Green supply chain coordination with profit-sharing and government intervention: a game-theoretic approach applied to the pharmaceutical industry

Amidst the global focus on sustainable development and environmental well-being, the adoption of green Supply Chain (SC) management has emerged as a pragmatic solution for mitigating Greenhouse Gas (GHG) emissions across various operational facets. This study employs a comprehensive approach, concurrently examining GHG emissions in production, transportation, and warehousing within a two-echelon SC framework involving a single vendor and buyer. Their joint objective is to optimize profitability while adhering to governmental regulations targeting GHG emissions reduction. The vendor’s visits to downstream sites are pivotal in fulfilling ordered products dispatched following fixed lead times. The buyer faces stochastic demand and employs a periodic inventory review policy, making service-level decisions contingent on market demand volatility and vendor visit intervals. The vendor’s production processes, requiring energy consumption, prompt investments in green technology to curtail emission rates. Governmental involvement extends to environmental safeguarding through tax policies. Introducing a game-theoretic approach, this study illuminates decision-making processes among SC stakeholders regarding replenishment strategies and emission reduction measures. Mathematical models and solutions for decentralized and centralized setups scrutinize how the SC leader orchestrates a profit-sharing contract to incentivize follower engagement in a comprehensive optimization strategy. The application of the proposed approach is investigated using real-world data from the pharmaceutical SC. In particular, a case study of the inventory control policy at the University of Michigan’s Central Pharmacy is presented to validate the model empirically. The results highlight the significant potential of green investments in reducing GHG emissions and emphasize the critical role of government incentives in driving these investments. The proposed coordination mechanism is shown to markedly enhance supply chain performance. Analytical findings indicate that government incentives lower both the minimum and maximum profit-sharing thresholds necessary for effective coordination, whereas high emission taxes without complementary incentives may discourage collaboration. Sensitivity analyses further reveal how holding costs, emission intensities, and energy prices differently affect service levels and green investments across decentralized and centralized structures. Notably, the study quantifies a 3% decline in service level when GHG emission taxes increase from 0.05 to 0.2, illustrating the need for balanced policy design in pharmaceutical supply chains. Computational experiments, calibrated with real-world pharmaceutical data, validate the model and demonstrate up to a 52% increase in total supply chain profit, over 20% improvement in service level, and reductions of up to 70% in transportation-related and 11.5% in production-related GHG emissions. These findings offer actionable insights for aligning environmental sustainability with profitability through contract-based coordination mechanisms.