In this paper characteristics of defining hyperplanes of constant returns to scale technology in DEA have been investigated. A defining hyperplane namely H is a type of hyperplane that with the elimination of H, the production possibility set (PPS) will be enlarged (In this paper a defining hyperplane exactly is the full dimensional efficient facet (FDEF) and may be found in Olesen and Peterson (1996, 2003)). The point of view of some of the characteristics is conceptual and the interpretation of defining hyperplanes of constant returns to scale technology can be achieved by these conceptual characteristics. However, some of the characteristics are practical and one can easily utilize them in practice. Some parts of topology and convex analysis have been considered to show the truth of characteristics.
As an important concept in data envelopment analysis (DEA), elasticity measure has wide theoretical and practical applications in formulating various economic concepts. Anchor points also appear to be particularly interesting and highly useful in DEA, especially for recognizing a decision making unit (DMU) as a benchmark. This paper is an attempt to use left-and right-hand elasticity measures to present a novel definition (characterization) for anchor points. The study results reveal that if there exists an increase in a bundle of input with no rate of change in a bundle of output or if there is a decrease in a bundle of output, but a bundle of input has no rate of change, then such an extreme point is the anchor point.
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