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Multimodal Fuzzy Downstream Petroleum Supply Chain: A Novel Pentagonal Fuzzy Optimization

Gul Freen1, Sajida Kousar1, Nasreen Kausar2, Dragan Pamucar3, Georgia Irina Oros4,*

1 Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
2 Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler, Istanbul, 34210, Turkey
3 Department of Logistics, University of Defence in Belgrade, Belgrade, Serbia
4 Department of Mathematics and Computer Science, University of Oradea, Oradea, 410087, Romania

* Corresponding Author: Georgia Irina Oros. Email:

Computers, Materials & Continua 2023, 74(3), 4861-4879.


The petroleum industry has a complex, inflexible and challenging supply chain (SC) that impacts both the national economy as well as people’s daily lives with a range of services, including transportation, heating, electricity, lubricants, as well as chemicals and petrochemicals. In the petroleum industry, supply chain management presents several challenges, especially in the logistics sector, that are not found in other industries. In addition, logistical challenges contribute significantly to the cost of oil. Uncertainty regarding customer demand and supply significantly affects SC networks. Hence, SC flexibility can be maintained by addressing uncertainty. On the other hand, in the real world, decision-making challenges are often ambiguous or vague. In some cases, measurements are incorrect owing to measurement errors, instrument faults, etc., which lead to a pentagonal fuzzy number (PFN) which is the extension of a fuzzy number. Therefore, it is necessary to develop quantitative models to optimize logistics operations and supply chain networks. This study proposed a linear programming model under an uncertain environment. The model minimizes the cost along the refineries, depots, multimode transport and demand nodes. Further developed pentagonal fuzzy optimization, an alternative approach is developed to solve the downstream supply chain using the mixed-integer linear programming (MILP) model to obtain a feasible solution to the fuzzy transportation cost problem. In this model, the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number. Furthermore, defuzzification is performed using an accuracy function. To validate the model and technique and feasibility solution, an illustrative example of the oil and gas SC is considered, providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.


Cite This Article

G. Freen, S. Kousar, N. Kausar, D. Pamucar and G. I. Oros, "Multimodal fuzzy downstream petroleum supply chain: a novel pentagonal fuzzy optimization," Computers, Materials & Continua, vol. 74, no.3, pp. 4861–4879, 2023.

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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