Network Median Problems with Continuously Distributed Demand

The network p-median (supply point location) problem has been generalized to the case where demand is continuously distributed. For p = 1 and uniformly distributed demand, and with the objective of minimizing distance, the interior points of an “edge” may be omitted from the search for an optimal supply point when that edge belongs to a “circuit.” Analogous conditions apply when demand is distributed in other than uniform fashion, and/or the objective is to minimize various forms of travel cost. In the case of p ≥ 2, with uniformly distributed demand and with the objective of minimizing distance, p-tuples of supply points, whose components are, respectively, interior points of p “mutually distant” edges, can be omitted from the search for p optimal supply points.