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In this article, we explore a certain kind of two-level trade credit in order to reflect the real-life situations. With this objective in view, we consider the case when the supplier offers two-level trade credit for the retailer for settling the account. If the retailer pays off all accounts at the end of the first credit period, then he/she can utilize the sales revenue to earn interest until the inventory cycle time. On the other hand, if the retailer cannot pay off the unpaid balance at the end of the first credit period, then he/she can decide to pay off the unpaid balance either after the end of the first credit period or after the second credit period. Here, in this situation, the retailer reduces the financed loan from constant sales and revenue received gradually and he/she still can utilize the sales revenue to earn interest when he/she pays off all accounts. Maximizing the profit is used as the objective to develop the inventory model. Based upon the obtained properties of the optimal solution, two theorems are developed to determine the optimal replenishment policy. Finally, computational developments are presented in order to illustrate numerically the main theoretical results which are proven in this article by using some mathematical solution procedures.

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Mathematical analytic techniques for determining the optimal ordering strategy for the retailer under the permitted trade-credit policy of two levels in a supply chain system