Optimal production control of a failure-prone machine

Eugene Khmelnitsky, Ernst Presman and Suresh Sethi

Annals of Operations Research, 2011, vol. 182, issue 1, 67-86

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

Date: 2011
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DOI: 10.1007/s10479-009-0668-3

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