unit. The review interval can be optimised by classical economic lot size computations. The expected time over which the economic order quantity (EOQ) will be demanded is used to determine the review interval, (see, for example, Brown 1982). Alternatively, may be set to a standard time unit such as, for example, half a day for a retailer, a week for a wholesaler, or a month for a manufacturer. The inventory review interval is usually decided by taking into account such factors as the nature of the business (the higher the volume of business the shorter the review interval will be to facilitate control), the lead times (if the lead time is one day it would not make much sense to set the review interval to one month), and inventory software related constraints. There is little guidance in the academic literature on setting appropriate inventory review intervals. Nevertheless, we remark that the forecast update interval is typically set to be equal to the inventory review interval, and this makes sense from a practical perspective.
As previously discussed, one may question the practical relevance of continuous review when most inventory control systems seem to be relying upon some sort of periodic review. However, continuous systems tend to be easier to analyse mathematically. In addition, as the review interval becomes shorter and shorter, periodic formulations become hard to distinguish from continuous ones. For daily or even half‐daily review intervals commonly used by retailers, the continuous assumption is a reasonable one (e.g. Cattani et al. 2011).
Fixing the inventory review interval to be the same for a number of SKUs facilitates their collective replenishment from a common supplier, and introduces some stability in the inventory and purchasing organisational functions. We do not mean to imply here that all periodic inventory control systems are necessarily easy to implement, but in an intermittent demand context at least, where we deal with very high numbers of items, these are more realistic than continuous policies. In the subsections to follow, the literature on periodic inventory control for intermittent demand items is summarised and the main approaches to managing intermittent demand stocks are discussed.
2.5.3 Periodic Review Policies
The inventory control systems have been claimed, on the basis of theoretical arguments, to be the best for the management of intermittent demand items (Sani 1995). Many policies have been developed in the academic literature, some giving optimal solutions (e.g. Veinott and Wagner 1965), and some not (e.g. Wagner 1975; Naddor 1975; Ehrhardt 1979; Ehrhardt and Mosier 1984; Porteus 1985). The policies that are non‐optimal are ‘heuristic’. ‘Heuristics’ here refer to the use of some (more) easily implementable rules and calculations, which reach a solution that may be close to optimal but does not necessarily achieve optimality (Sani and Kingsman 1997; Babai et al. 2010). Optimality is sacrificed in favour of some increased practical applicability.
In practice, systems are not used as much as systems. This emphasis is reflected in the academic literature, where the latter has been researched more extensively. We now turn our attention to the (or ‘order‐up‐to’) inventory policy and the reasons for its popularity.
Hadley and Whitin (1963) noted the differences, in the computational effort required, to generate results for the system and or type policies. They identified the circumstances under which the order‐up‐to policy is essentially optimal, meaning that the average annual costs differ so little from other policies that it is not worth making the additional computations. The answer depends on the relative magnitudes of the ordering and review costs. As previously discussed, the former comprises such things as raising invoices and the cost of the personnel working in relevant organisational departments. The latter reflects such things as inventory software investment and managerial time spent on reviewing SKUs' inventory positions.
When the ordering costs are low relative to review costs, an order‐up‐to policy should be almost optimal. All three policies (, , and ) incur the same review costs (for the same review interval, ), but the policy leads to more frequent ordering, everything else being equal. If the additional ordering cost is low, its impact on the relative cost performance of the policy is only minimal, and worth incurring in light of the ease of implementation of such policies.
Sani (1995) developed a stock control model that reflected the main characteristics of a real inventory system. The model was of the form where an overnight emergency delivery was offered in the case of a stockout. The model was used to conduct a sensitivity analysis of the inventory costs and customer service levels achieved by employing the real system. Sani argued that the system represents many real‐world cases and is intuitively and computationally more appealing to practitioners than the system. Moreover, using to coordinate ordering over multiple SKUs is preferable to using (which would vary across SKUs). It is also easier to optimise the system, as we know that the inventory position will be back up to at every review point. Finally, policies have been shown to be very robust (Bijvank et al. 2014) and that may help further explain their prevalence in real‐world applications. Most of the empirical studies in the area of intermittent demand forecasting and stock control have considered an
unit. The review interval can be optimised by classical economic lot size computations. The expected time over which the economic order quantity (EOQ) will be demanded is used to determine the review interval, 