This department is provided to answer technical questions regarding problems in production and inventory control. Readers are invited to contact George Johnson, APICS National Research Committee, Rochester Institute of Technology, College of Business, P.O. Box 9887, Rochester, NY 14623, (716) 475-2098 or via fax at (716) 475-5240.

By George Johnson, CFPIM

Dear APICS: How can I demonstrate how much additional inventory investment will be needed to increase my customer service level from its present 90 percent to 94 percent in a distribution environment?

Reply: You do not indicate how "customer service" is defined in your setting nor how safety stock quantities presently are determined, so this will have to be a wide-ranging answer. Let me begin by saying that you may not have to increase your investment at all, but merely redistribute the investment you already have if it is not in the most advantageous places. In fact, if this is the case, you may actually be able to increase service while simultaneously decreasing investment.

So, as a first step, check the mechanics of how your safety stocks presently are calculated. If they are based on rules which involve a "time supply" (e.g., six weeks supply for A items; three weeks for B items; one week for C items), you have just discovered an important improvement opportunity. (Note that I said, "based on" not "expressed as.")

Determining safety stocks on the basis of time-supply is fundamentally a flawed idea. Safety stock in a distribution environment is intended to buffer against higher-than-expected (hence, unexpected) demand, but time-supplies are calculated from expected usage figures. In a statistical sense, time-supply is based on central tendency, and buffering is intended to cope with dispersion (variation). Typically, both kinds of information are obtained from forecasting with the expected usage being a point estimate of future demand, and the unexpected use (or variability) represented by forecast error (e.g., standard deviation of forecast errors).

It is common for the variability of demand to differ from one item to the next, even if they happen to have the same expected usage rate. This has important implications for safety stock calculations. To illustrate, assume that items AA, BB and CC each have expected (i.e., forecast) usage rates of 600 units per week, and their variabilities (standard deviations of forecast error) are 100 units per week for (AA), 200 units per week for (BB), and 300 units per week for (CC).

Based on a rule that "safety stock should equal a one-week supply," all three items would have the same amount of safety stock, 600 units (1 week x 600 units expected use per week). The question is, do they all have the same potential service level? The answer is no. Even though they all are used at the same rate on average, the variability of CC is three times as much as that of AA. Under these conditions, item CC is more likely to stockout than are items AA or BB, both of which have less forecast error (variability) than CC.

So, if you have this situation, there is a clear opportunity to shift inventory dollars from items with less variable demand to those whose demand is more variable. This should improve service with the same total investment or perhaps even allow you to increase service and decrease investment. Keep reading for some ideas about how to calculate those new safety stocks.

Essentially, safety stock (SS) is conceived as a direct function of two things, 1) a safety factor (k), which is chosen to reflect the desired service level, and 2) the variability of forecast error during the replenishment lead time. The relationship is:

Safety Stock = Safety Factor x Standard Deviation of forecast error
during lead time

The safety factor (k) controls a tradeoff between service and inventory investment (i.e., higher service requires higher investment and there are diminishing returns). So choosing a safety factor gets to the heart of your question. However, there are several approaches to selecting a safety factor, and the most appropriate approach depends on the measure of customer service being used and whether the focus of control is on 1) the expected number of shortages of any size which occur in a specified period or 2) the expected number of units backordered in a specified period.

We have already dismissed as incorrect the simplest approach to setting safety stocks, which bases the quantities on time-supply targets. The next simplest approach is to choose the same safety factor for all items in an inventory (or a homogeneous subset of inventory). Assume that management wants to set as a policy a service level target of 90 percent. One approach to control for this objective is to focus on the probability of a stockout. For example, select a service factor (k) such that when replenishment orders are placed there is only a 10 percent chance of having a stockout of any size during the reorder cycle (100 percent - 10 percent = 90 percent service level).

Assuming that forecast errors for demand during lead time are normally distributed, then the relevant safety factor (k) can be obtained directly from a table of areas under the curve of a standardized normal distribution. Some of these probabilities (desired service levels) and their corresponding safety factors (k) are cited below (rounded):

Using this table to conclude the example above, the appropriate safety factor (k) to stock for a desired Service Level of 90 percent (or .90) would be 1.28.

Since the variation of forecast error doesn't change in this kind of "look-up" analysis (i.e., management is just exploring the effect on SS investment of one or another service level targets), you can quickly answer your own question by comparing the k-values needed for 90 percent service and for 94 percent service — in this case 1.28 vs. 1.56. K is the multiplier in the safety stock equation. If it increases by .28 over a base of 1.28, the increment in investment will be .28/1.28 = 21.9 percent. Thus, approximately a 22 percent increase in safety stock investment would be needed to achieve the improvement from 90 percent service to 94 percent service. This approach is appropriate to the situation where a service level is selected directly by management, where the control focus is on the probability of having a stockout of any size during a reorder cycle, and where forecast errors are normally distributed. (See Brown [1977] if not normal.)

