An integrated inventory model for supplier-manufacturer-retailer system with imperfect quality and inspection errors

This paper develops an integrated inventory model for a three‐stage supply chain system consisting of single‐supplier, single‐manufacturer, and single‐retailer. The demand is deterministic and the production process is imperfect and produces a certain number of defective items. The retailer conducts an inspection process to screen out the defective items from the shipment lot. The inspector may incorrectly classify non‐defective item as defective or incorrectly classify a defective item as non‐defective. This model provides an optimal solution for the expected integrated total annual cost. A numerical example is presented for illustrative purpose.