From a number of recently conducted value stream mapping (VSM) exercises we have realised there are at least two replenishment decisions, and three different lead times, in the manufacturing echelon of a supply chain. This is in contrast to the common modelling assumption where only one replenishment decision with one lead time is present per supply chain echelon. The first replenishment decision releases production orders to the shop floor to maintain control of the finished goods inventory (FGI) from which customer demand is satisfied. The second replenishment decision places orders to the supplier to replenish the raw materials inventory (RMI). The three different lead times are: a) The lead time experienced by the customer - the time between the customer placing an order and that order being satisfied from FGI. b) The production lead time - the time from releasing a production order to the shop floor pacemaker and that order being completed and the product arriving in the FGI. c) The supplier lead time $-$ the time from placing an order onto a supplier, and that order being received into the RMI. With this understanding, we develop a new stylized model of a manufacturer based on a set of difference equations. This allows us to develop both a z-transform transfer function model (facilitating a variance ratio analysis via discrete control theory) and a simulation model in Excel (to verify our work). Our parsimonious model is general enough to capture the rich dynamics of both make-to-stock and make-to-order settings. First order auto-regressive demand reveals how the three lead times influence the value stream dynamics. Finally, we analyse the economic impact the lead times have on inventory costs.