Sustainable partial backordering inventory model under linked-to-order credit policy and all-units discount with capacity constraint and carbon emissions

In today’s competitive market environment, providing different sorts of concessions are often observed from the suppliers/manufacturers to their customers for escalating the number of order quantity, as well as work mutually to control the rising level of carbon emission along with long-lasting financial benefits. So, it is challenging for researchers and industry to develop low carbon inventory models that can meet emission reduction targets while maintaining company’s profit. The credit function plays an important role within the organization. Furthermore, with the globalization of the marketing policy, the supplier may provide the retailer a discounted price if the quantity of purchase is large enough, and green inventory management reduces the environmental impact of a business without affecting its profitability. In this paper, we study a profit maximizing green economic order quantity (EOQ) model by considering capacity constraints under order-size dependent trade credit and all-units discount, along with minimizing carbon emissions for a cleaner environment. Shortages are allowed and partially backordered. The paper discusses all the potential cases, which may occur in green inventory models with carbon emission costs under different allowable delay-in-payments. We find that if retailers’ own warehouse capacity is relatively small, they always benefit from enlarging order quantities and renting an extra warehouse. Finally, some numerical examples are presented to illustrate the applicability of the proposed model. Sensitivity analysis of the major parameters is performed and some insights are obtained.