On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers

This paper presents a new experimental approach to the Weber problem in the presence of convex barriers by using the Varignon frame. The Varignon frame is a mechanical system of strings, weights and a board with holes that has been used to identify an optimal location for the classical Weber problem. We show through analytical results that the same analog can also be used for some of the Weber problems in the presence of barriers. Some examples from the literature are revisited through experiments. Findings are compared to those found in the literature. Practical use of the analog is discussed as it provides rapid solutions, allows for flexibility, and enables one to visualize the problem.

► We provide a new experimental approach to the Weber problem in the presence of convex barriers.
► We discuss optimality conditions of singular points under different barrier shapes.
► Examples from the literature are revisited.