Bi-level trade credit policy under pricing and preservation technology in inventory models for non-instantaneous deteriorating items under carbon tax policy

In today's era of sustainable development, green inventory systems with a motto to reduce carbon emissions are crucial for economic growth and development. Green inventory systems managing deteriorating items need special attention since spoilage and deterioration result in a significant loss of items which hampers customers' satisfaction. The deteriorating items have an adverse impact on demand as the products decay continuously which also has a strong influence on the customers' purchase decision. Thus, a price-sensitive demand is a more realistic assumption. Further, the main sources of carbon emissions in operating the inventory system are based on the storage amount and the frequency of delivery. Besides, in the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider a sustainable inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under bi-level trade credit and carbon tax policy in order to achieve sustainability goals. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. Firstly, a mathematical model is formulated for the given scenario so as to determine the optimal replenishment cycle time, selling price, and preservation technology investment strategies which maximize the total profit of the inventory system and some useful theoretical results have been framed to characterize the optimal solutions. An algorithm is designed to derive the optimal solutions of the model. Finally, numerical examples and managerial implications are incorporated to analyze the behavior of the proposed model.