Construction of convex three-dimensional sections in DEA models with selective convexity

The Data Envelopment Analysis (DEA) approach emerged at the end of the last century. This approach is a generalization of simple indicators of production units behavior to a multidimensional case. This approach leads in reality to the solution of large family of optimization problems. The Free Disposal Hull (FDH) models were proposed almost at the same time. However, production possibility set (PPS) of FDH models is non-convex. One can stress that the DEA and FDH technologies are two extreme cases for application and investigation of production unit’s behavior. However, some new models have appeared recently for investigation of complex production units. The models with selective convexity embrace a wide class of DEA models where such variables as percentages, ratios, averages, etc. are considered in order to expand the range of their applications. Any mathematical discipline is trying to use visualization for the interpretation and explanation of its important notions. This is especially important for DEA models, since this scientific instrument was intended also for managers and other practitioners, not only for scientists. However, there exist a small number of papers devoted to the visualization methods in the DEA area. In this paper, methods for constructions of convex three-dimensional sections in DEA models with selective convexity are considered. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.