The search for optimal organizational hierarchies with homogeneous manager cost functions

The problem of organizational structure formation is considered as a problem of discrete optimization, i.e., the search for an admissible hierarchy minimizing total costs on the maintenance of its managers. The problem is solved for the case of so-called homogeneous manager cost functions. It was proved that each manager of the optimal hierarchy has an approximately equal number of immediate subordinates and divides the department subordinate to him among them in a roughly identical proportion. Is deduced an analytic formula of the lower estimate of the optimal hierarchy cost that has many fields of application and in the majority of cases allows constructing suboptimal organizational hierarchies.