Optimal decisions in supply chains with a call option contract under the carbon emissions tax regulation

Carbon emissions tax has been recognized as an effective market-based mechanism to curb carbon emissions, which makes every participant in the supply chain rethink their optimal operational decisions. Motivated by an iron and steel supply chain under the carbon emissions tax regulation, this paper investigates the optimal operational decisions for both supplier and retailer in the supply chain with a call option contract. Specifically, this paper considers a supply chain consisting of one risk-neutral supplier and one risk-averse retailer. To effectively match supply with the uncertain demand while reducing the carbon emissions, the retailer can choose to purchase call options from the supplier, and thus is allowed to adjust the final order quantities after the demand realization. The optimal order and production policies with and without the call option contract are derived. Further, it is demonstrated that the call option contract can benefit both the retailer and supplier, improve the performance of the whole supply chain and decrease invalid carbon emissions. In addition, the introduction of call option contracts can mitigate the effect of carbon emissions tax and risk aversion on the order quantity of the retailer. Finally, numerical experiments based on a real-world iron and steel supply chain are conducted to validate the theoretical findings and provide useful managerial insights.