The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality

Abstract

The measurement of technical efficiency is a topic of great interest in microeconomics and engineering. Data Envelopment Analysis (DEA) is one of the existing techniques for measuring technical efficiency. One of the challenges related to DEA is to introduce a “well-defined” efficiency measure. Overall, it means that the technical efficiency measure should satisfy a list of mathematical and economical properties. Regarding this point, an unresolved question in the DEA literature to date, is whether any measure can satisfy both Indication, also called Pareto-efficiency identification, and uniqueness of the projection point generated by the corresponding efficiency optimization model. With this issue in mind, this paper introduces a new family of measures, inspired on the Range-Adjusted Measure (RAM), which satisfy a list of six properties. This family of measures will be called Generalized Range-Adjusted Measure (GRAM). Additionally, we show in this paper how GRAM can be implemented from a computational point of view and we also provide an economical interpretation of its dual program in terms of (shadow) profit maximization. Finally, an empirical example extracted from the literature serves to illustrate the new methodology.