An integrated single-vendor single-buyer production-inventory model for items with imperfect quality and inspection errors

In this paper, we develop an integrated vendor-buyer production-inventory model for items with imperfect quality and inspection errors. The production process is imperfect and produces a certain number of defective items with a known probability density function. We consider the policy in which the delivery quantity to the buyer is identical at each shipment. Once the buyer receives the lot, a 100% screening process of the lot is conducted, and the screening process and demand proceed simultaneously. The screening process is not perfect. The inspector may incorrectly classify a non-defective item as defective, or incorrectly classify a defective item as non-defective. The expected integrated total annual cost of the vendor and the buyer is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer.