Minisum location with closest Euclidean distances

This paper considers the problem of locating a facility not among demand points, as is usually the case, but among demand regions which could be market areas. The objective is to find the location that minimizes the sum of weighted Euclidean distances to the closest points of the demand regions. It is assumed that internal distribution within the areas is ‘someone else's concern’. A number of properties of the problem are derived and algorithms for solving the problem are suggested.