Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs

Abstract

In a recent paper to this journal, the authors developed a methodology that allows the incorporation of ratio inputs and outputs in the variable and constant returns-to-scale DEA models. Practical evaluation of efficiency of decision making units (DMUs) in such models generally goes beyond the application of standard linear programming techniques. In this paper we discuss how the DEA models with ratio measures can be solved. We also introduce a new type of potential ratio (PR) inefficiency. It characterizes DMUs that are strongly efficient in the model of technology with ratio measures but become inefficient if the volume data used to calculate ratio measures become available. Potential ratio inefficiency can be tested by the programming approaches developed in this paper.

Nonparametric production technologies with weakly disposable inputs

“…First, it is hoped that the assumption of weak input disposability in the convex technology T WID 0 , especially applied to a subset of inputs, would be attractive in practical applications with a group of closely related inputs, as an alternative to the standard VRS technology. Second, it should be interesting to extend the treatment of weak input disposability in the nonconvex technology T WID 1 to a related and mathematically more general model incorporating ratio inputs and outputs of Olesen et al (2015Olesen et al ( , 2017. From a practical perspective, it should also be worthwhile to explore the dual representation of technology T WID 0 and its use for evaluation and interpretation of the scale elasticity and returns to scale on the efficient frontier.…”

“…Olesen et al (2015Olesen et al ( , 2017 use the notion of selective convexity to define technologies in which some inputs and outputs are represented by ratio data, such as percentages and averages. This reflects the fact that ratio measures cannot be combined in convex combinations in the same way as volume measures.…”

Nonparametric Production Technologies with Multiple Component Processes

“…A principal problem with ratio measures is that they generally do not satisfy the standard convexity assumption and need to be modeled differently to the volume measures. A range of DEA models with a single proportional process and nonproportional ratio inputs and outputs is developed by Olesen et al (2015Olesen et al ( , 2017 who extend earlier ideas of Ruggiero (1996) and Podinovski (2005).…”

Is data envelopment analysis a suitable tool for performance measurement and benchmarking in non-production contexts?

“…Cf Emrouznejad and Amin (2009). for a general approach Olesen et al (2015Olesen et al ( , 2017. discuss efficiency measures and computational approaches for DEA models when ratio inputs and outputs cannot be avoided.…”