Retailer's optimal cycle times in the EOQ model with imperfect quality and a permissible credit period

This paper modifies two assumptions of the classical EOQ model to reflect the real-life situations. First, the classical EOQ model assumes that all units produced or purchased are of good quality. Second, the payment of an order is made on the receipt of items by the inventory system. So, we incorporate both Goyal [Journal of the Operational Research Society 36: 335-338 (1985)] and Salameh and Jaber [International Journal of Production Economics 64: 59-64 (2000)] to develop a production/inventory model of the retailer to allow items with imperfect quality under permissible delay in payments. In addition, the objective function is modeled as an expected total annual profit maximization problem. Then, two theorems are developed to efficiently determine the optimal cycle time and the optimal order quantity for the retailer. Numerical examples are given to illustrate these theorems. Finally, we deduce some previously published results of other researchers as special cases.