In today's constantly changing demographic and social conditions, the manpower planning of large companies is subject to constant challenges. The targeted control of influencing variables in personnel planning while simultaneously taking into account the occurring causal relationships and existing legal framework is complex and at the same time an essential component of medium- to long-term planning of corporate development.

Especially the public service with its clearly defined promotion guidelines and medium-term defined requirements offers the possibility to mathematically model and optimize processes. For this we develop mathematical models and solution algorithms, which suggest medium-term transitions of the existing personnel structure into future target structures. At the same time, our methods take into account the most diverse requirements for the personnel development to be carried out and map the underlying personnel body on an individual basis in order to take into account the manifold special cases.

The resulting high-dimensional optimization problems are difficult to solve with standard methods of mathematical optimization due to their size. By using selected techniques of combinatorial and integer optimization, our methods are nevertheless able to solve realistic problem sizes and generate proposals for controlling the transition of the personnel structure.

An example of optimized personnel development into a target state:

Optimierte Personalentwicklung in Zielzustand