Radial Data Envelopment Analysis models without inputs or without outputs

In this paper we consider radial DEA models without inputs (or without outputs), and radial DEA models with a single constant input (or with a single constant output). We demonstrate that (i) a Charnes et al. model without inputs (or without outputs) is meaningless; (ii) a Charnes et al. model with a single constant input (or with a single constant output) coincides with the corresponding Baker et al. model; (iii) a Baker et al. model with a single constant input (or a single constant output) collapses to a Baker et al. model without inputs (or without outputs); (iv) all Baker et al. models, including those without inputs (or without outputs), can be condensed to models having one less variable (the radial efficiency score) and one less constraint (the convexity constraint).