Optimal repairman assignment in two symmetric maintenance models

Two maintenance models (a warm and a cold stand-by model) consisting of m parallel groups of identical components are considered. Components have exponentially distributed times to failure. There is a single repairman who can be assigned to one of the failed components. It is shown for both models that the repairman should be assigned to an item of the group with the smallest number of functioning components. The optimality results are obtained by adapting an iterative method which proved to be successful in the study of routing models.