On a Closed-Loop Supply Chain with Graded Returns

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