A location–allocation problem with concentric circles

We consider a continuous location problem for p concentric circles serving a given set of demand points. Each demand point is serviced by the closest circle. The objective is to minimize the sum of weighted distances between demand points and their closest circle. We analyze and solve the problem when demand is uniformly and continuously distributed in a disk and when a finite number of demand points are located in the plane. Heuristic and exact algorithms are proposed for the solution of the discrete demand problem. A much faster heuristic version of the exact algorithm is also proposed and tested. The exact algorithm solves the largest tested problem with 1000 demand points in about 3.5 hours. The faster heuristic version solves it in about 2 minutes.