Optimal location-size of a facility on an plane with interaction effects of distance

A binomial model for the interaction effects of distance is used to obtain the probable demand for a facility located on a plane. Such demand expressed as a function of size, location, population profile and distribution on the plane, is shown (using arguments leading to the central limit theorem) to be normal. Optimization of expected cost criteria is then used to obtain optimal locations under uncertainty. Examples are resolved and the practical implications of the model suggested are drawn.