Self-healing packages in a supply chain are the current trend of the different studies as global warming is rising due to the increased carbon emission in the environment. This paper aimed to create a mathematical model of a three-level supply chain of self-healing packages, following the SSMD policy. This study also considered the direct and indirect carbon emission costs to have a sustainable supply chain. It was evident in the result that the different parameters such as the holding cost of products finished (h_m), tax per carbon emission (C_tax), energy loss rate (E_I), energy consumptions (H, C, E, S), fuel consumptions, fuel price (γ and ?), and industrial indirect emission factor (?_I1), greatly affected the total cost of the mathematical model. A three-level supply chain can benefit from the presented mathematical model. In addition, an industry utilizing self-healing packages can apply the three-level mathematical model created to manage the whole system.