This article is adapted from an article published February 3, 2021 by SCM Now, and is published with permission of the Association for Supply Chain Management.

This is the second of two articles discussing good inventory managing practices. The first described the role of cycle stock and how to determine appropriate levels. This article focuses on safety stock, inventory carried to prevent or reduce the frequency of stockouts and thus provide better service to customers, and is an extension of Crack the Code – Understanding Safety Stock, which appeared in the  July, 2011 SCM Now issue.

Safety stock, sometimes called buffer stock or reserve stock, can be used to accommodate:

Variability in customer demand or in demand from downstream process steps (where demand history is used to set cycle stock or order points)
Forecast errors (where forecasts are used to set cycle stock targets or order points)
Variability in supply lead times
Variability in supply quantity
If these variabilities are random, and are reasonably normally distributed, the following calculations will result in appropriate safety stock levels. If not, they may still give some guidance, and are generally preferable to the sometimes recommended rules of thumb, that safety stock be set at 10 percent, or 20 percent, or 50 percent, of cycle stock.

Calculating Safety Stock

Variability in Demand

To understand how we can avoid stockouts in the face of variable customer demand, a short lesson in statistics is in order. Figure 1 is a histogram, a plot showing the number of cycles at which each demand range occurs. If we consider rolls of a specific grade of paper made on a paper forming machine, with an average demand of 130 rolls per weekly production cycle, the histogram shows how many weeks the true demand was within each range. The histogram shows that, for the 52 production cycles within a year, the demand was very close to the average for 12 of those weeks. In this plot, the width of each bar represents 10 rolls; so on these 12, the demand was between 125 and 135 rolls. It was somewhat higher, 135 to 145 rolls, during 8 weeks, and 145 to 155 rolls during 5 weeks. As the range of demand values goes higher, the number of weeks within that range decreases. There is a similar pattern on the other side of the average; for 8 weeks, the demand was between 115 and 125 rolls, and between 105 and 115 for 5 weeks. This bell shaped curve is typical of many demand patterns.

Some products will have little variability and thus a very narrow histogram, while others will have higher variability and a wider histogram. The width of the curve and the underlying variability can be characterized by a statistical property called standard deviation and symbolized by sigma, σ. While the calculation of standard deviation is beyond the scope of this discussion, understanding σ can help us calculate how much safety stock we need to give us various levels of protection against demand variability.     

If we carry no safety stock and have only the 130 rolls of cycle stock, that will be enough to satisfy all demand for this product on half the cycles; half the time demand will be at 130 rolls or less, and half the time greater. With no safety stock, we will be vulnerable to stockouts on half the cycles. Statistics teaches us that if we carry extra stock equal to one σ, that will be enough to cover demand on 84% of all cycles, as shown in figure 2. Sigma is 28 rolls for this product, so if we carry 28 rolls of safety stock in addition to the 130 rolls of cycle stock, that should be sufficient to prevent stockouts on 84% of the cycles, about 44 weeks. If we carry safety stock equal to 2 σ, that should cover 98% of the cycles, as shown in figure 3.    

Thus the key to determining safety stock is deciding on the tolerance for stockouts, and then using that to determine how many sigma’s of variability you need to cover. For example, if you decide that you can tolerate stockouts on no more than 2% of the cycles, that sets the cycle service level goal at 98%, and we saw in figure 3 that that requires 2 σ of safety stock, or 56 rolls.  The percentage of cycles you hope not to have stockouts is called cycle service level (CSL), and the number of sigmas required to achieve that is called the service level factor or the Z factor.

The general equation for safety stock required to cover demand variability is:

Figure 4 shows the relationship between Z and service level. As can be seen, the relationship is highly non-linear: higher service level values, i.e. lower potential for stockout, require disproportionally higher safety stock levels. Statistically, 100% service level is impossible.          

Typical service level goals are in the 90 to 98 percent range, but good inventory management practice suggests that rather than using a fixed Z value for all products, Z be set independently for groups of products based on strategic importance, profit margin, dollar volume, or some other criteria. Doing this will place more safety stock in those SKUs with greater value to the business, and less safety stock in the products believed to be less important to business success.

