optimal manufacturer-retailer policies in a supply chain with defective product and price dependent demand

this study deals with a two-level supply chain consisting of one manufacturer and one retailer. we consider an integrated production inventory system where the manufacturer processes raw materials in order to deliver finished product with imperfect quality to the retailer, where number of defective product has a uniform distribution. the retailer receives product and conducts a 100% inspection. we assume that unit price charged by the retailer influences the demand of the product. thereby, this study establishes a link between the literature on shipment, ordering, pricing policies, imperfect quality and the joint economic lot-sizing literature. the objective is to maximize the total joint annual profits incurred by the manufacturer and the retailer. the retailer inspects the product and delivers perfect-quality product to the first market and the rejected products sent back to the manufacture to be sold in the second market. shortages are permitted for the retailer and are completely backordered. the researchers assume the policy in which the shipment quantity is delivered to the retailer is identical at each shipment.the numerical study shows that coordination between supply chain members increases when the defective percentage is reduced, and the warranty cost increases. the warranty cost has more effect on decreasing maximum total profit under individual optimization.