Coordinating a two-level supply chain with defective items, inspection errors and price-sensitive demand

This paper presents an integrated inventory model consisting of a vendor and a buyer with imperfect product, imperfect inspection and backorder. We intend to study both inventory and pricing decisions in supply chain system by assuming that the demand is sensitive to the buyer’s selling price. In addition, the production cost is formulated by considering raw material cost, labor cost and advertisement cost. The objective of the model is to determine the delivery quantity, number of deliveries, buyer’s selling price and number of backorders. An iterative procedure is developed to find the optimal solution. A numerical example is presented to illustrate the application of the model and a sensitivity analysis is performed to investigate the effect of the changes in key parameters to the model’s solution.The result show that the buyer’s selling price is sensitive to the changes of the defect rate and the probability of type I inspection error