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One of unrealistic assumptions in classical EOQ model is that the items received are all good quality. In real life, it is very difficult for all the products received to achieve a 100% qualified rate due to various imperfect production or transportation processes, which has effect on determining the order size and related inventory control parameters. In addition, nowadays trade credit is widespread and become an important form of company finance. Supplier realizes that retailers are interested to buy more items if they are offered some credit periods to pay the whole cost of items instead of paying immediately. This paper extends the work of Chung and Huang [29] by considering that shortages are allowed and occur as lost sales where the loss of stock out and the salvage of the residue are counted into the cost. An inventory model optimizing the retailer's expected profit per unit time is established under permissible delay in payments. Three theorems are developed to derive the optimal replenishment policy. Finally, sensitivity analysis on main parameters is given by numerical examples.

In the classical economic order quantity (EOQ) models, a common unrealistic assumption is that all the items received are of good quality. However, in realistic environment, a received shipment usually contains a fraction of imperfect quality items. These imperfect items may be scrapped, reworked at a cost, or salvaged at a discounted price. While the percentage of imperfect items is random, the optimal ordering cycle is rarely considered in current literatures. This paper revisits the model (Maddah and Jaber, 2008) and extends it by assuming that the ordering cycle is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate. The possibility of stockout or residue in the end of a cycle will be considered, and the loss of stockout and the salvage of the residue are counted into the cost. Besides, we consider consolidating the shipments of imperfect items over multiple deliveries. Thus, an integrated vendor-buyer inventory model for imperfect quality items with equal-size shipment policy is established to derive the optimal ordering cycle, ordering quantity, and number of deliveries. The computational method of the optimal delivery quantity per shipment and number of deliveries is given through theoretical results. Finally, sensitivity of main parameters is analyzed through simulation experiments and shown by some figures.