0.3
In Table 3.9, the first and third columns give all the potential combinations of demands during the lead time (two periods) and the review interval (one period), excluding the possibility of zero demand in the review interval, as this cannot yield unsatisfied demand in that period. The second column shows the stock on hand (SOH) for
The fourth column shows the unsatisfied demand, given the stock on hand in the second column and the review interval demand in the third column. Let us return to the case of a demand of eight units in the first two weeks and four units in the third week, shown in the bottom row of the middle section of the table. Now, the unsatisfied demand in the third period is shown as four units, avoiding double counting of the one unit of unsatisfied demand in the second week.
The probabilities in the fifth and sixth columns are multiplied together to give the chance of the combination of demand values in the lead time and the review interval (assuming independence of demands over time). This is then multiplied by the unsatisfied demand, in the fourth column, to give the expected unsatisfied demand. (The probabilities of demand over two weeks, shown in the fifth column, are calculated in the same way as for Table 3.3. The probabilities in the sixth column are taken directly from Table 3.7.) Finally, the overall expected unsatisfied demand per period of 0.132 and the mean demand of 1.1 per single time period are substituted into Eq. (3.4) to give a fill rate of 88.0%. As anticipated, Sobel's formula gives a higher fill rate than the traditional formula (84.4%) because it avoids the problem of double counting of backorders.
It is instructive to repeat these calculations for an OUT level of eight units. In this case, Sobel's formula gives a fill rate of 93.8%, which is exactly the same as the traditional formula (see Table 3.8). The reason is that, in this case, the maximum demand over the lead time (eight units) can deplete the stock to zero but cannot result in a backorder situation. Therefore, there will be no double counting of backorders from past periods.
Sobel's formula (Eq. (3.4)) is based on reviews every period (
3.6.4 Summary
In some ways, the fill rate is the most natural service measure for intermittent demand. The concept is straightforward to explain to managers and is often used in practice. However, the implementation of the fill rate calculation raises some technical issues. Adjustments are needed to avoid double counting of backorders. Although these adjustments do make the calculation more complex, they may be beneficial, particularly for those items with lumpy demand patterns. The formulae given in this section and in Technical Note 3.1 require distributions of demand over the lead time or longer. If the demand is assumed to be independent and identically distributed, then these distributions may be obtained from the distribution of demand per period. Selecting this distribution will become our focus of attention in Chapters 4 and 5.
3.7 Setting Service Level Targets
Once a choice of measure has been made, there is a need to set targets that appropriately reflect the organisation's broader goals. These may be applied universally, across all SKUs, or differentially, for different categories of SKUs. The setting of these targets is the subject of this section.
3.7.1 Responsibility for Target Setting
Who should be responsible for setting service level targets? Often, the sales department is allocated this responsibility. Snapp (2018) suggested that this may be misguided because sales people may not be fully aware of the supply chain implications of a change in the target service level. Similarly, the supply chain department may be unaware of the competitive implications in the market. Snapp recommended a cross‐functional approach, for example in a sales and operations planning (S&OP) process, to overcome silo‐oriented target service level setting. (Please refer to Jandhyala et al. 2018, for further information on S&OP.)
3.7.2 Trade‐off Between Service and Cost
At what levels should service level targets be set? This is not an easy question to answer. Nevertheless, if an organisation is clear on the priority level of inventory service as part of its positioning, and the costs it is prepared to bear, then it is in a good position to set service level targets strategically.
An assessment of service level options should be informed by an evaluation of the trade‐off between service level and cost. It is here that well‐designed inventory systems can be very helpful. An early example was given by Johnston (1980), who designed an interactive stock control system for builders' merchants. He included a facility to allow managers to experiment with alternative stocking strategies, using the system to provide estimates of the anticipated average stock values, stock turns, service levels, and expected lost sales per annum. This type of analysis can enable exchange curves to be drawn, such as that illustrated in Figure 3.2.
