A comprehensive extension of an integrated inventory model with ordering cost reduction and permissible delay in payments

Huang (2010) [1] proposed an integrated inventory model with trade credit financing in which the vendor decides its production lot size while the buyer determines its expenditure to minimize the annual integrated total cost for both the vendor and the buyer. In this paper, we extend his integrated supply chain model to reflect the following four facts: (1) generated sales revenue is deposited in an interest-bearing account for the buyer, (2) the buyer’s interest earned is not always less than or equal to its interest charged, (3) the total number of shipments in one lot size is the vendor’s decision variable to minimize the cost, and (4) it is vital to have a discrimination term which can determine whether the buyer’s replenishment cycle time is less than the permissible delay period or not. We then derive the necessary and sufficient conditions to obtain the optimal solution, and establish some theoretical results to characterize the optimal solution. Finally, numerical examples are presented to illustrate the proposed model and its optimal solution.