Weber Problems with a Line Barrier

Abstract

The special case of almost linear barriers in the plane that have only a finite number of passages is frequently encountered in practice. Line barriers with passages may be used to model rivers, border lines, highways, mountain ranges, or, on a smaller scale, conveyer belts in industrial plants. In all these examples trespassing is allowed only through a finite number of passages. Disregarding these types of barriers may lead to bad locational decisions, since long and almost linear barriers have a particularly big impact on travel distances and travel times.