A new measure of technical efficiency in data envelopment analysis based on the maximization of hypervolumes: Benchmarking, properties and computational aspects

Abstract

The measurement of technical efficiency attracts considerable interest in the literature. In fact, following on from the seminal works by Koopmans (1951), Debreu (1951), Shephard (1953) and Farrell (1957), a substantial amount of literature has been dedicated to methods for estimating production frontiers and measuring the technical efficiency of production units. Data Envelopment Analysis (DEA) has an important role among current techniques for determining technical efficiency due to its flexibility when it comes to confronting multiple inputs and outputs as well as its non-parametric nature. Many different DEA-based technical efficiency measures have evolved over the last forty years, including radial, hyperbolic, directional, (weighted) additive, slacks-based measures, etc. Nevertheless, there is still room for harnessing new measures that are capable of satisfying interesting properties. For instance, slacks-based measures generally yield solutions with zero values in some slacks, which may mean overloading some of the other dimensions to reach the efficient frontier, thereby involving unbalanced efforts that are unrealistic. Moreover, the projection point determined by standard measures is not unique which is a further weakness from a benchmarking perspective. The purpose of this paper is to propose a novel technical efficiency performance measure in DEA on the premise of maximizing the hypervolume, while dealing with these problems and satisfying additional properties at the same time. In particular, we prove that the new approach yields unique projection points, which is not a usual property of DEA technical efficiency measures. From a computational perspective, second-order cone programming is capable of solving the new measure. Finally, an empirical example extracted from the literature serves to illustrate the new methodology.