Production inventory optimization considering direct and indirect carbon emissions under a cap-and-trade regulation

Background: The latest global agreement on net-zero emissions encourages new studies on production inventory optimization that promote carbon emissions reduction without harming a company's profit performance, particularly because certain carbon-pricing regulations bind manufacturing companies. Methods: This study aims to develop a production inventory model that considers direct and indirect emissions in three emission scopes. It incorporates emissions from production, material handling, transportation, and waste disposal for further treatment under a carbon cap-and-trade regulation. With the help of Maple software, a convex total cost function was solved. Results: The results show that the optimum production quantity depends on the values of demand, setup cost, holding cost, fixed cost per delivery, fixed cost for waste disposal, and other parameters related to carbon prices. This study also found that the total cost was highly dependent on the values of the carbon cap, carbon price, and delivery distance. Meanwhile, changes in the delivery distance and fuel emissions standard significantly impacted total emissions. Conclusions: The proposed model can guide manufacturing companies in setting the optimum production quantity per cycle. Moreover, they must carefully manage the delivery and setting of the carbon cap and carbon price from the government.