Optimal dispersion and central places

This paper presents research into optimal dispersion models as applied to central places. The literature regarding location optimization and central places is reviewed and the motivation for employing dispersion models is identified. Models that employ the objective of maximal dispersion in the context of central places are formulated and solved in the context of both single- and multiple-good systems. Two methods for generating multiple-good systems are presented: a multiple-type dispersion model and a K-value constraint set formulation. Sequential solutions to dispersion models demonstrate how a system of central places could develop over time. The solutions to these models generate the patterns of central places expected under the organizing principles of central place theory. The objective of maximal dispersion is posited as both a motivating factor in central place location decisions, and as the optimal outcome of a mature system of central places.