Negative data in DEA: a simple proportional distance function approach

Abstract

The need to adapt Data Envelopment Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. A recent article in this journal proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accommodate the occurrence of negative data. In this contribution, we define and recommend a generalised Farrell proportional distance function that can do the same job and that maintains a proportional interpretation under mild conditions.

Keywords:

• data envelopment analysis
• linear programming
• optimization
• production
• finance

Acknowledgements

We are grateful to two referees for most constructive comments. The usual disclaimer applies.

Notes

1 In fact, it is often ignored that the model proposed by Banker et al (1984) does not satisfy the no free lunch axiom.

2 This important contribution is further discussed and contrasted with other proposals regarding negative data in Pastor and Ruiz (2007).