System Engineering and Productivity

System Engineering and Productivity

Designing a Bi-objective Mathematical Model for Cost and Environmental Pollution Control in Circular Supply Chain Management for Petrochemical Product Production

Document Type : Research Paper

Author
Koorosh Pouri
Ph.D, Department of Industrial Engineering, SR.C. Branch, Islamic Azad University, Tehran, Iran
10.22034/sep.2025.2060799.1321
Abstract
The aim of this paper is to investigate and propose a novel mathematical model to enhance the performance of production systems in the petrochemical industry by utilizing a closed-loop supply chain approach. The mathematical model is designed to optimize material flow, procurement, and product distribution within petrochemical systems, and is capable of accommodating uncertain demand. The objective functions considered include transportation and inventory costs (as the first objective function) and the level of pollution at treatment and distribution centers (as the second objective function). The primary goal of this research is to develop a mathematical model that simultaneously manages production costs and environmental pollution within the closed-loop supply chain of petrochemical products. The model seeks to find an optimal balance between costs and the environmental impacts arising from the production and distribution of petrochemical products. The proposed model is solved using the weighted sum method and the NSGA-II metaheuristic algorithm. According to the results obtained for the objective function, it is observed that the value of the objective function is highly sensitive to the weight assigned to the first objective. Increasing this weight leads to an increase in the objective function value, whereas a higher weight for the second objective results in a decrease in the objective function value. The findings indicate that the minimum value of the objective function is 35,996.988. Additionally, the results of the metaheuristic approach demonstrate that as the problem size increases, its computational complexity increases as well.

Highlights

  • This diagram illustrates the main stages of solving an optimization problem, from defining objectives and constraints to the final analysis of results.
  • Deterministic methods and sensitivity analysis are used to examine the effect of parameters and determine the optimal region.
  • By presenting a structured model, the author aims to achieve an efficient and reliable solution to the problem in question.

Keywords
Circular Supply Chain
Mathematical Modeling
Production Planning
Multi-objective optimization
Petrochemical industry
Subjects

Copyright © Koorosh Pouri

 

License

This article is released under the Creative Commons Attribution (CC BY 4.0) license. Anyone is free to copy, share, translate, and adapt this article for any purpose, whether commercial or non-commercial, as long as proper citation is given to the authors and original publication.

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System Engineering and Productivity
Volume 5, Issue 4 - Serial Number 17
Serial No. 17, Winter Quarterly
Winter 2026
Pages 125-148

  • Receive Date 16 May 2025
  • Revise Date 03 July 2025
  • Accept Date 11 July 2025
  • First Publish Date 31 July 2025
  • Publish Date 22 December 2025