A unified approach to radial, hyperbolic, and directional efficiency measurement in Data Envelopment Analysis

TL;DR

This paper presents a unifying framework for various Data Envelopment Analysis models, enabling systematic analysis of their properties and broad applicability to different data types.

Contribution

It introduces a general scheme encompassing multiple DEA models, allowing comprehensive property analysis and flexible application to arbitrary and mixed data.

Findings

Some properties hold for all models in the scheme.

Other properties vary and require individual assessment.

The framework aids in model selection and application to diverse data.

Abstract

The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the directional distance function models, and even permits their generalisations. The modelling is not constrained to non-negative data and is flexible enough to accommodate variants of standard models over arbitrary data. Mathematical tools developed in the paper allow systematic analysis of the models from the point of view of ten desirable properties. It is shown that some of the properties are satisfied (resp., fail) for all models in the general scheme, while others have a more nuanced behaviour and must be assessed individually in each model. Our results can help researchers and practitioners navigate among the different models and apply the models to mixed data.