A novel algorithm for complete ranking of DMUs dealing with negative data using Data Envelopment Analysis and...

Area of Science:

• Operations Research
• Management Science
• Econometrics

Background:

• Data Envelopment Analysis (DEA) faces challenges with high input-output ratios, leading to misclassification of inefficient Decision Making Units (DMUs) as efficient.
• This limitation moderates the ranking power of traditional DEA models, necessitating improved methodologies for accurate performance evaluation.

Purpose of the Study:

• To develop and validate an algorithm that enhances the ranking power of DEA by addressing the misclassification of DMUs.
• To introduce a combined Principal Component Analysis and Slacks-Based Measure (PCA-SBM) model for improved efficiency assessment.
• To present a PCA-integrated Super-Efficiency model (PCA-Super SBM) capable of ranking both extreme and non-extreme efficient DMUs.

Main Methods:

• The study proposes an algorithm integrating Principal Component Analysis (PCA) with the Slacks-Based Measure (SBM) to reduce misclassification of efficient DMUs.
• A Super-Efficiency model is combined with PCA (PCA-Super SBM) to enable complete ranking of all DMUs, including non-extreme efficient ones.
• The developed models are demonstrated to effectively handle negative data, a limitation in previous PCA-DEA studies.

Main Results:

• The PCA-SBM model demonstrated superior ranking power compared to the standard SBM model in case studies involving pharmaceutical companies and bank branches.
• The PCA-Super SBM model successfully ranked non-extreme efficient DMUs, outperforming the standard Super SBM model in complete ranking.
• Empirical evidence from pharmaceutical companies and bank branches validates the algorithm's applicability and performance, showing significant improvements in ranking accuracy.

Conclusions:

• The proposed algorithm, utilizing PCA-SBM and PCA-Super SBM, successfully overcomes the limitations of traditional DEA models in ranking DMUs.
• The methodology provides a robust solution for complete DMU ranking, encompassing inefficient, extreme efficient, and non-extreme efficient units with low complexity.
• The models' ability to handle negative data and their superior ranking power establish their effectiveness in performance evaluation across various sectors.