The above equation assumes that the standard deviation of demand is calculated from a data set where the demand periods are equal to the lead time or production cycle length. If not, an adjustment must be made to the standard deviation value to statistically estimate what the standard deviation would be if calculated based on the periods equal to the total lead time. As an example, if the standard deviation of demand is calculated from weekly demand data, and the lead time is 2 weeks, the standard deviation of demand calculated from a data set covering 2 week periods would be the weekly standard deviation times the square root of the ratio of the time units, or √2. Bowersox and Closs, in Logistical Management, use the term Performance Cycle (PC) to denote the total lead time. If we let T1 represent the time increments from which the standard deviation was calculated (1 week in the above example), PC to represent the total lead time or production cycle length, then

When procuring raw materials, the performance cycle includes the time to:

• Decide what to order (order interval or review period)
• Communicate the order to the supplier
• Manufacture or process the material
• Deliver the material
• Perform a store-in

Inside our own manufacturing facility, the performance cycle includes the time to:

• Decide what to produce
• Manufacture the material
• Release the material to the downstream inventory
• Return to the next cycle
• If we are carrying inventory in a finished product warehouse, and customers allow a delivery lead time greater than the time needed to deliver to the customer, then the remaining customer lead time can be subtracted from the Performance Cycle

The Performance Cycle can be considered the time at risk, i.e., the time between making a determination on how much to produce, and the time to make the next determination and have it realized.

If cycle stock has been calculated from historical demand, then the variance used in the safety stock calculation should be based on past demand variation. If forecasts are used to set cycle stock, then the thing requiring protection is forecast error. Standard deviation of forecast error would replace standard deviation of past demand in the safety stock formula, which would become:

It is critical that in these calculations, the same time units (days, weeks, etc.) be used for all variables.

If there is bias in the forecast, efforts must be made to improve the forecasting process to reduce and then eliminate the bias. Forecast bias will cause you to underestimate or overestimate the cycle stock needed.

It must be emphasized that the PC/T1 factor is a statistical adjustment to approximate the standard deviation of demand over the time period of the performance cycle and is just an approximation. It gives reasonable results in cases where the performance cycle is greater than the data collection time period, but can give very poor results going in the other direction, where PC is less than T1, especially when the time parameters are small, in going from weeks to days for example. If PC is much less than T1, you should try to measure demand variability or forecast error on a more frequent basis, to reduce T1 to a frequency closer to PC. Ideally, PC = T1 so that no adjustment is needed.

Seasonality

If seasonality is a significant cause for demand variability, it should be recognized and used to periodically adjust cycle stock to reflect the forecast demand during the various high and low periods. If not recognized, and treated as normal demand variability, it could cause a very high level of safety stock, while still not providing enough material to cover demand in the peak season.

 Variability in Lead Time

The equations in the preceding section calculate the safety stock needed to mitigate variability in demand or forecast error. If variability in lead time is of concern, the safety stock needed to cover that is:

The average demand term (Davg) is in the equation to convert standard deviation of lead time (σLT) expressed in time units into production volume units (such as cases, gallons, pounds, rolls).

Note that this equation needs no adjustment for Performance Cycle.

Combined Variability

If both demand variability and lead time variability are present, the safety stock required to protect against each can be combined statistically, to give a lower total safety stock than the sum of the two individual calculations. If demand variability and lead time variability are independent, i.e., the factors causing demand variability are not the same factors influencing lead time variability, and if both variabilities are reasonably normally distributed, the combined safety stock is Z times the square root of the sum of the squares of the individual variabilities:

The reasoning behind this is that if the two variabilities are independent, it is very unlikely that demand extremes will occur at the same time as very long lead times.

If σ_D and σ_LT are not statistically independent of each other, this equation can’t be used, and the combined safety stock is the sum of the two individual calculations.

Cycle Service Level and Fill Rate

The equations in the preceding sections will predict the safety stock needed so that a certain percentage, say 95 percent, of the replenishment cycles will be completed without a stockout. This is often called cycle service level (CSL).

