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A lower bound for weighted completion time variance


  • Nessah, Rabia
  • Chu, Chengbin


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.

Suggested Citation

  • Nessah, Rabia & Chu, Chengbin, 2010. "A lower bound for weighted completion time variance," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1221-1226, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1221-1226

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    References listed on IDEAS

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    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Linus Schrage, 1975. "Minimizing the Time-in-System Variance for a Finite Jobset," Management Science, INFORMS, vol. 21(5), pages 540-543, January.
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