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Single Machine Scheduling Problem When the Machine Capacity Varies Stochastically

Author

Listed:
  • Tetsuji Hirayama

    (The University of Tsukuba, Ibaraki, Japan)

  • Masaaki Kijima

    (The University of Tsukuba, Tokyo, Japan)

Abstract

We consider single machine scheduling problems when the machine capacity varies stochastically over time. Suppose that R ( t ) ≥ 0 processing requirements can be processed per unit of time at time t . First, we treat the general “machine capacity” R ( t ) and then consider the machine breakdown models where R ( t ) = 0 or 1. Jobs may arrive according to an arbitrary process. We show that simple priority rules are optimal under some assumptions. Specifically, the c μ rule minimizes the expected weighted total number of jobs if the processing requirements are exponentially distributed. The SEPT rule minimizes the expected total number of jobs if the processing requirements of jobs are stochastically ordered. The SERPT rule also minimizes it if the processing requirements form an ICR family.

Suggested Citation

  • Tetsuji Hirayama & Masaaki Kijima, 1992. "Single Machine Scheduling Problem When the Machine Capacity Varies Stochastically," Operations Research, INFORMS, vol. 40(2), pages 376-383, April.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:2:p:376-383
    DOI: 10.1287/opre.40.2.376
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    Cited by:

    1. Yarlin Kuo & Zi‐Ann Chang, 2007. "Integrated production scheduling and preventive maintenance planning for a single machine under a cumulative damage failure process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 602-614, September.
    2. Samuli Aalto & Urtzi Ayesta, 2009. "SRPT applied to bandwidth-sharing networks," Annals of Operations Research, Springer, vol. 170(1), pages 3-19, September.

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