Optimal Allocation of Machines to Distinguishable Repairmen in Order to Maximize Some Reward Functions

We consider N unreliable machines that are maintained by M repairmen. The time until failure of machine i , and its repair by repairman j , are exponentially distributed random variable with parameters λ i , and μ j , respectively. All failure times and repair times are independent. Machine i earns c i , per unit time, while it is working. We wish to maximize the expected total discounted reward. It is shown that when the following conditions are satisfied — c 1 ≥ … ≥ c N and c 1 /λ 1 ≥…≥ c N /λ N , the policy that assigns the fastest repairman to the machine with the lowest index is optimal. Moreover, it is shown that when the second condition is replaced by λ≤ … ≤λ N , then this policy maximizes, stochastically, the number of the most reliable machines at every time t .