Linear programming solutions and distance functions under α-returns to scale

This note generalizes analytical relationships among activity variables of Data envelopment analysis models previously derived in a previous article by the authors of this note. We relax the assumption of constant returns to scale by showing that the key results hold under a weaker assumption of homogeneity. We use the notion of α-returns to scale to extend the analysis to strictly increasing and decreasing returns, covering now the whole range of returns to scale for multi-output homogenous technologies.