3.2 shows an example of the trade‐off between fill rates and average inventory values. Curves such as this can be drawn for whole categories of stocks for which different service level targets may be applied. For example, separate analyses could be conducted for fast, medium, and slow‐moving SKUs and service level targets set accordingly for each stock category.
Exchange curves can be drawn only if the inventory system allows the simulation of inventories with different service level targets. At a higher strategic level, it is possible to design systems to allow experimentation on service level targets at a stocking location, or to examine the stock implications of merging two stocking points (Johnston et al. 1988).
Figure 3.2 Exchange curve.
3.7.3 Setting SKU Level Service Targets
It is natural to define fill rates in the same way at aggregate and SKU levels. Then, it is clear that fill rate targets set at an aggregate level can also be applied at SKU level. As previously mentioned, these targets can be set differentially by stock category.
An alternative approach is to treat the items in a class separately if they have different unit costs. Thonemann et al. (2002) presented a model to reduce the overall stock costs by assigning higher fill rate targets to lower cost items and lower fill rate targets to higher cost items, while ensuring that the overall fill rate target is met. Other authors (Zhang et al. 2001; Teunter et al. 2010, 2017) have proposed approaches based on ranking SKUs, using various criteria, and then treating the SKUs differentially. Some of these approaches will be reviewed in Chapter 11.
Systems having the facility to experiment with service level targets at the level of the individual SKU are available (for example, at the time of writing, RightStock from DBO Services and the Inventory Planner of Arkieva). In Figure 3.3 we show a screenshot of the Inventory Strategist function from RightStock.
In the example given in Figure 3.3, the current system target cycle service level is set to 95% (fifth row of the ‘Current parameters’ column). Managers may experiment with the setting of different targets for a particular SKU. In the example given above, these experiments are shown as three scenarios (target service levels of 93%, 97%, and 99.5%). The bar chart shows the effect of varying the target, with respect to the average cycle stocks (to cover expected demand) and safety stocks (to allow for uncertainty of demand). This enables managers to make more informed judgements as to the most appropriate service level for a specific SKU.
Figure 3.3 RightStock Inventory Strategist.
Source: Teunter et al. (2017), Figure 1.
In conclusion, we can use the ‘what if’ facilities of software packages to experiment with different target service levels, at the level of an individual SKU. This experimentation will show the predicted effect of different targets on inventory levels and, hence, on inventory investment. It is then a matter for managers to make a judgement about the most appropriate target, taking into account the investments that would be required.
3.7.4 Summary
In this section, we have seen that judgements need to be made before setting aggregate service targets. The choice of service level targets should be informed by the service offered by others and the degree to which inventory service is prioritised as a source of competitive advantage. Service targets may then be set for whole classes of SKUs or differentially for each individual SKU.
Software can be used to conduct experiments at aggregate or SKU level, to show the inventory consequences of different service level targets. It is important to undertake such evaluations to ensure that the balance being struck between service and costs is one that reflects the aims of the organisation as a whole.
3.8 Chapter Summary
In this chapter, we started by arguing for a more analytical approach to inventory management and not relying on ad hoc rules. Nevertheless, there is still room for managerial judgement. In fact, such judgement is essential for
1 Selecting an aggregate service measure (or set of measures) against which performance will be monitored.
2 Selecting an appropriate service measure at SKU level, which best reflects the costs to the organisation of backordering and not satisfying demand from stock.
3 Deciding on the best target service levels.
Judgement may also be exercised at the level of the individual SKU, by making adjustments to demand forecasts (to be discussed further in Chapter 10) or by making adjustments to orders, without adjusting demand forecasts. These adjustments can be beneficial in certain circumstances but may also worsen performance. If such adjustments are frequent, then ongoing assessments should be made to check that performance is being improved.
We have also reviewed issues in calculating cycle service levels and fill rates. Some of these issues are quite technical but it is important that they are resolved and the measures are calculated correctly, so that inventories are set at the right levels.
The usual calculation for cycle service levels, as given in many textbooks, has some limitations for intermittent demand. It will lead to an inflated assessment of customer service, as it will count a review interval with no stockouts as a success even if there has been no demand. For intermittent demand, we saw how an alternative measure can be calculated, based on a restriction to those review intervals in which there has been some demand.
The traditional calculation for fill rates is an approximation, as it can double count some stockouts. This can lead to an underestimate of the fill rate that may, in turn, lead to excessive stocks being held. The double counting problem is particularly concerning for SKUs with lumpy demand patterns. In fact, it is an issue for particularly volatile non‐intermittent demand as well. The formulae of Sobel (2004) and Zhang and Zhang (2007), although somewhat more complicated, can address this issue and give more reliable fill rate calculations.
The calculations for both the cycle service level and the fill rate rely on demand probabilities. These may be over the review interval, the lead time, or the whole protection interval, and can be found from the probabilities of demand in a single period. The estimation of these probabilities is central to supply chain forecasting. Over the next two chapters, we examine different probability distributions that can be used to represent demand, and then move on to their forecasting requirements.
Technical Note
Note 3.1 Fill Rate Expression of Zhang and Zhang
Zhang and Zhang (2007) gave a formal mathematical justification for their measure. Here, we give a more informal explanation. Zhang and Zhang's fill rate measure for periodic review systems with review interval R, and OUT level S, is given in Eq. (3.5).
