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Markovian approximation for manufacturing systems of unreliable machines in tandem

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  • Wai Ki Ching

Abstract

This paper studies production planning of manufacturing systems of unreliable machines in tandem. The manufacturing system considered here produces one type of product. The demand is assumed to be a Poisson process and the processing time for one unit of product in each machine is exponentially distributed. A broken machine is subject to a sequence of repairing processes. The up time and the repairing time in each phase are assumed to be exponentially distributed. We study the manufacturing system by considering each machine as an individual system with stochastic supply and demand. The Markov Modulated Poisson Process (MMPP) is applied to model the process of supply. Numerical examples are given to demonstrate the accuracy of the proposed method. We employ (s, S) policy as production control. Fast algorithms are presented to solve the average running costs of the machine system for a given (s, S) policy and hence the approximated optimal (s, S) policy. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 65–78, 2001

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  • Wai Ki Ching, 2001. "Markovian approximation for manufacturing systems of unreliable machines in tandem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 65-78, February.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:1:p:65-78
    DOI: 10.1002/1520-6750(200102)48:13.0.CO;2-5
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    1. Raman K. Nurani & Sridhar Seshadri & J. George Shanthikumar, 1997. "Optimal Control of a Single Stage Production System Subject to Random Process Shifts," Operations Research, INFORMS, vol. 45(5), pages 713-724, October.
    2. Genji Yamazaki & Takeshi Kawashima & Hirotaka Sakasegawa, 1985. "Reversibility of Tandem Blocking Queueing Systems," Management Science, INFORMS, vol. 31(1), pages 78-83, January.
    3. Ching, Wai Ki, 1997. "Markov-modulated Poisson processes for multi-location inventory problems," International Journal of Production Economics, Elsevier, vol. 53(2), pages 217-223, November.
    4. Ki Ching, Wai, 2001. "Machine repairing models for production systems," International Journal of Production Economics, Elsevier, vol. 70(3), pages 257-266, April.
    5. Sethi, Suresh & Yan, Houmin & Zhang, Qing & Zhou, Xun Yu, 1993. "Feedback production planning in a stochastic two-machine flowshop: Asymptotic analysis and computational results," International Journal of Production Economics, Elsevier, vol. 30(1), pages 79-93, July.
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