Reducing carbon emissions plays a significant role in developing sustainable inventory systems. In a seller-buyer relationship, an allowable delay in payment is considered for the buyer to manage the stock and simulate the demand. Deteriorating items that usually have specific maximum lifetimes have become a challenge for most firms. Contrary to the importance of these issues, very little research has studied the impact of carbon emissions on deteriorating inventory systems. This paper provides a price-dependent demand for perishable items when carbon cap-and-trade regulation fills the mentioned gap. This model provides a carbon reduction investment scheme and illustrates this investment’s effect on the inventory system. This paper determines the optimal replenishment cycle and selling price, in which: (a) perishable items have specific maximum lifetimes, (b) a specific period of delay in payment is allowed for the buyer to accumulate revenue, (c) carbon is emitted due to ordering and storage operations and carbon cap and trade is regulated along with allowable carbon reduction investment. After developing the model, optimal values are obtained from necessary and sufficient conditions of optimality. Numerical experiments are proposed to validate the model. By developing an algorithm, the optimal values of replenishment cycle, selling price, and carbon reduction technology investment are obtained, and the impact of carbon emissions and efforts to control emissions are outlined. Finally, some managerial applications are mentioned, and future research directions are exposed.@en

Incorporating qualities and environmental concerns have received significant attention in the literature on production and inventory management for deteriorating items; however, scarce papers have emphasized these two concurrently. Therefore, it is required to incorporate these two aspects for deteriorating items to fill this gap in the literature and provide a better insight into practice. This paper elaborates a sustainable production inventory model for poor quality deteriorating items which (a) items deteriorate at a constant rate and the deterioration progress can be controlled by investing in preservation technology; (b) carbon is emitted due to production operations, and it can be controlled by investing in carbon reduction technology; (c) a fraction of manufacture items are imperfect, and the quality can be enhanced by investing in quality improvement. The paper aims to discuss the impact of preservation and carbon reduction technologies on the total profit to help decision-makers make more efficient replenishment and pricing decisions. An algorithm is proposed to determine optimal values for five decision variables. A numerical experiment is illustrated to validate the mathematical formulation, and the impact of parameters on total profit and managerial insights are discussed using sensitivity analysis.@en