Imperfect production in three-layer supply chain systems incorporating deterioration and screening effect

This paper develops a three-layer supply chain for defective and non-defective types of produced items by supplier and manufacturer. The condition of the chain that without any financial liability on the manufacturer, defective items will be sent back to the supplier after screening. In the subsequent stage, the retailer accepts the non-defective items produced by the manufacturer after the screening and sends back the defective items to the manufacturer. Hence the retailer receives the perfect quality items for selling to the customers, but the retailer considers the effect of the deterioration of items. This model also considers the impact of several business strategies such as; optimal order size of raw materials, production rate, unit production cost, idle time costs of the supplier, and manufacturer in a collaborative marketing system, etc. to determine the optimum average profit of the integrated model. This study discusses the selling price of the retailer, demand rate of the customer, purchase cost of supplier and holding cost, which can be a significant breakthrough in expanding the profit of the business in real terms. Numerical example and sensitivity analysis are presented to illustrate the phenomenon of theoretical study and demonstrate the managerial implication of the model.