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 λi and μ, respectively. Machine i earns at rate ri while it is working. The service rate can be controlled, and a cost c(μ) is charged when the service rate is μ. We assume the following compatibility condition: λi < λj 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.
