Planar weber location problems with line barriers

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.

Keywords:

• Weber Problem
• Non-Convex Optimization
• Distance Function
• Line Barriers

Partially supported by a grant of the Deutsche Forschungsgemeinschaft

Partially supported by a grant of the Deutsche Forschungsgemeinschaft

Notes

Partially supported by a grant of the Deutsche Forschungsgemeinschaft