Problem of Maximum Flow in Networks

Abstract

The present chapter deals with the analogy that exists between the problem of maximum flow in networks [15] and equilibrium problems for physical systems described in Secs.7.2, 7.4 and 7.5 of the present chapter. We shall discuss models which differ among themselves only in the mechanical properties that cause constraints. In the first model these constraints are perfectly rigid and in others they are elastic. The problem under discussion constitutes a particular class of linear programming problems, and provides another example illustrating the significance and importance of analogies. The models are so simple that anybody with a moderate knowledge of mechanics can understand them. These models lead on the one hand to simple physical interpretations of the theoretical results, and, on the other hand, to the methods for obtaining numerical solutions that follow from the theory of equilibrium.