Inventory management in reverse logistics has been receiving increasing attention in recent years. Our modelling approach generalizes a whole class of various models that draw attention to different aspects of production, inventory, and recovery. A complete solution in the form of a theorem for that general model class is provided. Furthermore, the paper illustrates how that theorem can be applied to one of the mentioned models from the literature, Jaber and Saadany, 2009. The paper Jaber and Saadany, 2009 extends along this line of research and assumes that demand for manufactured items is different from that for remanufactured (repaired) ones. This assumption results in lost sales situations where there are stock-out periods for Manufactured and remanufactured items. However, in their paper the authors provide solution procedure in the form of algorithm and did not provide the complete explicit solution to this complex problem. We provide the solution in this paper.