In this paper, we characterize a subset of the production possibility set consisting of production points whose radial projection points lie on the same supporting hyperplane of the production possibility set (PPS). To this end, we consider the CCR and BCC models and establish some theoretical results by utilizing linear programming-based techniques. Determining such a subset of the PPS provides a means to perform sensitivity analysis of inefficient units. This allows us to categorize DMUs into classes with the same returns to scale. Both these issues are addressed as applications.