Optimal production control of a failure-prone machine
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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.
KeywordsManufacturing System Optimal Policy Inventory Level Admissible Control Hedging
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- Gershwin, S. B. (1994). Manufacturing systems engineering. Englewood Cliffs: Prentice Hall. Google Scholar
- Fleming, W. H., & Rishel, R. W. (1975). Deterministic and stochastic optimal control. Berlin: Springer. Google Scholar
- Kabanov, Yu. M. (1997). On the Pontryagin maximum principle for SDEs with Poisson type disturbances. In Stochastic and control of random processes. Proceedings of Steclov Mathematical Institute seminar. The Liptser festschrift (pp. 173–190). Singapore: World Scientific. Google Scholar
- Maimon, O., Khmelnitsky, E., & Kogan, K. (1998). Optimal flow control in manufacturing systems: production planning and scheduling. Dordrecht: Kluwer Academic. Google Scholar
- Sethi, S. P., & Thompson, G. L. (2000). Optimal control theory: applications to management science (2nd ed.). Dordrecht: Kluwer Academic. Google Scholar
- Yong, J., & Zhou, X. Y. (1999). Stochastic controls: Hamiltonian systems and HJB equations. New York: Springer. Google Scholar