Intermittent Demand Forecasting. John E. Boylan

an order and the received order being available for customers. This time interval is called the lead time, of length , and includes not only the external lead time (until receipt of order) but also the internal lead time (until availability for customers). (See Technical Note 2.3 for further discussion.) If the lead time were zero, and inventory review continuous, then inventory control would be redundant because there would be no need to keep anything in stock. However, the lead time will never be zero in practice and so enough needs to be held in stock to satisfy demand from the point in time when an order is placed to the point in time when the order is received and available for customers.

      For continuous review, the lead time is called the protection interval, because stocks are held to protect against a stockout during that period of time. (See Technical Note 2.4 for a discussion of an exception to this rule.) If the lead time is constant and known to be , then we have the problem of forecasting stochastic demand over lead time (). So if the lead time is, say, two months then the uncertainty we need to account for every time we place an order is the magnitude of the demand over the subsequent two months. In many real‐world applications, the lead time varies, as demand does, contributing further to the uncertainty underlying the inventory control system. We assume for the time being (as often happens in practice when modelling inventories) that the lead time is known and constant, but we will relax this assumption in Chapter 7.

      For periodic review systems, the protection interval not only includes the lead time but also an additional amount of time that needs to be taken into account. If orders are placed at the end of the review interval, of length , the uncertainty of the demand over this period also needs to be accounted for. For example, if the review interval in a periodic stock control system is one month and the lead time is two months then the following will happen. At the end of, say, December, let us suppose that the stock is at the order‐up‐to level, . Over what period of time does this stock level need to offer protection? At the review at the end of January, if stock has been depleted, then any order placed will not arrive until the end of March. Therefore, the stock level at the end of December needs to take into account uncertainty in demand during the review interval (January) as well as over the lead time (February and March). This explains why, in periodic stock control applications, we are interested in forecasting the stochastic demand over lead time plus the review interval (). Because of the greater uncertainty that we need to compensate for in periodic review systems, more needs to be kept in stock, everything else being equal, than in continuous review systems.

What is the more appropriate review system for intermittent demand items? Although this is discussed in more detail in Section 2.5, at this stage it is sufficient to say that practical considerations point to the periodic systems being preferred. Often, items may be produced on the same piece of equipment, purchased from the same supplier, or shipped using the same transportation mode. In any of these situations, co‐ordination of replenishments may be attractive (Silver et al. 2017). Periodic review is appealing because all items in the co‐ordinated group can be given the same review interval. Sani (1995) noted that reorder interval or product group review systems are the most commonly used in practice for intermittent demand items (see also Teunter and Sani 2009a).

      The main advantage of continuous review is that, to provide the same level of customer service, it requires less stock than periodic review. As previously discussed, this is because, in a periodic review system, stock is used to compensate for any uncertainties regarding demand over the review interval as well as the lead time. Under continuous review, the stocks are determined by considering lead time demand requirements only. Moreover, for intermittent demand items very little costs are incurred by continuous review as updates are made only when a transaction occurs. The relationship between ordering cost and inventory holding charge can be further explored so as to decide on the appropriateness of each type of system.

      Quantifying the advantages and disadvantages of periodic and continuous review is not straightforward. However, periodic policies are more simple and convenient than continuous policies, which is a very important point from a practical perspective. So we may conclude that the practical advantages of periodic review explain its popularity in real‐world applications.

      2.4.2 When are Forecasts Required for Stocking Decisions?

      So far, we have seen that the nature of a stock control system (periodic or continuous) affects the time interval over which a forecast is required. The second question we posed in the beginning of this section (and which has already been partly addressed), is: ‘How often should the test for reordering be made?’ Considering that question further reveals the difference between periodic and continuous review systems and the times when forecasts are needed for stocking decisions.

Before we address this question, it is essential to introduce the concept of inventory position. The inventory position is defined as the actual stock on hand (i.e. what we physically have in stock) for a particular SKU, plus any orders for that SKU pending to arrive, minus any demand that has not yet been satisfied and is to be satisfied as soon as some stock becomes available. This is expressed in Eq. (2.3).

(2.3)

      In continuous review systems, inventory parameters are not recalculated until the inventory position has fallen below a critical point or reached that critical point. This is known as the ‘order point’ but is also called a base stock or a minimum (Brown 1959). In this type of system, orders can be triggered only by a demand because the inventory position will not decline otherwise. (Exceptions may arise if the stock on hand (SOH) or backorders (BO) are found to be incorrectly recorded, or some of the stock on order (SOO) has been cancelled.) The triggering of an order is immediate with continuous review. Therefore, the issuing of stock, if available, at ‘issue points’, is generated immediately after demand has occurred.

Continuous systems require, as far as stock replenishment is concerned, forecasts at issue points only. Even if forecasts are automatically generated at other times, they are not relevant to ordering decisions; it is only those made immediately after a demand occurrence that affect orders. The decision may be to order nothing if demand has not been sufficiently large to deplete the inventory position to a level at, or below, the order point.

      We have already noted that a continuous recording of each transaction, leading to inventory records that are ‘live’ continuously, does not necessarily mean a continuous review of the stock requirements. Indeed, such reviews take place most commonly periodically, at the end of fixed time intervals. Let us suppose that the stock requirements are reviewed at the end of every day, and that daily demand data are used for the calculation of forecasts. If an item were demanded at 13:00 during the day, reducing the inventory position to below the order point, then in a strict continuous system, an order would be automatically generated immediately after 13:00. However, if stock requirements are not reviewed until close of business, then the order would be