6.5.1 Basic Model

Network models of an urban or metropolitan area are particularly convenient for the discussion of facility location problems. We shall therefore use such models throughout this section. Specifically, we shall be representing the various transportation arteries as links of a network and their intersections as nodes on it. Thus, travel is restricted to take place solely along the links and nodes of a network. A further assumption will be that demands for services will be generated only at a finite number of points, also designated as a set of nodes on the network.17 The latter assumption may initially appear to limit the potential usefulness of the models. However, one can always place as many nodes as desired along the links of the network to represent demand-generation points, and thus the models can be made as detailed and realistic as called for by the case at hand.

We shall use a "demand weight" hj, to indicate the rate (or "intensity") at which demands for service originate from node j. Otherwise, our notation will not differ from the one used so far.

17 This concept is very similar to the concept of "atoms" in an urban area, which was used in Chapter 5.