Optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy

The main purpose of this paper is to investigate the optimal retailer’s replenishment decisions under two levels of trade credit policy within the economic production quantity (EPQ) framework. We assume that the supplier would offer the retailer a delay period and the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer’s replenishment model under the replenishment rate is finite. Furthermore, we assume that the retailer’s trade credit period offered by supplier M is not shorter than the customer’s trade credit period offered by retailer N (M ⩾ N). Since the retailer cannot earn any interest in this situation, M < N.Based upon the above arguments, this paper incorporates both Chung and Huang [K.J. Chung, Y.F. Huang, The optimal cycle time for EPQ inventory model under permissible delay in payments, International Journal of Production Economics 84 (2003) 307–318] and Huang [Y.F. Huang, Optimal retailer’s ordering policies in the EOQ model under trade credit financing, Journal of the Operational Research Society 54 (2003) 1011–1015] under above conditions. In addition, we model the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal replenishment decisions. Then three theorems are developed to efficiently determine the optimal replenishment decisions for the retailer. We deduce some previously published results of other authors as special cases. Finally, numerical examples are given to illustrate the theorems obtained in this paper. Then, as well as, we obtain a lot of managerial insights from numerical examples.