A new family of models with generalized orientation in data envelopment analysis

TL;DR

This paper introduces a new family of quadratically constrained models with generalized orientation in data envelopment analysis, overcoming limitations of existing directional models and extending efficiency measures.

Contribution

The paper proposes a novel family of models with generalized orientation that address simultaneous input-output improvements and can be solved via linear programming in special cases.

Findings

New models overcome limitations of directional models.

Extended Farrell efficiency measure using the new models.

Models satisfy important monotonicity properties.

Abstract

In the framework of data envelopment analysis, we review directional models \citep{Chambers1996, Chambers1998, Briec1997} and show that they are inadequate when inputs and outputs are improved simultaneously under constant returns to scale. Conversely, we introduce a new family of quadratically constrained models with generalized orientation and demonstrate that these models overcome this limitation. Furthermore, we extend the Farrell measure of technical efficiency using these new models. Additionally, we prove that the family of generalized oriented models satisfies some desired monotonicity properties. Finally, we show that the new models, although being quadratically constrained, can be solved through linear programs in a fundamental particular case.