A variety of practical situations involve supplying a particular commodity by some locations to satisfy the demand at others. If the demands and the costs of producing varying amounts of commodity at each location are known, then the question is how much commodity should be supplied by each location in order to minimize the total system cost. Under some relatively general conditions, there will be an optimal solution with the property that the vector of amounts supplied by the various locations is one of a distinguished set of points. In the case of star networks, this combinatorial nature may be exploited to give a very eﬀicient algorithm for ﬁnding an optimal solution. A numerical example illustrates the results.
Strip, David R. and Engelbrecht-Wiggans, Richard, "The Design of Distributed Service Systems" (1979). Cowles Foundation Discussion Papers. 764.