Optimal control of production rate in a failure prone manufacturing system
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A manufacturing system producing a single commodity is considered. The manufacturing system can be in one of two states: functional and failed. It moves back and forth between these two states as a continuous-time Markov chain, with mean time between failures equals 1/q//1 , and mean time to repair equals 1/q//2 . When functional, the manufacturing system can produce at up to a maximum rate d. When failed, it cannot produce the commodity at all. The commodity is however in constant demand at a rate r (with r greater than d). The problem consists in choosing the production rate P(t), when the system is functional that optimizes production rate.