<p>The present manuscript delineates a comprehensive global sustainable two-level supply chain model (SCM) that incorporates the implications of a fuzzy environment in relation to an environmentally sustainable framework, particularly within the context of delayed payment schemes. The stakeholders involved in the supply chain, namely the seller and the buyer, aim to optimize their respective costs throughout the supply chain, whereby the seller proposes a credit scheme to the buyer as a mechanism to enhance profit margins; concurrently, the buyer consents to the credit policy to diminish inventory-related expenses, with the demand rate being characterized as triangular fuzzy. The seller is responsible for delivering the ordered quantity to the buyer while adhering to an acceptable delay in payment terms. Numerous challenges associated with global warming persist, including unregulated carbon dioxide (CO2) emissions from various sources, electricity consumption, and the release of greenhouse gases (GHGs), among others. A social inventory cost component is integrated into the model to address the reduction of carbon emissions, thereby contributing to environmental sustainability. An emission tax is incorporated to underscore the significance of environmental concerns during the operational execution of the supply chain model (SCM). The primary aim of the present study is to elucidate the effects of credit financing and fuzzy demand on the anticipated total cost. A numerical example along with sensitivity analysis has been provided to evaluate the robustness of the proposed model.</p>