Optimal pricing and replenishment decisions for non-instantaneous deteriorating items with a fixed lifetime and partial backordering under carbon regulations

Increasing strict carbon regulations enforced by regulators are encouraging companies to seek better ways to manage inventories with a desire to reduce carbon emissions from their operations. This work illustrates an inventory model to obtain the retailer’s optimal replenishment policy for non-instantaneous deteriorating items with fixed lifetime and partial backordering under cap-and-price, cap-and-trade, and carbon tax regulations with the goal of maximizing a retailer’s profit while simultaneously reducing total carbon emissions. To investigate the work from a more general perspective, the market demand structure of perishable products is considered deterministic in nature and is reliant on both the selling price and stock level, while the shortage of items is a decreasing function of waiting time up to the next replenishment. This study examines, for the first time, the best replenishment decisions for non-instantaneous deteriorating items with an expiration date after characterizing their properties theoretically under carbon regulations. Integrating all possible cases of the optimal solutions from theoretical outcomes, different numerical examples are demonstrated, and finally, several management insights are provided by investigating the changing pattern of the optimal strategies for variation in the system parameters. The derived outcomes highlight that the cap-and-price policy performs well both economically and environmentally for the inventory decision-maker when the penalty is less than or equal to the reward for each unit of carbon emission. Furthermore, in cap-and-price regulation, the total profit is increased by $$3.14\%$$ 3.14 % , $$8.10\%,$$ 8.10 % , and $$1.63\%$$ 1.63 % from cap-and-trade, carbon tax, and without carbon regulation, respectively, and the total amount of emission is decreased by 5.38% from cap-and-trade and carbon tax regulation.