Production trade-offs in data envelopment analysis models with ratio inputs and outputs

Data envelopment analysis (DEA) is a well-established method to evaluate the performance of a homogeneous set of organisations for benchmarking purposes. The standard constant and variable returns-to-scale (CRS and VRS) models (Charnes et al., 1978; Banker et al., 1984) were developed based on volume measures (i.e., absolute numbers) and the underlying production axioms were assumed on volumes too. Ratio measures (e.g., percentages, rates, and averages) are often used in DEA applications to represent quality indicators; however, they can violate some of the underlying production axioms that the standard CRS and VRS models assume, e.g., the convexity axiom, which presumes the production set is convex (Emrouznejad and Amin, 2009). Such violations can result in incorrect efficiency results. Olesen et al. (2015) developed ratio-VRS (R-VRS) and ratio-CRS (R-CRS) models to allow ratio measures (as their native types of data) to be used with volume measures simultaneously in the DEA models. However, these models have not been used in real-data applications. In this dissertation, we use an application to a large sample of secondary schools and a Monte Carlo simulation to examine the differences between using the ratio DEA (i.e., R-VRS and R-CRS) and the standard DEA models. Our results show that although the ratio DEA models correct the issues of using ratio measures, the cost is to obtain lower efficiency discrimination. To improve the discriminating power of the ratio DEA models, we extend the specification of production trade-offs to them and develop new models. Subsequently, we use the foregoing school application and incorporate seven production trade-offs identified between volume measures and ratio measures into the efficiency computation. The application results show that the incorporation of production trade-offs significantly improves efficiency discrimination.