Let A be a nonempty finite subset of the plane representing the geographical coordinates of a set of demand points (towns, …), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a ∈ A if the facility is located at x ∈ S is proportional to dist(x,a) – the distance from x to a – and that demand of point a is given by ωa, minimizing the total transportation cost TC(ω,x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector ω is not known, and only an estimator can be provided. Moreover the errors in such estimation process may be non-negligible. We propose a new model for this situation: select a threshold value B > 0 representing the highest admissible transportation cost. Define the robustness ρ of a location x as the minimum increase in demand needed to become inadmissible, i.e. ρ(x) = min{‖ω – &omegacirc;‖ : TC(ω, x) > B, ω ≥ 0} and find the x maximizing ρ to get the most robust location.
