Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit

In practice, in order to reduce default risks with credit-risk customers, a seller (e.g., a manufacturer or a retailer) frequently requests its credit-risk customers to pay a fraction of the purchase amount at the time of placing an order as collateral deposit, and then grants a permissible delay on the outstanding balance (i.e., a down-stream partial trade credit). By contrast, the seller usually receives a permissible delay on the entire purchase amount from the supplier (i.e., an up-stream full trade credit). In this paper, we propose an economic production quantity (EPQ) model for deteriorating items in a supply chain with both up-stream and down-stream trade credit financing. By using fractional programming results, we can prove that the optimal solution not only exists but also is unique. Moreover, we propose three discrimination terms to identify the optimal solution among possible alternatives. Finally, some numerical examples are presented to highlight the theoretical results and managerial insights.