Common Weights in DEA Models with Reduced Singular Value Decomposition

• Published in: Journal of Data Science Vol. 16; no. 2; pp. 419 - 430
• Main Authors: Naseri, Hassan, Najafi, S.Esmaeil, Saghaei, Abbas
• Format: Journal Article
• Language: English
• Published: 中華資料採礦協會 24-02-2021
• Subjects: Common Set of Weights; CCR; Multiple objective methods in optimization; Data Envelopment Analysis; Singular value decomposition
• ISSN: 1683-8602; 1680-743X; 1683-8602
• DOI: 10.6339/JDS.201804_16(2).0010

In DEA framework there are many techniques for finding a common set of efficient weights depend on inputs and outputs values in a set of peer Decision- Making Units (DMUs). In a lot of papers, has been discussed multiple criteria decision-making techniques and multiple objective-decision criteria for modeling. We know the objective function of a common set of weights is defined like an individual efficiency of one DMU with a basic difference: ＂trying to maximize the efficiency of all DMUs simultaneously, with unchanged restrictions＂. An ideal solution for a common set of weights can be the closest set to the derived individual solution of each DMU. Now one question can be: ＂are the closest set and minimized set, which is found in most of the techniques, are different?＂ The answer can be: ＂They are different when the variance between the generated weights of a specific input (output) from n DMUs is big＂. In this case, we will apply Singular Value Decomposition (SVD) such that, first, the degree of importance weights for each input (output) will be defined and found, then, the Common Set of Weights (CSW) will be found by the closest set to these weights. The degree of importance values will affect the CSW of each DMU directly.