Optimal allocation of a collective use center

In the paper we propose a method to define a place where a collective use center can be constructed. The center is intended to serve residents of some region. It is assumed that the center should be located in such a way that provide the best access for residents of the region. It is supposed that it will be built during $T$ years, and actively exploited during $k$ years. The problem is to choose a site that provides the most convenient access for most people of the region in the respective age groups during the whole time interval $[T,T+k]$. The dynamics of the number of residents of the settlements of the region is defined by a special system of equations. The theory of exact penalties is applied to analysis of the problem, and necessary optimality conditions are obtained. Bibliogr. 11.