Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem
Consider a production system with m unreliable machines, which are maintained by a single repairman. The time until failure of machine i and its repair time are exponentially distributed random variables with rates ?i and ?, respectively. Machine i earns at rate ri while it is working. The service rate can be controlled, and a cost c(?) is charged when the service rate is ?. We assume the following compatibility condition: ?i<?j implies that ri?rj. We consider both the optimal assignment of the repairman to the failed machines, and the optimal service rate. We demonstrate some monotone properties of the optimal policy.
control production markov process