Frontier Visualization for Nonconvex Models with Increasing and Decreasing Returns to Scale with the Use of Enumeration Methods

A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation of production units. Kerstens and Vanden Eeckaut were the first who considered the notion and evaluation of RTS for nonconvex Free Disposal Hull (FDH) models. Their methods are based on the comparison of the radial efficiency scores of a production unit in the FDH model and the corresponding non-increasing and non-decreasing RTS reference models. At the same time Cesaroni, Kerstens and Van de Woestyne noted the absence of papers in the world literature devoted to methods of frontier visualization in nonconvex models. In this paper, we developed methods for visualization of production function of nonconvex models and of the corresponding non-increasing and non-decreasing models. Our approach of frontier visualization can be used for decision making based on nonconvex models, it allows us to evaluate RTS for FDH models. Our results are confirmed by computational experiments in applications with real-life data sets.