Returns-to-scale properties in DEA models: the fundamental role of interior points

Attempts can be found in the data envelopment analysis (DEA) literature to identify returns to scale at efficient interior points of a face on the basis of returns to scale at points of the corresponding reference sets of the production possibility set. The purpose of this paper is to show that only an interior point of a face can identify returns-to-scale properties of points lying on this face. We consider all possible cases of dispositions of faces from this point of view. Returns-to-scale properties of the corresponding reference units are then established. We also show that to find returns-to-scale at an interior point of a face is a much easier problem than to find all vertices of this face.