Designing a Sustainable Inventory Routing Model for Multi-Commodity Hazardous Materials Under Uncertainty

Document Type : Research Paper

Authors

1 M.Sc. degree, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

2 Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

3 Postdoc Researcher, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

10.22084/ier.2025.31171.2208

Abstract

This study aims to design a sustainable decision-making model for optimizing the inventory routing of hazardous materials in the supply chain. Hazardous materials such as medical waste, fuel, and flammable chemicals play an essential role in industries and healthcare systems; however, due to their toxic and flammable nature, they pose serious threats to human health, public safety, and the environment. The importance of this issue becomes more evident when considering that even a single accident during the transportation of such materials can cause severe human, financial, and environmental damages. Therefore, it is crucial to develop integrated models that simultaneously address economic, safety, and environmental dimensions. A multi-objective mathematical model was developed in this research to optimize three key criteria: total cost, maximum accident risk, and environmental emissions. To enhance realism, demand uncertainty and transportation risk were modeled using a scenario-based approach, ensuring that the solutions remain feasible under different operating conditions. For solving the model, exact methods were applied to small-scale instances, while a hybrid algorithm based on NSGA-II combined with a local search procedure was designed and implemented for large-scale problems, ensuring both scalability and solution quality. Numerical results revealed that considering both risk and uncertainty in the decision-making process significantly reduces transportation hazards, improves environmental performance, and increases the overall sustainability of the supply chain. Sensitivity analysis further demonstrated that an increase in accident severity directly leads to higher network risk, forcing decision-makers to balance between costs and safety levels. Moreover, the proposed hybrid algorithm generated high-quality solutions within shorter computational times compared to exact approaches in large-scale cases. By integrating multi-objective modeling, scenario-based uncertainty, and metaheuristic optimization, this research provides an effective framework for the sustainable management of hazardous material transportation. The findings can assist supply chain managers and policymakers in making more informed decisions that simultaneously minimize costs, enhance safety, and protect environmental resources.

