A Quadratic Facility Location Problem

This article treats the problem of locating multiple new facilities with respect to multiple existing facilities when there is an interchange of materials between new facilities and between new and existing ones. The “cost” of a solution to the location problem is given as a weighted sum of the square of the Euclidian distances traveled in the interchange of materials. Necessary and sufficient conditions for an optimum location are developed, resulting in the simultaneous solution of a set of linear equations in order to obtain the optimum location. The solution procedure is demonstrated with an example problem.