Within an uncertain environment and following carbon trade policies, this study uses the Extended Exergy Accounting (EEA) method for coal supply chains (SCs) in eight of the world's most significant coal consuming countries. The purpose is to improve the sustainability of coal SCs in terms of Joules rather than money while considering economic, environmental, and social aspects. This model is a multi-product economic production quantity (EPQ) with a single-vendor multi-buyer with shortage as a backorder. Within the SC, there are some real constraints, such as inventory turnover ratio, waste disposal to the environment, carbon dioxide emissions, and available budgets for customers. For optimization purposes, three recent metaheuristic algorithms, including Ant Lion Optimizer, Lion Optimization Algorithm, and Whale Optimization Algorithm, are suggested to determine a near-optimum solution to an "exergy fuzzy nonlinear integer-programming (EFNIP)." Moreover, an exact method (GAMS) is employed to validate the results of the suggested algorithms. Additionally, sensitivity analyses with different percentages of exergy parameters, such as capital, labor, and environmental remediation, are done to gain a deeper understanding of sustainability improvement in coal SCs. The results showed that sustainable coal SC in the USA has the lowest fuzzy total exergy, while Poland and China have the highest.
