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A Bayesian Sequential Single Machine Scheduling Problem to Minimize the Expected Weighted Sum of Flowtimes of Jobs with Exponential Processing Times

Author

Listed:
  • Toshio Hamada

    (Himeji College of Hyogo, Himeji, Japan)

  • Kevin D. Glazebrook

    (University of Newcastle Upon Tyne, Newcastle Upon Tyne, United Kingdom)

Abstract

In this paper, we consider a scheduling problem in which m classes, J 1 , J 2 , …, J m , of independent jobs with ready time 0 are to be processed by a single machine. The number of jobs of class J i is n i and the processing times of these n i jobs are independent and identically distributed exponentially distributed with unknown parameter θ i , which has a conjugate gamma prior. The objective is to minimize the expected (weighted) sum of flowtimes of all the jobs, where R i is the weight for a job of class J i . The problem is formulated as a dynamic program and optimal strategies are derived.

Suggested Citation

  • Toshio Hamada & Kevin D. Glazebrook, 1993. "A Bayesian Sequential Single Machine Scheduling Problem to Minimize the Expected Weighted Sum of Flowtimes of Jobs with Exponential Processing Times," Operations Research, INFORMS, vol. 41(5), pages 924-934, October.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:5:p:924-934
    DOI: 10.1287/opre.41.5.924
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    Citations

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    Cited by:

    1. Li, Dong & Glazebrook, Kevin D., 2011. "A Bayesian approach to the triage problem with imperfect classification," European Journal of Operational Research, Elsevier, vol. 215(1), pages 169-180, November.
    2. Marbán Sebastián & Rutten Cyriel & Vredeveld Tjark, 2010. "Asymptotic optimality of SEPT in Bayesian Scheduling," Research Memorandum 051, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Marban, S. & Rutten, C. & Vredeveld, T., 2010. "Asymptotic optimality of SEPT in Bayesian scheduling," Research Memorandum 050, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Marban, S. & Rutten, C. & Vredeveld, T., 2010. "Tight performance in Bayesian scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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