This paper considers the general production and recovery EOQ model (GPRM), which generalizes the model of Saadany and Jaber (2008). In this general model, one supplier and one or several buyers constitute the underlying supply chain. The supplier is supposed to manufacture new products, which are then delivered to the buyers according to fixed demand rates. The supplier is also capable of recovering used products (cores),which are returned back by the buyers. Our modelling approach generalizes a whole class of various other 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.