Abstract: Today's research is interested in the inventory decision models that have real business applications. In real life business, a necessary replenishment decision context between a supplier and a distributor could be characterized by an arrangement on the trade credit scenario such as permissible delay in payments. During the delay period, the distributor can accumulate revenue on sales and earn interest on that revenue, so the trade credit policy can be used to allocate the profit between the upstream and downstream members in the supply chain and bear the risk of inventory jointly with the purpose to increase the efficiency of supply chain. Over the years, the extensive research papers of trade credit has been addressed, and some of the published results have noticed that in practice the distributor could also adopt the trade credit policy to deal with his/her customer, that is two levels of trade credit which is a new viewpoint to develop the distributor's replenishment model. Also to reduce default risks, a distributor frequently requests his/her bad credit customers to pay a portion of the purchase amount before the order is received, i.e., partially advance payments, which is an important aspect of trade credit policy, has been neglected for a long time in the literatures investigating inventory problems under varying trade credit conditions. So we focus on the context of two-level trade credit considering both partially advance payments and permissible delay in payments to determine the optimal replenishment cycle in a single deteriorating item supply chain. Firstly, based on the related theoretical research of deteriorating items and trade credit, it is assumed that the supplier offers a fixed credit period to the distributor in this paper, while the customers of the channel have to make partially advance payments to the distributor in turn. Then, by analyzing the cost structure of the distributor under every scenario for the three distinct cases of the system parameters, the proper mathematical model is established to find the optimal ordering cycle inorder to minimize the total cost incurred per unit time. The properties of the objective function are derived, and it is shown that there exists at most one minimum point under every situation within its feasible region. Upon the above analysis, several propositions are developed to efficiently determine the optimal ordering policy for the distributor. Finally, combining operations management practice, numerical examples are conducted to illustrate the effectiveness of the proposed model. This paper extends the published deteriorating EOQ models and enables managers to make ordering cycle decisions more effectively from the distributor's perspective.

Key words: EOQ, deteriorating item, two-level trade credit, partially advance payments, Inventory management