Business leaders often want to control the percentage of total volume ordered that is available to satisfy customer demand, not the percentage of cycles without a stockout. The former quantity is called fill rate, and is often considered to be a better measure of inventory performance. Figure 5 illustrates the difference. Where cycle service level is an indication of the frequency of stockouts, without regard to the total magnitude, fill rate is a measure of inventory performance on a volumetric basis.

The specific calculations of safety stock required to achieve a desired fill rate are very complex and beyond the scope of this article. An excellent discussion can be found in Chopra and Meindl’s Supply Chain Management. However, some observations are in order. With stable demand patterns and supply behavior (that is, low standard deviations of demand and lead time) fill rate will generally be higher than cycle service level, as illustrated in Figure 6. Although stockouts will occur, with low supply and demand variability the magnitude of each stockout will be small.  

With high variability in either demand or lead time, or both, the opposite will usually be found. Figure 7 illustrates a case where demand variability is high, where the standard deviation of demand is half of the average demand. Although there are few stockouts (because of the safety stock being carried) the magnitude of any stockout can be quite high. Thus, in this case, the fill rate is actually less than the CSL.

Negative Safety Stock

Although it is very counterintuitive, with very stable demand patterns and modest fill rate targets (say, 95%), you might achieve that fill rate with negative safety stock. Anytime that the fill rate target plus the standard deviation of forecast error is less than 100%, acceptable performance can be realized with no safety stock, or even negative safety stock, i.e., less than calculated cycle stock.

For example, if fill rate target is 95% and the standard deviation of forecast error is 3%, you can meet the target with only 98% of the calculated cycle stock.

I’m certainly not recommending that you undercut cycle stock in these situations, only pointing out that it is theoretically possible.

Alternatives to safety stock

These calculations sometimes result in safety stock recommendations that are more than the business leaders feel they can afford to carry however there can be alternatives. Sometimes, an expediting process can be designed that can prevent a stockout when safety stock is not sufficient to cover all random variation. For example, if the goal is 98 percent CSL, safety stock can be reduced by 38 percent (Z factor of 1.28 rather than 2.05) if calculated to give a 90 percent CSL where a contingency plan can be defined to prevent stockouts in the other 8 percent of cycles. The contingency plan must be planned and agreed upon in advance. It is unacceptable to ignore this step, hoping that something can be figured out when the time comes.

This practice is especially appropriate with very expensive products, which are very costly to carry in inventory. In one specific example involving an expensive but relatively lightweight product, total supply chain cost was reduced significantly by carrying small amounts of safety stock in overseas warehouses and then relying on air freight to cover demand peaks. The cost of air freighting a small percentage of total demand was minimal compared to the cost of carrying large safety stocks of this highly valuable material on an ongoing basis.

Another alternative to carrying safety stock is to consider if Make To Order (MTO) is possible. If lead times allow it, MTO completely eliminates the need for any safety stock (or cycle stock for that matter.) If lead time commitments will not allow full MTO, Finish To Order (FTO) can locate the safety stock where it is generally far less differentiated, so that demand variability will be much less (on a relative basis) and safety stock requirements will be lower than they would be with finished product inventory. Customers will sometimes be willing to accept longer lead times for highly sporadic purchases, making FTO or MTO more of a possibility.

The appropriate use of safety stock, perhaps coupled with occasional expediting processes, is key to operations managers’ ability to serve their customers.

About the Authors

Peter L. King, CSCP, is a Principal Consultant at Zinata Inc. specializing in the application of lean concepts to process manufacturing and global supply chains. Prior to this, he spent 40 years with DuPont in a variety of manufacturing automation, project management and lean continuous improvement programs. King also is the author of several books on lean, including Lean for the Process Industries – Dealing with Complexity.

Courtney Bigler is a supply chain professional with a degree in Operations Management from the Univ of Delaware and 12 years’ experience in forecasting and demand management in the medical devices, bottled water, and craft beer industries.