Volume 5, Number 1 A Compufafional Procedure for on Expanded Sfeiner-Weber Problem of Optimal Location Abbas Mieakhor and Charles D. Bennett* Introduction The purpose of this note is to present a reahstic approximation to the classi cal Steiner-Weber minimization problem for optimally locating a central facility by first constructing a continuous model employing population regions and second using a centroidal approach to aid in the solution of the regional location problem. The problem imder consideration can basically be stated as follows: Consider the problem of optimally locating a central facdity serving a com munity consisting of a large number of persons who wiU be using the facihty. Constructing a Cartesian coordinate system over the feasible community area and employing Euchdean measure of effectiveness in analyzing the problem, the central facility would be located where the sum of the distances from the central facility to each person in the community who will use the facility (weighted by some factors to allow for differences in trip frequency, cost per trip, etc.) was at a minimum. Mathematically, the problem can be stated (1) Min 2 w. [(x-Xj)^ -f (y-yj)^]^''^ x,y i=i where Xj, y^ and Wj are, respectively, the x-coordinate of the location of the resi dence of the i& person, the y-coordinate of the location of the ith person, and the product of the weighting factors for the i& person. Equation (1) could be used as a measure of effectiveness only if aU the ele ments of the sum were known, i.e., the location and weights for each person in the community. This information may not be known and the difficulty in obtain ing it may prove prohibitive. A high degree of reahsm could be maintained if the community comprising the residences concerned were viewed as a continuous area and sectioned into regions, each with some common characteristics, such as trip frequency, travel costs per trip, and population density. The resulting aerial location problem will still attempt to minimize the sum of the Euclidean distances from the centralzyxwvu ♦ Associate Professor of Economics and graduate student respectively, University of Alabama in Hunts-