Continuous models combining slacks-based measures of efficiency and super-efficiency

TL;DR

This paper introduces a new composite SBM model in data envelopment analysis that addresses discontinuity and overestimation issues in super-efficiency scores, extending the model to various orientations and returns to scale.

Contribution

It proposes a novel composite SBM model that fixes known problems in super-efficiency measurement and extends it to multiple orientations and variable returns to scale.

Findings

The composite SBM model effectively resolves discontinuity issues.

It provides more accurate super-efficiency scores.

Extensions include additive versions and different orientations.

Abstract

In the framework of data envelopment analysis (DEA), Tone (2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of the evaluated decision-making units (DMUs) into their efficiency scores, unlike classical radial efficiency models. Next, Tone (2002) developed the SBM super-efficiency model in order to differentiate and rank efficient DMUs, whose SBM efficiency scores are always $1$. However, as pointed out by Chen (2013), some interpretation problems arise when the so-called super-efficiency projections are weakly efficient, leading to an overestimation of the SBM super-efficiency score. Moreover, this overestimation is closely related to discontinuity issues when implementing SBM super-efficiency in conjunction with SBM efficiency. Chen (2013) and Chen et al. (2019) treated these problems, but they did not arrive to a fully satisfactory solution. In this paper, we review these papers and propose a new complementary score, called composite SBM, that actually fixes the discontinuity problems by counteracting the overestimation of the SBM super-efficiency score. Moreover, we extend the composite SBM model to different orientations and variable returns to scale, and propose additive versions. Finally, we give examples and state some open problems.