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Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Author

Listed:
  • Alan J. Soper

    (University of Greenwich)

  • Vitaly A. Strusevich

    (University of Greenwich)

Abstract

We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

Suggested Citation

  • Alan J. Soper & Vitaly A. Strusevich, 2020. "Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects," Journal of Scheduling, Springer, vol. 23(6), pages 665-680, December.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:6:d:10.1007_s10951-019-00628-4
    DOI: 10.1007/s10951-019-00628-4
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    References listed on IDEAS

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    1. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
    2. W-H Kuo & D-L Yang, 2008. "Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 416-420, March.
    3. Kuo, Wen-Hung & Yang, Dar-Li, 2006. "Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1184-1190, October.
    4. Gur Mosheiov, 1991. "V-Shaped Policies for Scheduling Deteriorating Jobs," Operations Research, INFORMS, vol. 39(6), pages 979-991, December.
    5. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
    6. Mosheiov, Gur, 2001. "Scheduling problems with a learning effect," European Journal of Operational Research, Elsevier, vol. 132(3), pages 687-693, August.
    7. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Simple matching vs linear assignment in scheduling models with positional effects: A critical review," European Journal of Operational Research, Elsevier, vol. 222(3), pages 393-407.
    8. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Time-Changing Effects and Rate-Modifying Activities," International Series in Operations Research and Management Science, Springer, number 978-3-319-39574-6, September.
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