We are not done with the discussion, however. It is quite likely that customers don't care as much about whether there is a stockout of any kind, as they do about how serious it is to them. And that depends on the nature of the unfilled demand and what can be done to recover from it. If they received some of every line item on their expendable hardware order (e.g., nuts, screws, cotter pins, etc.) along with a commitment to transship the missing balances immediately from an alternate location, they will be off their intended resupply plan but they won't be "dead in the water." On the other hand, if they received every component they ordered except there was a complete stockout of a custom chip required for a new product launch, they are going to be very unhappy.

This illustrates that some items and circumstances can be much more important than others to your customers. Items can also differ in importance to the distributing company. For example, if you must occasionally backorder some items because you don't have infinite resources to invest in safety stocks, you probably don't want to run out of items in the high volume/high margin category. It would have too great an impact on revenue. In these kinds of circumstances, it makes more sense to base service level on the second control approach — expected number of units short in some specified period — rather than on the mere probability of a stockout. Since safety stock is calculated at the item level, it is possible to selectively set the service level on the basis of expected number of units backordered — fewer units of the "important" items backordered; more units of the relatively "unimportant" items backordered. Of course this means that someone has to classify items according to their importance.

Robert Brown (1982, pg. 87) cites several example measures of customer service: "time, dollars, pieces, lines, customer orders, counting first-pass fill, and eventual fill within a specified time limit." He follows this with an instructive illustration (Brown, pp. 114-117) based on a customer order for 15 line items. For the same set of actual results, there are various levels of calculated customer service depending on which measure is used. These outcomes include, 93.3 percent fill based on lines complete; 71.2 percent based on pieces complete; 69.9 percent complete based on dollars, or 0 percent since not all lines were shipped complete. This provides a sense of how much customer service can vary depending on the choice of measure. In selecting specific measures it might be in a company's best interest to consider not only what seems important for internal control purposes, but also to find out how its customers measure customer service on their incoming shipments!

The degree of customer service actually realized is also a function of more than just safety stock investment. It is affected, for example, by lot size, by the ability to expedite replenishment orders, by the ability to transship from one stocking location to another, and by demand management activities.

Lot size inventory (not safety stock) affects service in the sense that larger lots, which are ordered less frequently (i.e., longer time-supplies), reduce the number of opportunities per year for a stockout to occur. The ability to expedite replenishment orders can prevent anticipated shortfalls. Transshipment capability enables inventory to be moved from one location with less demand to another with more demand.

Then there is the safety stock itself which, as noted above, is a function of the variability of forecast error as well as the safety factor. If the variability can be reduced through cooperative efforts with customers, by better forecasting or by demand management activity in some form, then less safety stock investment will be required for a given level of customer service.

While approaches to controlling service and investment in more complex situations are beyond the length of a monthly column, I want to point out sources you can consult about this subject and leave you with some general thoughts from their authors.

Brown (1977, chapter 10) provides a thorough analysis of safety stock strategies, including discussion of measures of service, various control approaches and decision rules. Of the basic underlying measures of service, probability of a stockout and the expected amount of demand backordered, he notes: 1) the expected backorders focus is most appropriate facing field demand (e.g., at satellite warehouses), because it allows an emphasis on minimizing backorders for a given investment; 2) the focus on stockouts in any reorder cycle is more appropriate for upstream settings (e.g., national warehouse). The logic here is that with a good planning and control system, it is plausible to expedite a few orders to avoid projected stockouts. However, this would be impractical at the field level where many more orders are involved.

Silver and Peterson (1985) also provide detailed approaches to determining safety stock levels. In Chapter 7 they discuss 1) equal time supplies (which they note is an erroneous approach), 2) fixed safety factor, 3) cost per stockout occasion, 4) fractional charge per unit short, 5) fractional charge per unit short per unit time, 6) specified probability of no stockout per replenishment cycle, 7) specified fraction of demand to be satisfied directly from shelf, 8) specified ready rate, 9) specified average time between stockout occasions, 10) minimization of expected total stockout occasions per year subject to a specified total safety stock, and 11) minimization of expected total value short per year subject to a specified total safety stock.

Whew! What started out sounding like a simple question turned out to be quite complex as potential realities were explored. I hope this background doesn't discourage you from asking the kinds of questions about safety stock decisions that could help your company achieve better results. Certainly, if the decisions are now based on time-supply, there is a clear opportunity to improve service and investment. If the needed approach is more complex than the second method we discussed — setting a service level directly — you will have to do some digging to really understand your situation and devise a sound approach to better decisions.

Good luck and you can begin your reading with the references cited below.

References

1. Brown, Robert, "Advanced Service Parts Inventory Control," Materials Management Systems, Inc., Norwich, VT: 1982.
2. Brown, Robert, "Materials Management Systems," Wiley-Interscience, 1977.
3. Silver, Edward; Peterson, Rein, "Decision Systems for Inventory Management and Production Planning," John Wiley & Sons, 1985.

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