Constant returns-to-scale production technologies with fixed ratio inputs and outputs

In practical applications of data envelopment analysis, inputs and outputs are often stated as ratio measures, including various percentages and proportions characterizing the production process. Such ratio measures are inconsistent with the basic assumptions of convexity and scalability required by the conventional variable and constant returns-to-scale (VRS and CRS) models. This issue has been addressed by the development of the Ratio-VRS (R-VRS) and Ratio-CRS (R-CRS) models of technology, both of which can incorporate volume and ratio inputs and outputs. In this paper, we provide a detailed standalone development of the special case of the R-CRS technology, referred to as the F-CRS technology, in which all ratio inputs and outputs are of the fixed type. Such ratio measures can be used to represent environmental and quality characteristics of the production process that stay constant while simultaneously allowing the scaling of the volume of production. We illustrate the use of the F-CRS technology by an application in the context of school education.