There are long history of the studies on production planning and scheduling. In this talk, the trend of the research on production planning and scheduling, computer integrated manufacturing, and supply chain management are discussed from several directions. First, these problems are classified according to the constraints and objective functions of each problem. The system boundary is one of the key issues which distinguish the problem formulation. Then, these problems are classified according to the treatment of production demand. How to express the future demand and its uncertainty is used to classify the problems. Finally, the effect of advanced optimization methods on the formulation of the problem is discussed.