Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing and back order

In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of  periods, and the retailer in turn provides a trade credit of  periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. In this paper along with deterioration and expiration date, we consider shortages that are very rarely investigated by researches. Therefore, this paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, (c) deteriorating items not only deteriorate continuously but also have their expiration dates and (d) there is a shortage allowed in each time period. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights.