Cooperative vendor-buyer model with imperfect quality, inspection errors, and shortage backordering

In this paper, we develop an integrated vendor-buyer inventory model for item with imperfect quality and inspection errors. We assume that market demand is influenced by buyer's selling price and marketing effort. The production process is imperfect and produces a certain number of defective items. The delivery quantity from vendor to buyer is identical at each shipment. After the delivery arrives at the buyer, an inspection process is conducted. The inspection process is not perfect. The inspector may incorrectly classify a non-defective item as defective, or incorrectly classify a defective item as non-defective. An optimal solution of the model is provided and the expected joint total profit is derived. A numerical example is provided to illustrate the solution procedure presented in this paper.