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Neutrosophic Mathematical Programming for Optimization of Multi-Objective Sustainable Biomass Supply Chain Network Design

Mohammad Fallah*, Hamed Nozari
Department of Industrial Engineering, Islamic Azad University, Central Tehran Branch, Tehran, Iran
* Corresponding Author:Mohammad Fallah. Email:
(This article belongs to this Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2021, 129(2), 927-951.

Received 15 May 2021; Accepted 21 July 2021; Issue published 08 October 2021


In this paper, a multi-objective sustainable biomass supply chain network under uncertainty is designed by neutrosophic programming method. In this method, for each objective function of the problem, three functions of truth membership, non-determination and falsehood are considered. Neutrosophic programming method in this paper simultaneously seeks to optimize the total costs of the supply chain network, the amount of greenhouse gas emissions, the number of potential people hired and the time of product transfer along the supply chain network. To achieve the stated objective functions, strategic decisions such as locating potential facilities and tactical decisions such as optimal product flow allocation and vehicle routing must be made. The results of the implementation of neutrosophic programming method show the high efficiency of this method in achieving the optimal values of each objective function. Also, by examining the rate of uncertainty, it was observed that with increasing this rate, the total costs of supply chain network design, greenhouse gas emissions and product transfer times have increased, and in contrast, the potential employment rate of individuals has decreased.


Neutrosophic mathematical programming; sustainable supply chain; biomass supply chain; neutrosophic set; uncertainty

Cite This Article

Fallah, M., Nozari, H. (2021). Neutrosophic Mathematical Programming for Optimization of Multi-Objective Sustainable Biomass Supply Chain Network Design. CMES-Computer Modeling in Engineering & Sciences, 129(2), 927–951.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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