Time-optimal control of parts-routing in a manufacturing system with failure-prone machines

We consider the time-optimal control of a dynamic system with jump parameters. The motivating example is that of a parts-manufacturing system in which machines fail and are reputed according to known Markov processes. It is desired to obtain a feedback control of parts-routing to machines, which minimizes the expected completion time of a given production target. Using a Dynamic Programming approach, we derive optimality conditions. These are used for solution of a simple example. It is seen that closed form solutions would be very hard to obtain for large problems, so alternative approaches are also discussed.