OLESEN, O.B., PETERSEN, N.C. and PODINOVSKI, V.V., 2015. Efficiency analysis with ratio measures. European Journal of Operational Research, 245 (2), pp.446–462
In applications of data envelopment analysis (DEA) data about some inputs and outputs
is often available only in the form of ratios such as averages and percentages. In this
paper we provide a positive answer to the long-standing debate as to whether such data
could be used in DEA. The problem arises from the fact that ratio measures generally do
not satisfy the standard production assumptions, e.g., that the technology is a convex set.
Our approach is based on the formulation of new production assumptions that explicitly
account for ratio measures. This leads to the estimation of production technologies under
variable and constant returns-to-scale assumptions in which both volume and ratio measures
are native types of data. The resulting DEA models allow the use of ratio measures “as
is”, without any transformation or use of the underlying volume measures. This provides
theoretical foundations for the use of DEA in applications where important data is reported in the form of ratios.
This paper was accepted for publication in the journal European Journal of Operational Research and the definitive published version is available at http://dx.doi.org/10.1016/j.ejor.2015.03.013.