Returns to scale in convex production technologies

The notion of returns to scale (RTS) is well-established in data envelopment analysis (DEA). In the variable returns-to-scale production technology, the RTS characterization is closely related to other scale characteristics, such as the scale elasticity, most productive scale size (MPSS), and global RTS types indicative of the direction to MPSS. In recent years, a number of alternative production technologies have been developed in the DEA literature. Most of these technologies are polyhedral, and hence are closed and convex sets. Examples include technologies with weakly disposable undesirable outputs, models with weight restrictions and production trade-offs, technologies that include several component production processes, and network DEA models. For most of these technologies, the relationship between RTS and other scale characteristics has remained unexplored. The theoretical results obtained in this paper establish such relationships for a very large class of closed convex technologies, of which polyhedral technologies are an important example.