An algorithm for facility location in a districted region

The problem of facility siting in a districted region is discussed and a two-stage algorithm proposed. The first stage consists of solving a particular facility siting problem (for example, a <I>p</I>-median problem, or a maximal location covering problem) in each district for all possible allocations of facilities to a district with respect to the number of facilities allocated in each district. The second stage is the allocation of resources (facilities) among the districts. A greedy algorithm is proposed to solve the resource allocation problem with a criterion of minimizing the sum of weighted distances under convex conditions.