integrated production-inventory model with price-dependent demand, imperfect quality, and investment in quality and inspection

In practice, manufacturing systems are never perfect and may have low quality outputs. therefore, different decisions such as reprocessing, sale at lower prices or diminishing are made according to industry and market. this paper investigates the importance of supply chain coordination through developing two models in centralized decision-making for an imperfect quality manufacturing system with probabilistic defect rate. moreover, two types of errors in inspection process are considered: type i error (classifying perfect products as defective ones) and type ii error (classifying defective products as perfect ones). moreover, a cost function for investment on products quality as well as selling price is considered. the algorithms to find the optimal solution for both models are suggested. numerical results show that even by less consumer prices; more profit, more satisfied customer, and improved quality can be achieved through coordination in supply chain.