The paper examines a longitudinal model of a manpower system in which the demands for effective manpower are determined by the state of a finite Markov chain, and there are delays in training an adequate supply of effective manpower. An operational method of calculating optimal appointment policies is presented. This calculation can in turn be used to find the equilibrium operating rules for the system. The model is a useful device for measuring the impact of alternate assumptions about continuation rates, manpower utilization policies, the demands, and the transition probabilities in the demand process. (Author)