We propose a unified modelling framework, based on a queuing network representation, for describing, comparing and contrasting classical and new multi-stage production-inventory control policies with lot sizing. The classical policies that we consider are installation stock reorder point policies, echelon stock reorder point policies and classical kanban policies, which we refer to as installation kanban policies. The new policies that we propose are echelon kanban policies and hybrid policies, which combine reorder point and kanban policies. The combination of reorder point and kanban policies can be done in a synchronized or an independent way, leading to synchronized and independent hybrid policies, respectively.