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Scheduling to Minimize the Number of Late Jobs When Set-Up and Processing Times are Uncertain

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  • Stephen J. Balut

    (U.S. Naval Postgraduate School, Monterey, California)

Abstract

The n job, one-machine scheduling problem is considered where set-up and processing times are random and the objective is to minimize the number of late jobs. In the deterministic case, Moore's algorithm is known to produce an optimal schedule. A chance-constrained formulation of the nondeterministic problem is derived in which a job is processed if the probability that it will be completed prior to its due date is greater than a specified level. A deterministic equivalent problem is achieved to which application of a modification of Moore's algorithm is proven to produce an optimal schedule.

Suggested Citation

  • Stephen J. Balut, 1973. "Scheduling to Minimize the Number of Late Jobs When Set-Up and Processing Times are Uncertain," Management Science, INFORMS, vol. 19(11), pages 1283-1288, July.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:11:p:1283-1288
    DOI: 10.1287/mnsc.19.11.1283
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    Cited by:

    1. Soroush, H. M., 1999. "Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs," European Journal of Operational Research, Elsevier, vol. 113(2), pages 450-468, March.
    2. Baker, Kenneth R., 2014. "Minimizing earliness and tardiness costs in stochastic scheduling," European Journal of Operational Research, Elsevier, vol. 236(2), pages 445-452.
    3. 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.
    4. Sam Ransbotham & Ishwar Murthy & Sabyasachi Mitra & Sridhar Narasimhan, 2011. "Sequential Grid Computing: Models and Computational Experiments," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 174-188, May.
    5. Wu, Wei & Hayashi, Takito & Haruyasu, Kato & Tang, Liang, 2023. "Exact algorithms based on a constrained shortest path model for robust serial-batch and parallel-batch scheduling problems," European Journal of Operational Research, Elsevier, vol. 307(1), pages 82-102.
    6. Jang, Wooseung, 2002. "Dynamic scheduling of stochastic jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 138(3), pages 518-530, May.
    7. 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.
    8. 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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