A Simple Approach to Linear Facility Location

A linear facility is to be located to minimize weighted shortest distances from demand points to the facility. This paper reports on a naive but effective approach. The approach is simple to understand and computer implementation is straightforward. A graphical version may also be used. The approach generalizes to models with more elaborate cost structures than simple proportionality to distance. The analysis addresses uniqueness issues and characterizes the line with respect to other notions of best linear fits.