Returns to Scale Revisited - Towards Cross-RTS
Rödder, W.
Kleine, A.
Dellnitz, A.
Data Envelopment Analysis
SSRN Working Paper, Dezember 2012.

In recent DEA literature we observe an increasing interest in crosswise evaluation of DMUs by other DMUs. One reason for this interest is an obvious shortcoming with the so called 'self-appraisal' approach which permits each unit to score its own (in-) efficiency in the most favorable way. A supervising institution might oppose such opportunistic attitude and force the DMUs to accept the weight system of a so called peer DMU as a common denominator for them all. This unification has far-reaching consequences, however. Inefficient DMUs now must improve their respective (cross-)efficiency from the viewpoint of a peer rather than from their own position. Efficiency is one economic aim for units such as fabs, projects or non-profit utilities -- returns to scale is the other. In this paper exact measures of the DMUs' returns are developed, be them efficient or not, and generalized even for non-unique returns. A natural analogue for cross-efficiencies then are cross-returns. Cross-returns to scale again are returns of DMUs from the viewpoint of other DMUs. The peer-seeking approach for good cross-efficiencies now is completed by a likewise challenging search for acceptable returns to scale. Numerical examples and respective illustrations complement all theoretical considerations. A real world application for automotive suppliers demonstrates the relevance of such theory.