ABSTRACT
Network representation provides a powerful setting to display a variety of situations. In the past, we may have seen network illustrations for problems in transportation, production-distribution, scheduling, and other areas of resource utilization. In this chapter, we study the problems in location analysis that can be represented and analyzed using networks. Typically, nodes in a network represent either demand points, customers, or possible location site, whereas the branches connecting these node symbolize the available paths. New facilities may be located anywhere on the network, either on a branch or on a node. Such problems are referred to as network location models. Nodes, perhaps representing cities or a large concentration of populations, may in fact present more plausible sites for locating the new service facilities. If the facilities can be located only on the nodes, then the problems are called a vertex problem. On the other hand, if a facility can also be located on a branch, that is on a path joining two nodes, then it may be possible to reduce the value of the solution in a minimax (minimize the maximum value) objective. These problems are referred to as absolute p-center problems. In the next section we study the vertex problem, and p-center problems are discussed later in the chapter.
