An optimum decision-making strategy to maximize total profit in a two-period closed-loop supply chain dealing with greenhouse gases

The increasing global demand for raw materials has led to excessive waste production and environmental degradation, necessitating the adoption of Closed-Loop supply chains (CLSCs). However, current models often lack a comprehensive approach that integrates consumer preferences, carbon emission reduction strategies, and strategic collaborations among supply chain members. This study develops an optimal decision-making strategy for maximizing profitability and reducing carbon emissions in a two-period CLSC involving four key players, including manufacturer, retailer, collector, and recycler. Using a Stackelberg game-theoretic approach, we analyze seven alliance models and a baseline scenario (non-alliance) to assess their impact on economic and environmental outcomes. The results reveal that the seventh alliance, which includes all four players, achieves the highest total profit of 1830.81 units, marking a 71.16% improvement over the baseline model. Moreover, this alliance facilitates a 44.84-unit reduction in carbon emissions, demonstrating the potential for achieving both financial and sustainability benefits. The analysis also shows that strategic alliances improve cost efficiency, with a 15.3% reduction in marginal costs, and enhance supply chain resilience, reducing demand fluctuations by 12.7%. Furthermore, sensitivity analysis indicates that an increase in consumer sensitivity to carbon reduction from 0.3 to 0.9 leads to a 19.2% rise in demand for green products and a 14.8% increase in overall profit. These findings provide actionable insights for business leaders and policymakers. Companies can enhance CLSC performance through strategic alliances, dynamic pricing models, and sustainability-focused marketing campaigns. Meanwhile, policymakers can design carbon pricing policies, tax incentives, and regulatory frameworks that promote environmentally responsible business practices.