Determining a common set of weights in data envelopment analysis by bootstrap
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ORIGINAL RESEARCH
Determining a common set of weights in data envelopment analysis by bootstrap Akbar Amiri1 · Saber Saati2 · Alireza Amirteimoori3 Received: 30 August 2019 / Accepted: 6 July 2020 © Islamic Azad University 2020
Abstract Data envelopment analysis (DEA) is a model for measuring the efficiency of decision-making units (DMUs). The majority of DEA models suffer from drawbacks, in particular, changes in the weights of inputs and outputs. Consequently, the efficiency of DMUs is measured with different weights and so it is important to establish how to evaluate all DMUs using a common weight to optimize their efficiency at the same time. This study provides a new algorithm to overcome the weaknesses of the previous model. The proposed algorithm based on the bootstrap simulation establishes a bound for the input and output weights. Common weights are obtained by solving this model using bounded weights. According to the results of a numerical example solved by this model, it outperforms conventional models in terms of ranking DMUs. Keywords Bootstrap · Common weights · Data envelopment analysis · Efficiency · Ranking
Introduction Efficiency measure was considered by researchers because of its importance in performance assessment of a company, organization or each decision-making unit (DMU). Data envelopment analysis (DEA) is one of the methods of efficiency measurement, and it employs for efficiency evaluation of homogeneous units which is considered to have different values of inputs and outputs. For the first time based on Farrell [1], who was the founder of a nonparametric method in efficiency evaluation, the model was presented in two inputs and one output, and because of the bounded of input and output, it wasn’t successful. Charnes et al. [2], in 1978, introduced the CCR model. This model was used to measure and compare the relative efficiency of organizational DMUs with multiple inputs and multiple outputs, and they consider it as a useful tool for evaluating the performance in organizations. This model is based on linear * Saber Saati s_saatim@iau‑tnb.ac.ir 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 Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
programming approach and for each unit of the organization runs individually. This sometimes causes weaknesses in the resolution of DMUs and non-real distribution of weights to inputs and outputs of the model. In other words, in this model, a large weight is assigned to outputs that are not very important or small weight is assigned to inputs that are of great importance. To solve this problem, a common set of weights (CSW) is employed. With employing a common set of weights, performance evaluation of DMUs becomes fairer. Common weight is a method that developed to answer the questions and deficiencies of DEA. This method for the first time was proposed by Cook et al. [3], In c
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