Economic order quantity and purchasing price for items with imperfect quality when inspection shifts from buyer to supplier

Traditional Economic Order Quantity (EOQ) models, implicitly assume that all items that are received are perfect. Although recent EOQ models for items with imperfect quality, which relax this assumption, are closer to real-world problems, they implicitly assume that suppliers do not conduct a full inspection. In this paper, we study the relationship between buyer and supplier with regard to conducting the inspection and resulting in a change the buyer's economic order quantity and purchasing price. We model and analyze the problem under two conditions: (1) assuming there is no relationship between the buyer's selling price, buyer's purchasing price, and customer demand; (2) assuming there is relationship between the buyer's selling price, buyer's purchasing price, and customer demand. Numerical examples are provided to illustrate the models.