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A lower bound for weighted completion time variance

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  • R. Nessah

    (UMR CNRS 8179 - 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., 1995. "Minimization of agreeably weighted variance in single machine systems," European Journal of Operational Research, Elsevier, vol. 85(3), pages 576-592, September.
    2. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1996. "Scheduling to minimize the coefficient of variation," International Journal of Production Economics, Elsevier, vol. 44(3), pages 249-253, July.
    3. 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.
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    5. 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.
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    8. 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.
    9. 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.
    10. 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.
    11. Alan G. Merten & Mervin E. Muller, 1972. "Variance Minimization in Single Machine Sequencing Problems," Management Science, INFORMS, vol. 18(9), pages 518-528, May.
    12. A. Federgruen & G. Mosheiov, 1996. "Heuristics for Multimachine Scheduling Problems with Earliness and Tardiness Costs," Management Science, INFORMS, vol. 42(11), pages 1544-1555, November.
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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. 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).
    3. 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.
    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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