Optimal ordering policy with trade credit and variable deterioration for fixed lifetime products

In a supply chain, the supplier frequently offers the retailer a trade credit period, and the retailer in turn provides a trade credit period to her/his customer to stimulate sales and reduce stock inventory. 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. However, only a few researchers take the expiration date of a deteriorating item into consideration. 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) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer's optimal cycle time not only exists but also is 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.