Keywords

Main Subjects


  • Chopra, S., & Meindl, P., (2019). “Supply chain management and operation”. XI Pearson (Vol. XI). https://books.google.com/books/about/Supply_Chain_Management.html?id=g2WvvAEACAAJ
  • Alkaraan, F., Elmarzouky, M., Lopes de Sousa Jabbour, A. B., Chiappetta Jabbour, C. J., & Gulko, N., (2025). “Maximising sustainable performance: Integrating servitisation innovation into green sustainable supply chain management under the influence of governance and Industry 4.0”. Journal of business research, 186. https://doi.org/10.1016/j.jbusres.2024.115029
  • Barbosa-Póvoa, A. P., da Silva, C., & Carvalho, A., (2018). “Opportunities and challenges in sustainable supply chain: An operations research perspective”. European journal of operational research, 268(2): 399–431. https://doi.org/10.1016/j.ejor.2017.10.036
  • Robertson, M., (2022). “The History of Transportation”. Leland-West Insurance. https://www.lelandwest.com/planes-trains-automobiles-the-history-of-transportation.cfm
  • Hu, H., Li, J., & Li, X., (2018). “A credibilistic goal programming model for inventory routing problem with hazardous materials”. Soft computing, 22(17): 5803–5816. https://doi.org/10.1007/s00500-017-2663-y
  • Alinaghian, M., & Zamani, M., (2019). “A bi-objective fleet size and mix green inventory routing problem, model and solution method”. Soft computing, 23(4): 1375–1391. https://doi.org/10.1007/s00500-017-2866-2
  • Timajchi, A., Mirzapour Al-e-Hashem, S. M. J., & Rekik, Y., (2019). “Inventory routing problem for hazardous and deteriorating items in the presence of accident risk with transshipment option”. International journal of production economics, 209: 302–315. https://doi.org/10.1016/j.ijpe.2018.01.018
  • Sun, Y., Li, X., Liang, X., & Zhang, C., (2019). “A bi-objective fuzzy credibilistic chance-constrained programming approach for the hazardous materials road-rail multimodal routing problem under uncertainty and sustainability”. Sustainability (switzerland), 11(9). https://doi.org/10.3390/su11092577
  • Violi, A., Laganá, D., & Paradiso, R., (2020). “The inventory routing problem under uncertainty with perishable products: an application in the agri-food supply chain”. Soft computing, 24(18): 13725–13740. https://doi.org/10.1007/s00500-019-04497-z
  • Hu, H., Li, J., Li, X., & Shang, C., (2020). “Modeling and Solving a Multi-Period Inventory Fulfilling and Routing Problem for Hazardous Materials”. Journal of systems science and complexity, 33(3): 760–782. https://doi.org/10.1007/s11424-019-8176-2
  • Tavana, M., Tohidi, H., Alimohammadi, M., & Lesansalmasi, R., (2021). “A location-inventory-routing model for green supply chains with low-carbon emissions under uncertainty”. Environmental science and pollution research, 28(36): 50636–50648. https://doi.org/10.1007/s11356-021-13815-8
  • Rahbari, M., Arshadi Khamseh, A., Sadati-Keneti, Y., & Jafari, M. J., (2022). “A risk-based green location-inventory-routing problem for hazardous materials: NSGA II, MOSA, and multi-objective black widow optimization”. Environment, development and sustainability, 24(2): 2804–2840. https://doi.org/10.1007/s10668-021-01555-1
  • Fattahi, P., & Tanhatalab, M., (2022). “Stochastic inventory-routing problem with lateral transshipment for perishable product”. Journal of modelling in management, 17(2): 539–568. https://doi.org/10.1108/jm2-09-2019-0230
  • Foroozesh, N., Karimi, B., & Mousavi, S. M., (2022). “Green-resilient supply chain network design for perishable products considering route risk and horizontal collaboration under robust interval-valued type-2 fuzzy uncertainty: A case study in food industry”. Journal of environmental management, https://doi.org/10.1016/j.jenvman.2022.114470
  • Sadati-Keneti, Y., Sebt, M. V., Tavakkoli-Moghaddam, R., Rahbari, M., & Jafari, M. J., (2023). “Risk assessment in the supply chain of hazardous materials with carbon cap and trade mechanism: multi-objective red deer algorithm”. Annals of operations research. https://doi.org/10.1007/s10479-023-05531-y
  • Pasandideh, S. H. R., Rahbari, M., & Sadati-Keneti, Y., (2023). “A Lagrangian relaxation algorithm and hybrid genetic algorithm-black widow optimization for perishable products supply chain with sustainable development goals consideration”. Annals of operations research. https://doi.org/10.1007/s10479-023-05532-x
  • Pérez-Lechuga, G., Martínez-Sánchez, J. F., Venegas-Martínez, F., & Madrid-Fernández, K. N., (2024). “A Routing Model for the Distribution of Perishable Food in a Green Cold Chain”. Mathematics, 12(2). https://doi.org/10.3390/math12020332
  • Delshad, M. M., Chobar, A. P., Ghasemi, P., & Jafari, D., (2024). “Efficient Humanitarian Logistics: Multi-Commodity Location– Inventory Model Incorporating Demand Probability and Consumption Coefficients”. Logistics, 8(1). https://doi.org/10.3390/logistics8010009
  • Abbasi, S., Ardeshir Nasabi, M., Vlachos, I., Eshghi, F., Hazrati, M., & Piryaei, S., (2024). “Designing a Sustainable Nonlinear Model Considering a Piecewise Function for Solving the Risk of Hazardous Material Routing-Locating Problem”. Sustainability (switzerland), 16(10). https://doi.org/10.3390/su16104112
  • Alves da Silva Mundim, A., Oliveira dos Santos, M., & Morabito, R., (2024). “Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels”. RAIRO - operations research. https://doi.org/10.1051/ro/2024162
  • نخعی نژاد، مهدی، محزون، محمد و سالکی، میلاد، (1403). «ارائه مدل زنجیره‌تأمین سبز با درنظر گرفتن هزینه انتشار کربن دربخش‌های حمل‌ونقل و نگهداری در وسایل نقلیه ناهمگن». نشریه پژوهش‌‌های مهندسی صنایع در سیستمهای تولید، (۲۴)۱۲، 77-91. https://doi.org/ 10.22084/ier.2024.29726.2179
  • دارستانی، حسین، جوادی، بابک، موسی‌زاده، محمد و ابدالی، محمدرضا، (1403). «طراحی مدل دوهدفه شبکه زنجیره‌تأمین گوشت با درنظر گرفتن قابلیت ارتجاعی تحت شرایط عدم‌قطعیت». نشریه پژوهش‌های مهندسی صنایع در سیستمهای تولید، (۲۴)۱۲، 147-165. ۱۴۷-۱۶۵. https://doi.org/ 10.22084/ier.2024.29296.2166
  • Floudas, C. A., (1995). “Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications”. Oxford University Press. https://academic.oup.com/book/407