In response to the global imperative of mitigating greenhouse gas emissions (GHGs) and the shifting landscape of business models toward multi-channel structures, this study delves into the intricacies of a green supply chain. Operating through both online and traditional channels with uncertain demands, the producer’s distribution strategy prompts an exploration of supply chain dynamics. Utilizing an integer programming model, this study calculates optimal prices, optimizes total profit, and minimizes transportation costs to curtail carbon dioxide emissions, depending on the transportation mode. Additionally, this study incorporates renewable energy sources into the production and transportation processes to further minimize carbon dioxide emissions. The integration of renewable energy not only supports environmental goals, but also contributes to the overall profitability of the supply chain by reducing energy costs. Employing a theoretical technique for linearization, the model, resolved through the Jimenez and TH methods, demonstrates efficacy in reconciling economic and environmental goals. The Jimenez method enables the transformation of fuzzy parameters into deterministic equivalents, allowing for a more reliable optimization during uncertainty, while the TH method provides an interactive fuzzy multi-objective approach, aligning the model’s dual objectives for both economic and environmental goals. Notably, when transportation costs to both markets are equal, the model prioritizes devices with a lower environmental impact, showcasing adaptability. Furthermore, the proposed solution empowers decision makers to influence pricing and enhance the entire supply chain’s profitability. In conclusion, this research offers nuanced insights, strategically aligning economic viability with environmental sustainability in the discourse on green supply chains.