Three-layer supply chain – A production-inventory model for reworkable items

This article develops an integrated production-inventory model considering perfect and imperfect quality items, product reliability and reworking of defective items in the environment of supply chain management. Manufacturer, supplier and retailer are the members of the supply chain where supplier delivers raw materials to the manufacturer and sends back the defective raw materials after completion of inspection at a single lot with less market price. In this system, production starts to produce good items at the beginning of the production. The production system may undergo an “out-of-control” state from an “in-control” state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more capital. The defective items produced in “out-of-control” state are reworked at a cost just after the regular production time. This model considers the impact of business strategies such as optimal order size of raw materials, production rate and unit production cost, and idle times in different sectors in a collaborating marketing system. An analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit. A numerical example along with four graphical illustrations is considered and its sensitivity analysis is provided to test feasibility of the model.