Global warming, driven by excessive carbon emissions, harms nature and society. Governments’ carbon reduction policies are crucial for sustainable industrial growth, integrating eco-friendly practices into production decisions. In addition, sellers often demand upfront payment for goods as a performance guarantee, receive a portion upon delivery, and finalize the transaction on credit. This advance-cash-credit (ACC) payment scheme is becoming increasingly common. Based on the above, this study proposes a production–inventory model with a carbon cap-and-trade policy and an ACC payment scheme and discusses optimal production and replenishment strategies. We also consider deteriorating raw materials, deteriorating finished products, and an imperfect production system. Mathematical methods and numerical examples are discussed to clarify the solution process, and a sensitivity analysis of parameters is performed. We demonstrate that under the two-stage trade credit and ACC scheme, a larger credit payment component enables the production–inventory system to generate higher total profits, and that a lower charged interest, higher earned interest, or later overall payment (for the ACC scheme) leads to lower carbon emissions. Furthermore, changing carbon emission quota does not affect annual carbon emissions but increasing carbon trading price does, thereby encouraging companies to reduce annual carbon emissions under a carbon cap-and-trade policy.
