Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method

Abstract

Data envelopment analysis methods classify the decision making units into two groups: efficient and inefficient ones. Therefore, the fully ranking all DMUs is demanded by most of the decision makers. However, data envelopment analysis and multiple criteria decision making units are developed independently and designed for different purposes. However, there are some applications in problem solving such as ranking, where these two methods are combined. Combination of multiple criteria decision making methods with data envelopment analysis is a new idea for elimination of disadvantages when applied independently. In this paper, first the new combined method is proposed named TOPSIS-DEA for ranking efficient units which not only includes the benefits of both data envelopment analysis and multiple criteria decision making methods, but also solves the issues that appear in former methods. Then properties and advantages of the suggested method are discussed and compared with super efficiency method, MAJ method, statistical-based model (CCA), statistical-based model (DR/DEA), cross-efficiency—aggressive, cross-efficiency—benevolent, Liang et al.’s model, through several illustrative examples. Finally, the proposed methods are validated.

Keywords:

• data envelopment analysis (DEA)
• multiple criteria decision making (MCDM)
• TOPSIS-DEA method
• decision making unit (DMU)
• the frontier of efficiency and anti-efficiency

Acknowledgements

The author is very grateful to Dr. Ali Emrouznejad (Professor and Chair in Business Analytics in Aston University) for reading carefully the paper, his comments and suggestions which have improved the paper.