Stochastic control in manpower planning

Our concern is with control problems which arise in connection wi th a discrete time Markov chain model for a graded manpower system. In this model, the members of an organisation are classified into distinct classes. As time passes, they move from one class to another, or to the outside world, in a random way governed by fixed transition probabilities. The emphasis is, then, placed on examining means of reaching and then retaining the structure best adapted to the aims of the organisation, with the assumption that only the recruitment flows are subject to control. Attainability and maintainability have received a great deal of attention in recent years. However, much of the work has been concerned with deterministic analysis, in the sense that average values are used in place of random variables. We adopt, instead, a stochastic approach to the study of these forms of control. We present some of the problems encountered when evaluating probabilities related to the distribution of stock numbers at different steps and we give a detailed numerical comparison of different recruitment strategies. An iterative method is developed to compute exact values of the probabilities of attaining and maintaining a structure in one step. It is designed for the special but very important case of systems in which promotion is only possible to the next highest grade. Its efficiency makes possible the use of exact results in the comparison of the recruitment strategies, which was formerly accomplished by means of simulation techniques only. As to the comparison itself, it emerges that the strategy which, at each step, steers the system as far as possible towards the goal is superior to all deterministic strategies. Also, this strategy is shown to come close to providing the highest level of control that is possible