Data envelopment analysis (DEA) is a well-established instrument to detect the (in-)efficiencies and returns to scale of a certain set of decision making units (DMUs). Here for a long time the so-called self-appraisal – in which each DMU optimizes its individual weighting scheme – was the predominant approach. The derived weighting scheme then allows the user to determine both above stated indices. But what does such a scheme imply for the remaining DMUs – since they are integral part of all calculations?
The first contribution, which tackles this question, is that of Sexton et al. (1986); in this paper the authors develop the cross-evaluation approach – called peer-appraisal. More precisely: each determined weighting scheme is applied to the activities of all DMUs to get their cross-efficiencies. However, as mentioned above, (cross-)efficiency is only one economic indicator. Hence it would seem natural to treat the stated question in the light of returns to scale (RTS).
Consequently, in this contribution we develop a cross-evaluation approach which comprises RTS – this leads us to the new concept of cross-returns to scale. Finally, an economic analysis of this new measure concludes this talk.
Keywords: BCC-efficiency -- returns to scale -- cross-efficiency -- cross-returns to scale