Читать книгу Intermittent Demand Forecasting - John E. Boylan - Страница 41

Having taken contractual and other constraints into account, a careful evaluation of whether an item should be stocked at all is needed. Such decisions typically rely upon an evaluation of the cost of keeping an item in stock, and the cost of not having an item in stock (see, for example, Croston 1974; Tavares and Almeida 1983). These are the two pillars upon which much inventory theory has been built, and so a detailed discussion of them is warranted.

The cost of keeping an item in stock is typically estimated based on the inventory holding charge (), which is used to calculate the cost of keeping one unit of a particular item in stock over a specified time interval (unit time). The inventory holding charge is invariably expressed as a fraction applied to the unit cost of an item (). Suppose for example that we operate with monthly time units and the inventory holding charge for a particular item is for each item unit per unit of time (one month in this case). Further assume that the cost of this item is . Then it costs £10 ( multiplied by ) to keep one unit of this item in stock for a month. The inventory holding charge is typically determined in an approximate manner to reflect such costs as the opportunity cost (i.e. the cost of not being able to invest the money, tied up in stock, elsewhere), warehousing space costs, potential pilferage and spoilage, and cost of obsolescence.

Usually, the inventory holding charge is set to be the same across an entire stock base. (At the time of writing, inventory holding charges in the range 10%–25% over a year reflect a good proportion of real‐world cases.) However, this ignores the fact that intermittent demand items have a higher risk of obsolescence. This should be reflected by inventory holding charges that are higher than those imposed on faster‐moving SKUs. Better informed inventory systems do distinguish between non‐intermittent and intermittent SKUs, fixing the inventory holding charge for the former category and appropriately inflating it for the latter. The necessary degree of inflation depends on the industry and the nature of the products, which determines both the cost and environmental implications of disposing of an obsolete item. In our experience, it would vary between 3% and 5% over and above the inventory holding charge assumed for the faster‐moving SKUs (see, for example, Trimp et al. 2004). The inventory holding charge does not take into account ordering costs, which are often omitted from stock/non‐stock rules. Ordering costs do tend to feature in determining inventory replenishment policies, to be discussed later in this chapter.

The cost of not having an item in stock is typically estimated based on a charge that specifies the penalty cost of running out of stock. Such a charge will be different for cases where sales are lost and those where unsatisfied demand may be backordered (i.e. satisfied as soon as some stock becomes available again). Let us focus on the backorder case here; we return to the differences between lost sales and backordered demand later in the chapter. The backordering charge () may take different forms: (i) a specified fractional charge (of the unit cost) per unit short (regardless of the duration of the stockout) or (ii) a specified fractional charge per unit short per unit time.

In the first case, the backordering charge is typically set subjectively to reflect costs arising from expediting orders, loss of customers' goodwill, and negative word of mouth publicity. Expediting charges arise by ordering emergency replenishments from suppliers, which come at a (considerably) higher cost than normal replenishments.

The second case is more relevant in a maintenance spare parts context, as each unit short could result, for example, in a machine being idled, with the idle time being equal to the duration of the shortage. So, for the example considered above (with monthly time units and ), if /unit short/unit time, it costs per unit short per month.

In both cases, the backordering charge is typically in the range of 5 up to 30 (or even more) times higher than the inventory holding charge, and this reflects the asymmetric costs of under‐stocking and over‐stocking. All else being equal, it always costs more to run out of stock by one unit than to keep in stock one unit that remains unused over a unit time period.

Then, why do we consider the possibility of not stocking an item at all? This is because, over time, it may indeed be more beneficial to allow for a potential (forthcoming) shortage, rather than having to carry an item in stock for a very long time. For example, if is five times , and (for monthly time buckets) unit sized demands occur on average every six months or more, then it is cost beneficial not to stock that particular item.

Early work in this area by Tavares and Almeida (1983) proposed a rule, along the lines discussed above, for the stock control of very slow moving spare parts in large production systems, such as ship repair yards and light steel mills. The decision rule was developed in order to decide whether it is economic to have one item in stock or none. In particular, a threshold level of the mean demand was proposed, equal to , the ratio of the holding charge () to the backordering charge (), with the latter covering additional delivery and penalty costs. The mean demand per unit time () is then compared to that threshold value in order to make a decision. If the mean demand is less than the threshold, then the recommended stock () is zero; if the mean demand is greater than (or equal to) the threshold, then the recommended stock is one, as shown in Eq. (2.1).

(2.1)

For the example offered above, . So if the mean demand is (one unit is requested for that item every six months, on average), then we should not stock that item. (The symbol [lambda] is often used to denote the mean demand per unit time, and it is the standard symbol for the mean of the Poisson distribution, to be discussed in Chapter 4.)

Johnston et al. (2011) examined the inventory system at Euro Car Parts and demonstrated that, for practical purposes, stock/non‐stock decisions may rely upon the number of movements over a particular time interval. ‘Movements’ are demand incidences that lead to an issue of stock. For unit sized demands, the number of demand incidences is equal to the demand over the same time interval.

The rule offered by Johnston et al. (2011) was derived empirically, following a comprehensive analysis of the stock base of the company. The researchers evaluated the stockout and inventory implications associated with alternative stock/non‐stock cut‐off points and found that a boundary of three movements (over a year) offered the best results: if there are three or more movements per year, then stock this item; else, do not keep it in stock. The implementation of the new rule at Euro Car Parts resulted in a 29% improvement in stock turn, at a time when no other major changes were made to the distribution system. (Stock turn, also known as inventory turnover, measures how many times an organisation has sold and replaced inventory during a given period and is discussed further in Chapter 3.)