Intermittent Demand Forecasting. John E. Boylan

day. From a stock replenishment perspective, this is not continuous review. It is, in fact, a periodic system, to which we now turn.

      In periodic review systems, the simplest case is when stock is reviewed at the end of every period (). In that case, if no items were demanded during a period, then the inventory position at the end of that period would be no lower than at the end of the previous period, and could be higher if a new order has arrived (as for continuous review, and with the same exceptions). Also, the required inventory level will not increase after zero demand, unless demand is forecasted to increase because of factors such as promotions, which are very much the exception for intermittent demand items.

      Generally, then, the inventory position will not reduce and the required inventory level will not increase after zero demand, meaning that an order will be triggered only if there has been some demand. Hence, it is only those forecasts that are made immediately after the end of a period with a demand occurrence which may generate an issue point and initiate an issuing of stock.

      Now suppose that stock is reviewed at the end of every second period (). For an order to be generated, there must have been some demand in the preceding two periods. However, this may not have occurred in the most recent period but in the period before that. So, in this case, we cannot restrict our attention to those periods with some demand. Forecasts affecting ordering decisions may be generated after a period of zero demand as well as after a period with some demand. The same argument applies for any length of review interval () of two periods or more. In the general case, the condition for an order to be able to be triggered at the end of a review interval of length is that there has been some demand in the last periods. It is only at the end of those review intervals satisfying this condition that forecasts may generate an issue point.

Stocking/non‐stocking reviews are not generally undertaken on an individual item basis; more commonly, the stock range is reviewed collectively. This is done periodically, usually less frequently than the standard stock replenishment reviews, and not always at regular intervals. As discussed earlier, forecasts of mean demand are required whenever such reviews are conducted. At the level of the individual SKU, this may be at any point in time: it may or may not coincide with the previous periods having had some demand. No conditioning on previous periods experiencing demand is needed in this case. So, it does not matter whether stock/non‐stock reviews are conducted at the end of every period, or at regular or irregular intervals, or whether it is done collectively or individually. As long as reviews are not triggered by demand occurrences, forecasts may be needed at any point in time for an individual SKU, to inform decisions regarding cessation of replenishment (‘non‐stock’).

      From a practical perspective, we will wish to use the same forecasting methods irrespective of the length of review interval and regardless of whether the forecast is used to decide how much stock to replenish or whether to continue stocking the item. Therefore, a forecasting method should provide good results when evaluated only after issue points (generated by review intervals containing some demand) or at any point in time. As we shall see in Chapter 6, this consideration is important in the evaluation of forecasting methods for intermittent demand.

      Returning to the question of the frequency of testing for reordering, the ideal system from an inventory holding perspective is the continuous system with immediate reordering. However, this is not always desirable from a supplier perspective, and so a periodic system with reviews at the end of every period may be more realistic, and will probably incur a relatively small additional inventory cost when compared to the ideal system. Longer reviews may be suggested for some items, but an evaluation of the inventory costs should be performed before extending review intervals. Naturally, it is desirable that forecasting methods can perform well, whatever the length of review interval.

      2.4.3 Summary

      The fundamental purpose of any inventory control system is to provide answers to the following four questions (Brown 1967):

      1 How should the stock status records be maintained?

      2 How often should the test for reordering be made?

      3 When should a replenishment order be placed?

      4 How large should the replenishment order be?

      In this section, we have been concerned with the first two questions. We have considered the relationship between recording of transactions and review of inventory and explained why ‘true’ continuous inventory review is less likely to be encountered in practice than periodic review. The differences between periodic and continuous review systems have also been discussed in detail with regard to their rationale, the time intervals over which uncertainties in demand need to be taken into account, and the forecasts that are relevant for replenishment purposes.

      Having established the importance and forecasting implications of the first two questions, we now move to the second two questions. It will take a number of chapters to answer these questions fully, but the first step is to determine the most appropriate inventory policy. To inform this decision, we now provide an overview of stock control policies that may be used for intermittent demand items.

2.5 Overview of Stock Rules

Before we review stock rules, it is important to revisit the concept of inventory position. As discussed in Section 2.4, the inventory position is defined by taking the stock on hand, and adding any stock on order, and subtracting any backorders.

      The opportunity of backordering demand is not always present. In retailing, for example, the lack of availability of an item usually leads to lost sales or sales of a substitutable product. Modelling ‘lost sales’ is far more difficult than assuming that demand may be backordered. This is because when customers are not willing to wait for their demand to be satisfied in the future, the amount of sales being lost is very hard to estimate. As we discussed in the previous chapter, sales are often used as a proxy for demand, when lost sales are not known. In a business‐to‐business context, where there is a record of the amount of items requested by the customer, lost sales will be known. However, these customers will often be willing to wait. So sales will not be lost, although there will be penalties that need to be paid for delaying the delivery of orders, and eventual loss of some customers, or adverse effects on their goodwill.

      The measurement of the service level is affected by whether demand can be backordered or not. Achieved service levels reflect how often, or how much, demand is satisfied by the stock on hand, discussed in more detail in the next chapter. When sales are lost, the greater the uncertainty of the magnitude of that loss, the less clear the picture we have on the service our customers receive. Please note that service does not have any quality‐related connotations in this book. It refers solely to availability of products.

      In general, and unless we refer to the retailing sector, the case of backorders is far more relevant than the case of lost sales. The remainder of our discussion on inventory modelling, and its interface with forecasting, is focused on the case of backordering demand.

      2.5.1 Continuous Review Systems

With regard to continuous review systems, the two most commonly encountered policies are of the or