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Optimal production control of a failure-prone machine

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  • Eugene Khmelnitsky
  • Ernst Presman
  • Suresh Sethi

Abstract

We consider a problem of optimal production control of a single unreliable machine. The objective is to minimize a discounted convex inventory/backlog cost over an infinite horizon. Using the variational analysis methodology, we develop the necessary conditions of optimality in terms of the co-state dynamics. We show that an inventory-threshold control policy is optimal when the work and repair times are exponentially distributed, and demonstrate how to find the value of the threshold in this case. We consider also a class of distributions concentrated on finite intervals and prove properties of the optimal trajectories, as well as properties of an optimal inventory threshold that is time dependent in this case. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Eugene Khmelnitsky & Ernst Presman & Suresh Sethi, 2011. "Optimal production control of a failure-prone machine," Annals of Operations Research, Springer, vol. 182(1), pages 67-86, January.
    • Handle: RePEc:spr:annopr:v:182:y:2011:i:1:p:67-86:10.1007/s10479-009-0668-3
    DOI: 10.1007/s10479-009-0668-3
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    References listed on IDEAS

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    1. Lou, S. & Sethi, S. P. & Zhang, Q., 1994. "Optimal feedback production planning in a stochastic two-machine flowshop," European Journal of Operational Research, Elsevier, vol. 73(2), pages 331-345, March.
    2. T. Bielecki & P. R. Kumar, 1988. "Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, INFORMS, vol. 36(4), pages 532-541, August.
    3. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
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    2. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2013. "Optimal Production Management When Demand Depends on the Business Cycle," Operations Research, INFORMS, vol. 61(4), pages 1046-1062, August.

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