An Integrated Inventory Model for Imperfect Production with Environmental Costs and Carbon Taxation

This study introduces a joint inventory framework that links the vendor and the buyer, while addressing the production of both good-quality and defective units. During inspection, the defective items are separated to ensure that only flawless products are delivered to the buyer in several shipments. Instead of being discarded, the rejected units are directed to a secondary market where they are accepted at a lower price, which helps in minimizing waste. The model also integrates environmental aspects by considering carbon emissions generated in manufacturing, transportation, and storage activities. To promote greener practices, a carbon tax is incorporated, aligned with real-world pricing mechanisms and environmental regulations. This tax motivates firms to control emissions and adopt sustainable operations. The paper further develops a mathematical model to identify the optimal delivery schedule and cycle length under the effect of carbon taxation. A numerical example is presented to demonstrate the applicability of the model. The sensitivity analysis shows that while rising demand boosts profits, higher production speeds may decrease them, and increased carbon costs lower vendor earnings. These findings highlight the importance of strategic demand management, balanced production planning, and the adoption of eco-efficient technologies.