Production technologies with ratio inputs and outputs

Applications of data envelopment analysis often incorporate inputs and outputs stated as proportions or percentages, which are typically used to represent socio-economic quality characteristics the production process. As is well known, use such ratio measures inconsistent with assumption convexity required by conventional variable constant returns-to-scale (VRS CRS) technologies, additional scalability in case CRS. Several existing approaches modelling technologies assume that either we know exact volume numerators denominators all or, alternatively, do not have information. The former always realistic latter equivalent benchmarking each decision making unit against a significantly reduced subset observed units, has negative impact on discriminating power model. In this paper, develop new under assumptions VRS CRS bridge gap between two known approaches. They applicable general scenario can specify some lower upper bounds for measures, should be unproblematic most practical settings. We demonstrate usefulness advantages developed approach an application context school education.