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Optimal Control of Discrete and Continuous Time Maintenance Systems with Variable Service Rates

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  • Wayne Winston

    (Indiana University, Bloomington, Indiana)

Abstract

A maintenance system consists of o finite number of machines and a single-server repair facility that may be operated at several rates. Machines are subject to failure and machines that fail are sent to the repair facility. Under the assumption that costs depend on the repair rate and lost production, we derive conditions that ensure that, for a discrete time maintenance system, the optimal repair rate is a non-increasing function of the number of machines in good condition. By considering a continuous time maintenance system as a limit of a sequence of discrete time maintenance systems, we derive analogous conditions that ensure that the optimal repair rate for the continuous time maintenance system is a non-increasing function of the number of machines in good condition.

Suggested Citation

  • Wayne Winston, 1977. "Optimal Control of Discrete and Continuous Time Maintenance Systems with Variable Service Rates," Operations Research, INFORMS, vol. 25(2), pages 259-268, April.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:2:p:259-268
    DOI: 10.1287/opre.25.2.259
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    Cited by:

    1. Chen, Mingchih & Feldman, Richard M., 1997. "Optimal replacement policies with minimal repair and age-dependent costs," European Journal of Operational Research, Elsevier, vol. 98(1), pages 75-84, April.
    2. Frostig, Esther, 1999. "Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem," European Journal of Operational Research, Elsevier, vol. 116(2), pages 274-280, July.
    3. F. A. Van Der Duyn Schouten & P. Wartenhorst, 1993. "A two‐machine repair model with variable repair rate," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 495-523, June.

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