The Generalized Market Area Problem

This paper considers the production-transportation problem of a firm with a finite number of production (supply) facilities of known location, facing demand distributed over a subset (market region) of K-dimensional Euclidean space. The demand for a single good is described by a demand density function which is continuous almost everywhere on the market region.

Production cost functions exist at each production facility and transport cost functions refer to delivering the good from the production facility to the consumer. The objective is to set production at each production facility and to select a supply policy such that total production and transportation costs are minimized.

The problem is formulated in its entirety and later simplified through suboptimization. Necessary conditions for an optimal solution are derived and economic interpretations are provided.