# A novel data envelopment analysis ranking based on a robust approach

## TL;DR

This paper introduces a robust DEA ranking method that evaluates the stability of efficiency under data variations, providing a normalized, universal, and extendable ranking approach for decision-making units.

## Contribution

It presents a new DEA ranking based on robust optimization, with a linear approximation that maintains ranking order and extends to generalized models.

## Key findings

- Preserves ranking order compared to classical DEA.
- Provides a normalized, universal ranking method.
- Easily extendable to models with interval data.

## Abstract

We propose a novel DEA ranking based on a robust optimization viewpoint: the higher ranking for those DMU's that remain efficient even for larger variations of data and vice versa. This ranking can be computed by solving generalized linear fractional programming problems, but we also present a tight linear programming approximation that preserves the order of rankings. We show some remarkable properties of our approach: It preserves the order of rankings compared to the classical approach. It is naturally normalized, so it can be used as universal ranking of DMU's of unrelated models. It gives ranking not only for inefficient, but also for efficient decision making units. It can also be easily extended to generalized model, for instance to deal with interval data. We present several examples confirming the desirable properties of the method.