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An almost exact solution to the min completion time variance in a single machine

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  • Nasini, Stefano
  • Nessah, Rabia

Abstract

We consider a single machine scheduling problem to minimize the completion time variance of n jobs. This problem is known to be NP-hard and our contribution is to establish a novel bounding condition for a characterization of an optimal sequence. Specifically, we prove a necessary and sufficient condition (which can be verified in O(nlogn)) for the characterization of five scheduling positions in the optimal sequence. Applying this characterization, we propose a new approach to derive the highest lower bound for the minimal completion time variance, outperforming the existing bounds for this problem. The numerical tests indicate that the novel lower bound is, on average, less than 0.01% far away from the optimal solution, outperforming all the existing lower bounds on the minimum completion time variance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:294:y:2021:i:2:p:427-441
    DOI: 10.1016/j.ejor.2021.01.038
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    References listed on IDEAS

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    2. 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.
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    9. 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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    Cited by:

    1. 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.
    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).

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