.
    12. Kubiak, Wieslaw & Cheng, Jinliang & Kovalyov, Mikhail Y., 2002. "Fast fully polynomial approximation schemes for minimizing completion time variance," European Journal of Operational Research, Elsevier, vol. 137(2), pages 303-309, March.
    13. T. Badics & E. Boros, 1998. "Minimization of Half-Products," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 649-660, August.
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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, 2022. "A multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications," International Journal of Production Economics, Elsevier, vol. 251(C).
    4. 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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