Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data

Abstract

Several methods have been proposed in data envelopment analysis (DEA) for measuring efficiency in problems with interval or ordinal data. In this study, we review the weaknesses and drawbacks of these methods and show how converting ordinal or interval data into precise data can lead to violations of established DEA axioms. One of the axioms violated by these conversion processes is the inclusion of observations axiom, which requires a consistent definition of the production possibility set. We describe the special properties of ordinal and interval data together with their effect on the DEA-based rankings using a theorem and an example. We also propose a new algorithm and apply random dataset generation to overcome the problems arising from violations of the inclusion of observations axiom in DEA settings with ordinal or internal data. Several numerical examples are presented to demonstrate the applicability and exhibit the efficacy of the proposed method.