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Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties

Author

Listed:
  • John Mittenthal

    (Rensselaer Polytechnic Institute, Troy, New York)

  • M. Raghavachari

    (Rensselaer Polytechnic Institute, Troy, New York)

Abstract

We address the problem of scheduling n jobs on a single machine, which is subject to random breakdowns, to minimize an expected sum of nonregular penalty functions. A simple recourse model is considered when the penalty function is the squared deviation of job completion times from a common due date, and a deterministic equivalent objective function is developed. Characterizations of optimal schedules for this quadratic objective function are established both when the common due date is a decision variable and when it is given and fixed. Most importantly, the V-shaped nature of optimal schedules is investigated for a class of Poisson processes, { N ( t ), t > 0}, describing the number of breakdowns in the interval (0, t ). In addition, relationships to a class of bicriteria models are demonstrated.

Suggested Citation

  • John Mittenthal & M. Raghavachari, 1993. "Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties," Operations Research, INFORMS, vol. 41(4), pages 786-796, August.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:4:p:786-796
    DOI: 10.1287/opre.41.4.786
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    Citations

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    Cited by:

    1. Ramesh Bollapragada & Norman M. Sadeh, 2004. "Proactive release procedures for just‐in‐time job shop environments, subject to machine failures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 1018-1044, October.
    2. Meng, Lingyun & Zhou, Xuesong, 2011. "Robust single-track train dispatching model under a dynamic and stochastic environment: A scenario-based rolling horizon solution approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1080-1102, August.
    3. X. Cai & F. S. Tu, 1996. "Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early‐tardy penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1127-1146, December.
    4. Zhenpeng Li & Congdian Cheng, 2023. "The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
    5. Allahverdi, Ali, 1999. "Stochastically minimizing total flowtime in flowshops with no waiting space," European Journal of Operational Research, Elsevier, vol. 113(1), pages 101-112, February.
    6. Xiaoqiang Cai & Xianyi Wu & Xian Zhou, 2021. "Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns," Annals of Operations Research, Springer, vol. 298(1), pages 43-64, March.
    7. Yin, Yunqiang & Luo, Zunhao & Wang, Dujuan & Cheng, T.C.E., 2023. "Wasserstein distance‐based distributionally robust parallel‐machine scheduling," Omega, Elsevier, vol. 120(C).
    8. Xiaoqiang Cai & Xiaoqian Sun & Xian Zhou, 2004. "Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 800-817, September.
    9. Soroush, H.M., 2007. "Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 181(1), pages 266-287, August.
    10. Mittenthal, John & Raghavachari, M. & Rana, Arif I., 1995. "V- and GG-shaped properties for optimal single machine schedules for a class of non-separable penalty functions," European Journal of Operational Research, Elsevier, vol. 86(2), pages 262-269, October.
    11. 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.
    12. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.
    13. Al-Turki, Umar M. & Mittenthal, John & Raghavachari, M., 1996. "A dominant subset of V-shaped sequences for a class of single machine sequencing problems," European Journal of Operational Research, Elsevier, vol. 88(2), pages 345-347, January.
    14. Ali Allahverdi & John Mittenthal, 1994. "Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(5), pages 677-682, August.
    15. X. Cai & S. Zhou, 1997. "Scheduling stochastic jobs with asymmetric earliness and tardiness penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 531-557, September.

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