Annals of Operations Research

, Volume 182, Issue 1, pp 67–86 | Cite as

Optimal production control of a failure-prone machine

  • Eugene Khmelnitsky
  • Ernst Presman
  • Suresh P. SethiEmail author


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.


Manufacturing System Optimal Policy Inventory Level Admissible Control Hedging 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Eugene Khmelnitsky
    • 1
  • Ernst Presman
    • 2
  • Suresh P. Sethi
    • 3
    Email author
  1. 1.Dept. of Industrial EngineeringTel-Aviv UniversityTel-AvivIsrael
  2. 2.Central Economics and Mathematics Institute of the Russian Academy of SciencesMoscowRussia
  3. 3.The University of Texas at DallasRichardsonUSA

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