This contribution focusses on the dynamics of material flows in supply chains under pull, push and mixed production strategies. For this purpose, a mathematical input-output model of commodity flows is generalised and analysed in some detail for the case of linear supply chains. In particular, it is investigated under which conditions the effect of instabilities like the Bullwhip effect can be minimised. The presented results allow some new insight into the dynamics of manufacturing systems, which will be of importance for the development of new approaches for production planning and control.