The problem of locating rectangular plants with minimal cost for the connecting network

We present a method for the hierarchical decomposition of the problem of locating rectangular plants with minimal cost for their connecting network into an optimal ordering problem (the upper level) and two problems of the construction of an optimal flow (the lower level). We obtain the following results: (1) we find necessary and sufficient conditions for the local extremum and give an algorithm for constructing locally optimal solutions; (2) for large-scale problems, we present a solution algorithm based on random search, heuristics, and the decomposition method proposed; (3) for the search for the global extremum, we present an algorithm that is based on the branch and bound method.