Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs

Applications of data envelopment analysis (DEA) often include inputs and outputs represented as percentages, ratios and averages, collectively referred to as ratio measures. It is known that conventional DEA models cannot correctly incorporate such measures. To address this gap, the authors have previously developed new variable and constant returns-to-scale models and computational procedures suitable for the treatment of ratio measures. The focus of this new paper is on the scale characteristics of the variable returns-to-scale production frontiers with ratio inputs and outputs. This includes the notions of the most productive scale size (MPSS), scale and overall efficiency as measures of divergence from MPSS. Additional development concerns alternative notions of returns to scale arising in models with ratio measures. To keep the exposition as general as possible and suitable in different contexts, we allow all scale characteristics to be evaluated with respect to any selected subsets of volume and ratio inputs and outputs, while keeping the remaining measures constant. Overall, this new paper aims at expanding the range of techniques available in applications with ratio measures.