Integrating machine learning and distributionally robust optimization for sustainable agricultural supply chains under global warming uncertainty

Agricultural supply chains face substantial challenges in ensuring food security and sustainability, particularly due to the impacts of climate change, including global warming. To optimize resource use and minimize waste, it is essential to manage these supply chains effectively, especially in the face of uncertainty. This research addresses the crucial challenge of designing a sustainable closed-loop agricultural supply chain network, with a specific focus on jujube products in the context of temperature-yield uncertainty. The model enhances economic sustainability by minimizing costs, social sustainability through job creation requirements, and environmental sustainability by implementing carbon emission caps, while taking into account decisions regarding facility locations, inter-facility flows, inventory, and shortage management. Our main contribution is a distributionally robust optimization approach that integrates a K-means clustering machine learning algorithm to generate scenarios from historical data patterns, addressing the dynamic and interrelated uncertainties in temperature-yield data. The framework incorporates closed-loop principles through thermochemical conversion processes that transform agricultural waste into value-added biochar products. A comprehensive case study of the jujube industry in South Khorasan Province, Iran, validates the model's effectiveness. Results demonstrate that moderate conservatism levels ($\omega$ between 0.8 and 1.2) achieve an 88% reduction in operational risk variability while incurring only a 3% cost increase. A comparative analysis reveals that the proposed approach achieves a 0.95 risk-adjusted performance score, outperforming traditional stochastic programming and robust optimization alternatives. This research provides agricultural supply chain managers with practical guidelines for managing temperature-yield uncertainty.