Joint Pricing and Inventory Model for Deteriorating Items with Maximum Lifetime and Controllable Carbon Emissions under Permissible Delay in Payments

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.