A Novel TOPSIS-Least Squares Approach for Classifying DMUs: A Comparative Analysis with DEA
Subject Areas : International Journal of Industrial MathematicsFatemeh Zarabi 1 , F. Rezai Balf 2 *
1 - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
2 - Department of Mathematics, Islamic Azad University, Qaemshahr, Iran
Keywords: Data Envelopment Analysis, Classifying, TOPSIS, Least Squares.,
Abstract :
Data Envelopment Analysis (DEA) is a non-parametric mathematical programming technique used to evaluates the performance of a set of homogeneous Decision-Making Units (DMUs) and assess their efficiency. DEA differentiates efficient units from inefficient ones by establishing a production or efficiency frontier. Any unit located on this frontier is considered efficient, while others are classified as inefficient. This paper presents a novel approach to distinguishing between efficient and inefficient units, and compares its results with the DEA technique. Our method is based on the combination of two techniques: TOPSIS and Least Squares (TLS). First, the TOPSIS method is employed, where the distance of each DMU from the positive ideal solution is considered as an input index, and its distance from the negative ideal solution is regarded as an output index. Then, using the Least Squares method, the units are separated into two groups: efficient and inefficient. The proposed TLS approach offers several advantages over the traditional CCR-DEA model, including computational similarity, flexibility, and transparency in classification. These features make it a valuable alternative for scenarios where DEA may not provide sufficient adaptability.
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