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