The general problem is that of locating a central facility in a network so as to minimize the sum of its distances from the sources of flow to it, each distance being appropriately weighted to reflect the associated flow volume and/or cost. In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle. The first algorithm is based on a reduction procedure that may also yield useful simplification of problems involving general networks.

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The problem treated is that of locating n centers (processing facilities) in a network, so as to minimize the total transportation cost associated with their use. On the assumption that all movements occur between a vertex and a center nearest it, Hakimi has shown that only vertex locations for the centers need be considered. The present paper shows that this conclusion remains valid under alternative assumptions more appropriate for some applications.

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