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Single-machine scheduling with past-sequence-dependent setup times and learning effects: a parametric analysis

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  • V. Mani
  • Pei-Chann Chang
  • Shih-Hsin Chen

Abstract

In this article, we consider the single-machine scheduling problem with past-sequence-dependent (p-s-d) setup times and a learning effect. The setup times are proportional to the length of jobs that are already scheduled; i.e. p-s-d setup times. The learning effect reduces the actual processing time of a job because the workers are involved in doing the same job or activity repeatedly. Hence, the processing time of a job depends on its position in the sequence. In this study, we consider the total absolute difference in completion times (TADC) as the objective function. This problem is denoted as 1/LE, spsd/TADC in Kuo and Yang (2007) (‘Single Machine Scheduling with Past-sequence-dependent Setup Times and Learning Effects’, Information Processing Letters, 102, 22–26). There are two parameters a and b denoting constant learning index and normalising index, respectively. A parametric analysis of b on the 1/LE, spsd/TADC problem for a given value of a is applied in this study. In addition, a computational algorithm is also developed to obtain the number of optimal sequences and the range of b in which each of the sequences is optimal, for a given value of a. We derive two bounds b* for the normalising constant b and a* for the learning index a. We also show that, when a < a* or b > b*, the optimal sequence is obtained by arranging the longest job in the first position and the rest of the jobs in short processing time order.

Suggested Citation

  • V. Mani & Pei-Chann Chang & Shih-Hsin Chen, 2011. "Single-machine scheduling with past-sequence-dependent setup times and learning effects: a parametric analysis," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 2097-2102.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:12:p:2097-2102
    DOI: 10.1080/00207721003718436
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    Cited by:

    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
    2. Baruch Mor & Gur Mosheiov, 2018. "A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection," Annals of Operations Research, Springer, vol. 271(2), pages 1079-1085, December.

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