The dynamics of professional organizations and bodies is an important branch of demography and Operations Research (manpower planning). The population dynamics in hierarchical groups is determined by the rate of intake, the age distribution at entry into a given rank, the number of exits (deaths or dismissals), the statutory retirement age, and the change in total population size. The rapid increase in life expectancy, especially observed in ages over 60, has brought an increase in the average age of the members of Learned Societies and similar institutions. Given a constant total membership size of an Academy, the demography of a closed population of this kind is simple:
the annual intake is strictly determined by the number of exits, i.e. deaths. The only degree of freedom one has is the age of entry, e.g. at election. To counteract the trend of ageing new members have to be elected at increasingly young ages. However, this would have the drawback of
reducing the rate of membership renewal. The purpose of this paper is to study the optimal trade-off between a young
age structure and a substantial rate of intake. A distributed parameter control model is presented and solved by using (an extension of) Pontryagin's maximum principle. It turns out that the shadow price of an member is under rather general conditions U-shaped. The resulting recruitment policy combines quite young entrants ('scientific excellence') and old elections ('awarding for life long achievement') in an optimal way. Several Academics cope with their 'over-ageing' by a fixed age of exit that free seats. In a sense, our analysis has also an impact to the 'demography of seniors' where economically active individuals are separated from the retired population. |
