| Abstract: | The Weber problem for a given finite set of existing facilities in the plane is to find the location of a new facility such that the weithted sum of distances to the existing facilities is minimized. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders or mountain ranges are frequently encountered in practice. Structural results as well as algorithms for this non-convex optimization problem depending on the distance function and on the number and location of passages through the barrier are presented. |
