This problem deals with the location of facilities that are obnoxious in the sense that nearness of the facility to fixed points, which may represent population centers or other installations, is undesirable. Two model formulatons are given. In the first formulation we minimize the maximum weighted distance in the system subject to constraints which require that the distances between the facilities and fixed points must exceed specified values. In the second formulation, the smallest weighted “facility-to-fixed-point” distance in the system must be maximized, given that every fixed point must be within “reach” of the closest facility. Certain useful duality relationships are established between these problems. A one-dimensional problem is solved using an algorithm that incorporates a version of the set covering problem.