Intermittent Demand Forecasting. John E. Boylan

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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 form. After each transaction, the inventory position is compared with a control number, , the order point. If the inventory position is less than (or in some cases at or than ), a replenishment order is released. The replenishment order can be for a standard order quantity or, alternatively, enough may be ordered to raise the inventory position to the value , the order‐up‐to level, or OUT level. (This is also known as the ‘replenishment level’.) If all demand transactions are unit sized, the two systems are identical because the replenishment requisition will always be made when the inventory position is exactly at (so that ). If the demand sizes vary, then the replenishment quantity in the policy also varies. In Figure 2.3, we show graphically the operation of the policy and its equivalence to , assuming unit sized transactions. We further assume, for ease of presentation, that no stockouts occur (i.e. backordered demand does not need to be accounted for).

Figure 2.3 Continuous review

and

policies for unit sized transactions.

When the inventory position drops to (exactly) the order point (), then an order for a fixed quantity is placed or, equivalently, enough is ordered to raise the inventory position up to the OUT level . Note that, at the time of ordering, the inventory position always equals the stock on hand because there are no pending receipts from the supplier(s). Once the order is placed, the inventory position increases to (stock on hand) + (stock on order) (=) and decreases thereafter in exactly the same way as the stock on hand. The quantity ordered is received after the lead time (), at which point in time the inventory position equals again the stock on hand.

      The problem is to find the optimal values of the control parameters and . (See Technical Note 2.5 for discussion of equivalence with optimisation.) Optimality here refers to a solution that has been explicitly developed based on minimising the total inventory cost (Ordering cost + Holding cost + Backorder cost). In theory, optimisation of the two control parameters,

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