The Role of Misclassification and Carbon Tax Policies in Determining Payment Time and Replenishment Strategies for Imperfect Product Shipments

The study constructed a supply chain inventory model for sellers and buyers that integrates payment-time-dependent demand, product defects, misclassification risks, and carbon emission tax considerations. The model was designed to optimize payment time, replenishment time, and order quantities to maximize the seller’s profit per unit time. Theoretical analysis showed that profit exhibited joint concavity with respect to both payment time and replenishment time. An algorithm was also formulated to derive optimal solutions. Finally, numerical experiments and sensitivity analyses validated the model and offered practical insights for managing inventories involving imperfect products. Results indicated that higher responsiveness of demand to payment timing, greater demand coefficients, better product prices, and higher scrap values led to increased seller profits, while greater misclassification, credit default risks, and carbon tax rate reduced it. These insights help decision-makers select suitable parameter values for efficient operations.