A supply chain inventory model with imperfect quality and stochastic demand

Here, we develop a supply chain inventory model consisting of a vendor and a buyer. We assume that the lot transferred from vendor to buyer contains a proportion of defective items and the demand is assumed to be normally distributed. To screening the received items, the buyer conducts an inspection process to guarantee that the items sold to the end customers are in good quality. However, the inspection process is imperfect. The inspector may incorrectly classify non-defective item as defective or incorrectly classify a defective item as non-defective. A mathematical model is developed to minimise total supply chain cost. An efficient algorithm is proposed to determine simultaneously shipment lot, safety factor and number of deliveries for each production run. Finally, numerical example is provided for illustrative purposes.