A manufacturing/remanufacturing system is investigated with the consideration of required minimum quality of end-of-used products. A constant demand is satisfied by remanufacturing end-of-used products and manufacturing raw materials outsourced from outside. It is assumed in this system that the buyback price and remanufacturing cost are related to the different quality level of end-of-used products. For remanufacturing, only the used products that satisfy a required minimum quality level will be recycled. Thus, the returning rate is a function of the required minimum quality level. Functions of returning rate, buyback price and remanufacturing cost, which are closely connected to the quality level of end-of-used products, are investigated here. Treating the required minimum quality level of end-of-used products, the length of a cycle, the number of manufacturing lots and remanufacturing lots in a cycle as decision variables, the mathematical models with the objective of minimizing the average total cost are constructed. Through construction of a solution process based on Tabu Search algorithm and calculating examples, the validity of the models is illustrated.