A Unified Approach to Radial, Hyperbolic, and Directional Distance Models in Data Envelopment Analysis

The paper analyzes properties of a large class of ``path-based'' Data Envelopment Analysis models through a unifying general scheme, which includes as standard the well-known oriented radial models, the hyperbolic distance measure model, and the directional distance measure models. The scheme also accommodates variants of standard models over negative data.Path-based models are analyzed from the point of view of nine desired properties that a well-designed model should satisfy. The paper develops mathematical tools that allow systematic investigation of these properties in the general scheme including, but not limited to, the standard path-based models. Among other results, the analysis confirms the generally accepted view that path-based models need not generate Pareto--Koopmans efficient projections, one-to-one identification, or strict monotonicity