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Single‐ and multiple‐processor models for minimizing completion time variance

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  • Nicholas G. Hall

Abstract

This article concerns the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs. Optimality conditions for the problem are developed, based on its equivalence to an easy scheduling problem. It seems that this problem inherently has a huge number of optimal solutions and an algorithm is developed to find many of them. The model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem. In this more general case also, the algorithm permits great flexibility in finding an optimal schedule.

Suggested Citation

  • Nicholas G. Hall, 1986. "Single‐ and multiple‐processor models for minimizing completion time variance," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(1), pages 49-54, February.
    • Handle: RePEc:wly:navlog:v:33:y:1986:i:1:p:49-54
    DOI: 10.1002/nav.3800330105
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    Citations

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    Cited by:

    1. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    2. J. Steve Davis & John J. Kanet, 1993. "Single‐machine scheduling with early and tardy completion costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 85-101, February.
    3. Gur Mosheiov, 2000. "Minimizing mean absolute deviation of job completion times from the mean completion time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 657-668, December.
    4. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    5. Kerem Bülbül & Safia Kedad-Sidhoum & Halil Şen, 2019. "Single-machine common due date total earliness/tardiness scheduling with machine unavailability," Journal of Scheduling, Springer, vol. 22(5), pages 543-565, October.
    6. Wlodzimierz Szwarc, 1989. "Single‐machine scheduling to minimize absolute deviation of completion times from a common due date," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 663-673, October.
    7. 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.
    8. Bernard Dickman & Yonah Wilamowsky & Sheldon Epstein, 2001. "Multiple common due dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 293-298, June.
    9. Enrique Gerstl & Gur Mosheiov, 2014. "Single machine just‐in‐time scheduling problems with two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 1-16, February.
    10. Hamilton Emmons, 1987. "Scheduling to a common due date on parallel uniform processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 803-810, December.

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