alt="s"/> and , should occur in parallel recognising that cost interactions exist between them. Alternatively, the parallel optimisation may be for and (rather than and ) (see, for example, Wagner 1975). In practice, though, in our experience, a separate (independent) optimisation of these parameters is the norm because of its relative simplicity. Further arguments in support of this approach relate to its near‐optimal behaviour (Porteus 1985).
2.5.2 Periodic Review Systems
In periodic review systems, the inventory decision rules most usually take the form of a or policy, the former being the one to be discussed in more detail in this book. Under the regime of both policies, after every periods (constant inventory review interval) enough is ordered to raise the inventory position up to the ‘order‐up‐to level’, . The difference between the two policies is that the policy requires the inventory position to be less than or equal to (or in certain cases strictly less than ) before an order is placed. Therefore, the policy always results in higher ordering costs because even a unit‐sized transaction during the review interval will trigger a replenishment requisition, whilst the policy will place an order only if the cumulative demand, over the review interval, exceeds some minimum level. The can be viewed as the periodic implementation of the system because the reduces to for .
In Figure 2.4, we show graphically the operation of the policy. For ease of presentation, we assume that no stockouts occur (i.e. backordered demand does not need to be accounted for). We further assume that the review interval is shorter than the lead time (as is typically the case in practice in wholesaling), i.e. . In particular, we assume that .
At time , the inventory position (which is assumed to be, for presentation purposes, at that point in time equal to the stock on hand (SOH)) is compared with the OUT level and enough is ordered to raise it up to that level. Once the order has been placed, then the inventory position equals and decreases thereafter in exactly the same way as the stock on hand. At time , the stock on hand has been further depleted and the quantity ordered at is the stock on order; the inventory position is contrasted again to and is raised up to that level. At time , the order placed at is received and added to the stock on hand; the order placed at is the stock on order and the inventory position is raised again up to .
The system depicted in Figure 2.4 is based on a fixed OUT level, , that does not change over time. The same is true for the control parameters , , and in Figure 2.3. Although it is actually common practice in industry for the control parameters to be fixed over long periods of time, more responsive inventory systems rely upon an update at each stock review occasion. So, for the system, the OUT level would be updated at every time interval . This issue is discussed further later in this chapter.
With regard to the review interval, for both and systems, this can be either optimised or, as most often happens in practice, set
alt="s"/> and 
