Deterministic Production/Location Models on a Line

Abstract

In this chapter the most elementary production/location models are presented. The basic features of these models are that the firm is assumed to use two inputs to produce one output, and the set of feasible plant locations is either assumed to be a line segment, or more generally, can be shown to be a line segment for the given assumptions regarding the locations of the input sources and output market. There are several reasons for beginning with this apparently simplistic case. First, most production/location research has dealt with this case. Second, it is a natural introduction to the more general, but complicated, network and planar problems. Many of the results that hold for more general models can be proved, illustrated, and explained more easily for the linear case, and then extended to the more complicated cases using technical mathematical properties. Third, the simpler structure of the location on a line problem makes it easier to study the interrelationships of the production and location decisions. Some theorems that can be obtained for two inputs and location on a line cannot be obtained for general networks or the plane. In particular, much of the parametric analysis cannot be demonstrated as strongly and precisely for the more general models.