This study configures various carbon regulation mechanisms to control carbon emissions following clean technology strategies in engine oil production. Considering clean technology strategies for designing a sustainable supply chain (SSC) in the engine oil industry, two carbon reduction policies, namely, carbon capacity and carbon emissions tax, are discussed to study the effects of environmental factors. A mixed-integer linear programming model that examines demand, technology, budget, carbon policies, and capacity constraints under several uncertainties is proposed for engine oil production from petrochemical resources, refinery plant production, and distribution system capacities. This study controls and mitigates risk and timing decisions for output decisions from a hybrid robust-heuristic-based method, wherein a modified scenario-based GA is used to eliminate the effect of uncertainties. The results indicate high-quality convergence of solutions for different strategic scenarios. We successfully apply the introduced model to address a real-world supply chain (SC) of the engine oil industry. The proposed model improves the state-of-the-art models for the engine oil SC. Finally, the study finding shows that managers can improve technologies with the lowest possible cost, maximum product profitability, and minimum possible losses in the production process and product quality through the carbon tax policy to reduce the environmental effects.