Central Facilities Location

Abstract

The problem of central facilities location consists of designating m of n communities (m < n) as centers in such a way that the average distance or time travelled per person is a minimum.The average distance (or time) is equal to the sum of the products of population and miles (or minutes) travelled divided by the sum of the populations.Define a; = the population of the ith community si = the miles (or minutes) which individuals from the ith community S = the average of the distances (or times) travelled by all in-must travel to a center dividuals.The average distance is i=l Hence, minimizing the sum of population-miles minimizes the average distance.Alfred Weber pioneered Location Theory [I].He considered the location of an industry between two resources and a single market where the criterion was minimization of transport cost.However, it is only in the last decade with the advent of mathematical programming and computer-aided computation that the problem has received real attention from the standpoint of research.Wersan, Quon and Charnes [2] presented one of the earliest of the modern considerations of locational problems.They located solid waste disposal sites to minimize haul costs in a metropolitan en-