In recent years, the reduction of carbon emissions from supply chains has become a critical concern. This paper presents a three-echelon supply chain inventory model that considers carbon emissions from manufacturing, transportation, storage, and disposal of deteriorating products. The model includes an inspection by the manufacturer to prevent the supply of defective goods and utilizes a third-party logistics company (3PL) that employs a single setup, multiple delivery system. The aim is to apply various regulatory strategies, such as carbon tax, carbon offset, and carbon cap-and-trade, to minimize expected total cost and decrease carbon emissions. The model determines delivery numbers, intervals, and quantities for the 3PL and buyer, as well as the manufacturing quantity for the manufacturer, based on buyer demand. The study concludes that the carbon cap-and-trade strategy is the most effective of the three regulatory strategies analyzed. The proposed model helps supply chain managers reduce their carbon footprint by making informed decisions on inventory, transportation, storage and disposal strategies. This study's findings provide valuable insights to policymakers on effective carbon regulation policies and the development of sustainable and cost-effective supply chain management practices.