Optimal policies for machine repairmen problems

n unreliable machines are maintained by m repairmen. Assuming exponentially distributed up-time and repair time we find the optimal policy to allocate the repairmen to the failed machines in order to stochastically minimize the time until all machines work. Considering only one repairman, we find the optimal policy to maximize the expected total discount time that machines work. We find the optimal policy for the cases where the up-time and repair time are exponentially distributed or identically arbitrarily distributed up-times and increasing failure rate distribution repair times.