Development of opened-network data envelopment analysis models under uncertainty

Hasan Hosseini-Nasab; Vahid Ettehadi

doi:10.3934/jimo.2022027

Article Contents

2023, Volume 19, Issue 3: 1963-1982. Doi: 10.3934/jimo.2022027

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Development of opened-network data envelopment analysis models under uncertainty

Hasan Hosseini-Nasab^, and
Vahid Ettehadi

Yazd University, Yazd, Iran

^*Corresponding author: Hasan Hosseini-Nasab
^*Corresponding author: Hasan Hosseini-Nasab

Received: April 2021

Revised: November 2021

Early access: March 2022

Published: March 2023

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Abstract

Efficiency evaluation is a very important and key issue in competitive conditions. Organizations and companies face various uncertainties, and this makes it extremely difficult and complex to evaluate their efficiency. In this research, opened-network data envelopment analysis models have been developed in uncertain space for three uncertain states, including: uncertain outputs, uncertain inputs, and simultaneous uncertain inputs and outputs. The proposed models have been used to evaluate the efficiency of 10 two-stage processes, seller and buyer in a supply chain, and the impact of data uncertainty is examined. The results obtained from the developed models have been compared with the results of traditional DEA network models. The validity and accuracy of the developed models have also been examined. The results have shown that the reliability of the proposed models is higher than the traditional DEA network model. Also, by examining the efficiency of decision-making units in different conditions of data uncertainty and deviations, it was determined that the greater the range of this deviation, the lower the efficiency score of different units will be, which is consistent with reality.

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Mathematics Subject Classification: Primary: 90C08, Secondary: 90C70.

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Figure 1. Series Structure

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Figure 2. Series Opened-network Mode

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Figure 3. The Structure of the Network under Study

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Figure 4. Efficiency of Different Decision Units

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Table 1. Summary of the Subject Literature

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Table 2. Input and Output Data in Data Envelopment Analysis Model

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Table 3. Results of a Robust Model of Open Network Data Envelopment Analysis($ \hat \alpha $ = 0.05)

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Table 4. Results of a Robust Model of Open Network Data Envelopment Analysis ($ \hat \alpha $ = 0.1)

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Table 5. Results of Robust Model of Open Network Data Envelopment Analysis and Traditional Model

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Table 6. Pearson Correlation Coefficient for Different Models

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Table 7. Information of Decision Units in Terms of Deviation of the Second Stage Outputs

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Table 8. Results with a Deviation Percentage of 10%

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