Sustainable Ordering Policies with Capacity Constraint Under Order-Size-Dependent Trade Credit, All-Units Discount, Carbon Emission, and Partial Backordering

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In today's competitive business situation, the supplier frequently offers his or her retailers a permissible delay period to stimulate sales. In addition, the capacity of any warehouse is limited in practice; thus, the retailer needs an additional rented warehouse to store the excess units when the order quantity exceeds the capacity of the own warehouse. 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. Green inventory management reduces the environmental impacts of a business without lacking its profit. Considering all of the factors mentioned above, in this paper, we study a green economic order quantity model with capacity constraint under order-size-dependent trade credit and all-units discount along with minimizing carbon for a cleaner environment. The paper discusses all the potential cases, which may occur in green inventory models with carbon emission cost under different allowable delay in payments. Shortages are allowed and partially backordered. The main objective is to determine the sustainable optimal ordering strategies for retailers and decide whether a rented warehouse (RW) is to obtain ordering and replenishment policies for a retailer such that the retailer’s annual profit is maximized. First, we prove that the conditions of the objective functions have interior minimizer value and the closed-form optimal solution is found. Next, an algorithm is developed to determining the global optimal solution of the problem. Finally, some management insights are drawn by observing the applicability of the developed algorithm and also by performing sensitivity analyses on different parameters.