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 lambda(i) and mu, respectively. Machine i earns at rate r(i) while it is working. The service rate can be controlled, and a cost c(mu) is charged when the service rate is mu. We assume the following compatibility condition: lambda(i) < lambda(j) implies that r(i) greater than or equal to r(j). 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. (C) 1999 Elsevier Science B.V. All rights reserved.