Science and technology practitioners have been studying how to take economical, social and environmental advantage of industrial residuals and discarded products. In this sense, this paper presents a Material Requirements Planning (MRP) optimization model for a particular production systemthat, besides manufacturing a final product and its main assembling component, it recovers units of the component from units of the returned product as well. It is assumed that the demand for the final product is independent of the amount of the returned product available, and that the market for the final product is not segmented. Considering that all parameters of the MRP mathematical model have deterministic nature, we prove that this production planning problem is NP-hard. We also show computational experiments with the model using an optimization solver and analyze some possible industrial scenarios, as well.