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A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop

Author

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  • Yoav Ben-Yehoshua
  • Eyal Hariri
  • Gur Mosheiov

Abstract

A popular measure used in service systems is that of total absolute deviation of job completion times (TADC). It is relevant to settings where the objective is to balance the level of service provided to different customers. During the last decade, TADC has been studied in various machine settings, and under various assumptions on the job processing times. In this note, we study TADC on a two-machine no-wait proportionate flow shop, i.e. a flow shop with machine-independent processing times, and with no buffer between the machines. A very surprising and unique result is introduced: a simple index policy (the well-known largest processing time (LPT) first sequence) is shown to be optimal for instances of no more than seven jobs. This property does not hold for larger instances. We show that for instances of eight and nine jobs, there are exactly two schedules which are candidates for optimality. For the 10-job instance, the number of candidates increases. This uncommon behaviour of the optimal solution and, consequently, the complexity of the problem studied here, remain open questions, and are challenging topics for future research.

Suggested Citation

  • Yoav Ben-Yehoshua & Eyal Hariri & Gur Mosheiov, 2015. "A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop," International Journal of Production Research, Taylor & Francis Journals, vol. 53(19), pages 5717-5724, October.
    • Handle: RePEc:taf:tprsxx:v:53:y:2015:i:19:p:5717-5724
    DOI: 10.1080/00207543.2014.991843
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    Cited by:

    1. Allahverdi, Ali, 2016. "A survey of scheduling problems with no-wait in process," European Journal of Operational Research, Elsevier, vol. 255(3), pages 665-686.
    2. 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.
    3. 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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