On classifying decision making units in DEA: A unified dominance-based model

TL;DR

This paper introduces a unified dominance-based model for classifying decision making units in DEA, providing a more comprehensive and computationally efficient approach to assess both DEA and Pareto efficiencies simultaneously.

Contribution

It proposes a novel single-stage dominance-based classification method that unifies DEA and Pareto efficiency assessments for decision making units.

Findings

The method efficiently classifies DMUs in both input and output orientations.

It demonstrates that Farrell efficiency is based on FGL dominance.

Numerical example illustrates the effectiveness of the proposed approach.

Abstract

In data envelopment analysis (DEA), the concept of efficiency is examined in either Farrell (DEA) or Pareto senses. In either of these senses, the efficiency status of a decision making unit (DMU) is classified as either weak or strong. It is well established that the strong DEA efficiency is both necessary and sufficient for achieving the Pareto efficiency. For the weak Pareto efficiency, however, the weak DEA efficiency is only sufficient, but not necessary in general. Therefore, a DEA-inefficient DMU can be either weakly Pareto efficient or Pareto inefficient. Motivated by this fact, we propose a new classification of DMUs in terms of both DEA and Pareto efficiencies. To make this classification, we first demonstrate that the Farrell efficiency is based on the notion of FGL dominance. Based on the concept of dominance, we then propose and substantiate an alternative single-stage method. Our method is computationally efficient since (i) it involves solving a unique single-stage model for each DMU, and (ii) it accomplishes the classification of DMUs in both input and output orientations simultaneously. Finally, we present a numerical example to illustrate our proposed method.