摘要 : 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 co... 展开 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 ω_a, 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 ω-circumflex 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 - ω-circumflex||: TC(ω,x) > B,ω ≥ 0} and find the x maximizing ρ to get the most robust location. 收起