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Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion

Author

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  • Sergey Kovalev
  • Mikhail Y. Kovalyov
  • Gur Mosheiov
  • Enrique Gerstl

Abstract

The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with n≥8 $ n \ge 8 $ . We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an O(n3) $ O(n^3) $ time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.

Suggested Citation

  • Sergey Kovalev & Mikhail Y. Kovalyov & Gur Mosheiov & Enrique Gerstl, 2019. "Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion," International Journal of Production Research, Taylor & Francis Journals, vol. 57(2), pages 560-566, January.
    • Handle: RePEc:taf:tprsxx:v:57:y:2019:i:2:p:560-566
    DOI: 10.1080/00207543.2018.1468097
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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. Abdennour Azerine & Mourad Boudhar & Djamal Rebaine, 2022. "A two-machine no-wait flow shop problem with two competing agents," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 168-199, January.

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