Sustainable inventory optimisation: balancing demand dynamics with eco-friendly packaging and carbon emission constraints

In this paper, we investigate inventory models for deteriorating items influenced by advertisement frequency, price, and sustainable packaging. The demand is sensitive to these factors, while deterioration depends on the product's expiry date. Partial backlogging is allowed. Our model incorporates carbon tax policies, recognising that carbon emissions in inventory management arise primarily from transportation, holding, and deterioration of inventory. We aim to optimise inventory policy, market price, and marketing strategy to achieve maximum total profit. An algorithm is developed to solve the model, and a numerical illustration is provided to demonstrate its effectiveness. The impact of various parameters on the optimal policy is highlighted through a sensitivity analysis, presented in a tabular format. Based on our analyses, we derive several key decision-making insights for practitioners.