On a Closed-Loop Supply Chain with Graded Returns

We use optimal control theory to determine the optimal manufacturing, remanufacturing, and disposal rates in a closed-loop supply chain. The returned items are of different quality levels. The firm grades the returned items according to their quality. Each class of returned items is remanufactured and stocked separately. Also, all items are subject to deterioration and the deterioration rate depends on the class. Finally, each class of items is sold to a different segment of customers. An illustrative example is presented along with a sensitivity analysis on some of the system parameters.