Purpose: To create a rich, realistic, and relevant model of a manufacturer and to understand how three different lead times influence its order and inventory dynamics. The three lead times are the lead time experienced by the customer, the lead time for the shop floor to produce finished goods inventory (FGI), and the lead time for the supplier to deliver raw material inventory (RMI). Method: We use value stream mapping (VSM) to summarise recent empirical casework to develop a generic representation of a manufacturer. The manufacturer receives and satisfies orders from customers, sets production targets, and issues supplier replenishment orders. The VSM is then converted into a difference equation model that we simulate in Excel, and a z-transform based block diagram and transfer function model, from which we obtain analytical results. We assume demand is a first-order auto-regressive process forecasted with conditional expectation. Findings: We derive the inventory optimal replenishment rule for setting the in-house production targets. We also derive the optimal policy for generating replenishment orders to issue to an external raw material supplier. We obtain expressions for the bullwhip effect in both the in-house production and the supplier orders. We reveal how the demand and lead times affect the variance of the FGI and RMI levels as well as the variance of the production and supplier orders. We compare our new results with established results in the literature. In many cases there is a direct mapping from existing models to our model. However, there is a structural difference in the RMI variance ratio when the customer lead time is less than the production lead time. Finally, we conclude with an economic analysis of the FGI and RMI. Interestingly, under negatively correlated demand the RMI costs are not always increasing in the customer lead time. There is an odd-even lead time effect, it is not always economically advantageous to increase the customers lead time. Originality: When the customer lead time is greater than or equal to the production lead time (and one period to account for the sequence of events), the supply chain echelon operates in a make-to-order (MTO) mode; when the customer lead time is shorter, it operates in a make-to-stock (MTS) mode. We believe this is the first paper that is capable of understanding the dynamics when an MTS system transitions into an MTO system. Limitations: We take a linear approach to our modelling work. We have not considered the impact of capacity constraints, non-negative production orders, non-negative FGI and RMI, and random yields from the production system and/or supplier. It would also be interesting to identify optimal production planning and supplier scheduling algorithms that account for the impact of the bullwhip effect on the capacity usage of the production system and the supplier.