On some relations between several generalized convex DEA models

Abstract

The purpose of this paper is to establish a topological relation between several known production models, precisely a link between -convex and Cobb–Douglas production models. The framework is based on the algebraic structures of the technology sets, issued from data envelopment, respecting either the assumption of constant elasticity of substitution and transformation (CES–CET) or -returns to scale. It is shown that the Painlevé–Kuratowski limit of the CES–CET technology provides either -convex or inverse -convex technologies. Also, -returns to scale models have topological limits relevant with constant return to scale -convex (or inverse -convex) technologies.

Keywords:

• Non-parametric production models
• Painlevé–Kuratowski limit
• lattice
• CES–CET model
• generalized convexity
• -returns to scale

Notes

No potential conflict of interest was reported by the authors.