Bootstrap Method and Common Set of Weights in Data Envelopment Analysis to Differentiate Efficient Units

Subject Areas : Statistics

Akbar Amiri ¹ , saber saati mahtadi ² , alireza amirteimoori ³

1 - Department of Mathematics, Lahijan branch, Islamic Azad University, Lahijan, Iran
2 - Department of Mathematics, North Tehran branch, Islamic Azad University, Tehran, Iran
3 - Department of Applied Mathematics, Islamic Azad University, Rasht, Iran

Received: 2020-02-27 Accepted : 2020-11-22 Published : 2022-03-21

Keywords: مجموعه وزن‌های مشترک, تحلیل‌پوششی‌داده‌ها, رتبه‌بندی, بوت‌استرپ,

Abstract :

Data Envelopment Analysis (DEA) is a broad range of mathematical models for measuring the relative efficiency of a set of homogeneous decision units with similar inputs and outputs. Multiple models of data envelopment analysis render a set of weights for input and output variables of each decision unit to calculate the relative efficiency of those units based on them. The calculation of different weights for the same indices in a set of homogeneous decision units is not realistic. Therefore, the Common Set of Weights (CSW) method was used to solve this problem and the Bootstrap method was used to determine which common set of weights would minimize the number of efficient units. The rank of a unit can provide useful information to decision-makers on the optimal activities of decision units. The priority order of units defines the superiority of a unit in terms of efficiency and effectiveness over others. Calculating unit efficiency for data envelopment analysis models can be a good criterion for ranking one unit. However, the main problem arises when several efficient units all rank first. This study aimed at proposing a model for ranking efficient units using the Bootstrap method to determine the common set of weights in data envelopment analysis by finding a possible confidence interval for the weights using the Bootstrap method. This led to the estimation of a set of possible common weights for the data envelopment analysis. Efficient units were then identified and ranked based on these weights..

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