[Zurück]

G. Feichtinger:
"Dynamics and control of age-structured populations";
Vortrag: Workshop on the Management of Natural Resources and Dynamic Optimization, Girona (eingeladen); 30.05.2008.

The practical motivation for this paper is provided by the recruitment problem faced by many organizations of fixed size: to keep average age young (and thus keep innovation and productivity high) while at the same time keeping levels of recruitment high. A typical example is an academy of sciences. The problem is formalized by an infinite-horizon optimal control model for a first order PDE with a non-local dynamics (a McKendrick type equation). Based on the non-standard necessary optimality condition proved in the paper, the following results are established:
(i) stationarity of the optimal recruitment density;
(ii) strong ergodicity of the optimal solution;
(iii) principle of "bi-polar" recruitment in the case where the productivity of the organization is measured by the average age of the members.
An interesting interpretation of this result is that an academy of awards should focus on awarding relatively young talents for recent outstanding achievements, and, on the other hand, old persons for their all-life-long contributions.
In the second part of the paper some applications in manpower planning (Person-flow models) are given.