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The single‐machine absolute‐deviation early‐tardy problem with random completion times

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  • Umar M. Al‐Turki
  • John Mittenthal
  • M. Raghavachari

Abstract

We consider sequencing n jobs on a single machine subject to job completion times arising from either machine breakdowns or other causes. The objective is to minimize an expected weighted combination of due dates, completion times, earliness, and tardiness penalties. The determination of optimal distinct due dates or optimal common due dates for a given schedule is investigated. The scheduling problem for a fixed common due date is considered when random completion times arise from machine breakdowns. The optimality of a V‐shaped about (a point) T sequence is established when the number of machine breakdowns follows either a Poisson or a geometric distribution and the duration of a breakdown has an exponential distribution. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • Umar M. Al‐Turki & John Mittenthal & M. Raghavachari, 1996. "The single‐machine absolute‐deviation early‐tardy problem with random completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 573-587, June.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:4:p:573-587
    DOI: 10.1002/(SICI)1520-6750(199606)43:43.0.CO;2-4
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    References listed on IDEAS

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    1. Uttarayan Bagchi & Robert S. Sullivan & Y. L. Chang, 1986. "Minimizing mean absolute deviation of completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(2), pages 227-240, May.
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    3. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
    4. Sarin, Subhash C. & Erel, Erdal & Steiner, George, 1991. "Sequencing jobs on a single machine with a common due date and stochastic processing times," European Journal of Operational Research, Elsevier, vol. 51(2), pages 188-198, March.
    5. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    6. John Mittenthal & M. Raghavachari, 1993. "Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties," Operations Research, INFORMS, vol. 41(4), pages 786-796, August.
    7. Cheng, T. C. E. & Gupta, M. C., 1989. "Survey of scheduling research involving due date determination decisions," European Journal of Operational Research, Elsevier, vol. 38(2), pages 156-166, January.
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