Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers

In practice, a credit-worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his/her supplier (i.e., an up-stream full trade credit). By contrast, a retailer usually requests his/her credit-risk customers to pay a fraction of the purchase amount at the time of placing an order, and then grants a permissible delay on the remaining balance (i.e., a down-stream partial trade credit). In addition, many products such as blood banks, pharmaceuticals, fruits, vegetables, volatile liquids, and others deteriorate constantly and have their expiration dates. However, not many researchers have taken the expiration date of a deteriorating item into consideration. The purpose of this paper is to establish optimal lot-sizing policies for a retailer who sells a deteriorating item to credit-risk customers by offering partial trade credit to reduce his/her risk. The proposed model is a generalized case of many previous models. By applying theorems in pseudo-convex fractional functions, we can easily prove that the optimal solution not only exists but is also unique. Moreover, we propose three discrimination terms, which can easily identify the optimal solution among all possible alternatives. Finally, some numerical examples are presented to highlight the theoretical results and managerial insights.