Robust integrated multi-modal network design for green petroleum distribution under uncertainty.

Globally, a significant volume of petroleum products is transported daily through logistic networks to meet diverse regional demands, where unreliable or delayed delivery can lead to serious economic, social, and political consequences. The primary contribution of this research is the development of a comprehensive, robust multi-period mathematical model for the integrated planning of a green multi-modal petroleum product logistic network. This model advances current frameworks by simultaneously integrating pipeline, rail, and road transportation; synchronizing strategic facility development with operational flow allocation under uncertainty; and selecting the optimal network topology from both economic and environmental perspectives. It supports decisions on the location of distribution centers and the construction of pipelines and railways within budget constraints, aligning infrastructure investment with operational efficiency. A real-world case study in central Iran, solved via the Augmented Epsilon Constraint method, validates the approach. Targeted rail and pipeline investments reduce total transportation costs and cut CO₂ emissions by ~ 27.5% compared to the cost-only optimum. Out-of-sample tests across different uncertainty scenarios confirm the robust model's superiority. It achieves 100% feasibility, vs. 50% for the nominal model, lowers average cost by 4.7%, reduces average emissions by 30.4%, and improves uncertainty regret indices by up to ~ 92%. These findings highlight the model's resilience and ability to deliver sustainable, cost-effective petroleum logistics under real-world uncertainty.