The relationship between returns-to-scale properties of interior points and vertex points in DEA models

A study was conducted to investigate the relationship between returns-to-scale properties of interior points and vertex points in DEA models. The study considered some examples that revealed that the returns to scale of the Banker, Charnes, Cooper (BCC)-projected activity was unable to be found by observing only the returns-to-scale characteristics of production units in its respective reference set. Some theorems were proved that established that the returns to scale of points on the facet determined by efficient units was found by observing the returns-to-scale characteristic of some interior point of this facet. The scale elasticity was found to be a measure of the increase in output relative to a proportional increase in all inputs, evaluated as the marginal change at a point in input-output space.