Deciding "How Many Times the Average to Keep in Stock" in Demand Planning — How Safety Stock Works

Some companies decide how much inventory to hold with a multiplier, such as “twice the average” or “one month’s worth.” It is an easy rule to understand, but there is no basis for saying what the multiplier should be. You end up repeating adjustments: raise the multiplier for items that kept running out, lower it for items left over.

This article explains how to set an inventory target with the idea of “safety stock” instead of a multiplier. The short answer is that safety stock is not some multiple of the average; it is determined by four things: demand variability, the lead time, the ordering policy, and how strongly you want to avoid stockouts. The formulas are simple enough to calculate in a spreadsheet, and a worked example using Excel functions is included.

The scope is inventory that is replenished and used, such as goods bought for resale or parts. The formulas are the standard ones taught in logistics and inventory management lecture materials, and every number in the worked examples is a fictitious value made up for explanation. The formulas rest on assumptions and some items do not fit them, so the last section covers how to tell those items apart.

Why “a multiple of the average” cannot decide it

Suppose two items each sell an average of 20 units a day. Item A sells steadily, between 18 and 22 units every day. Item B sells 5 units on some days and 40 on others. Because the averages are the same, deciding by “a multiple of the average” gives them the same inventory, but item B is clearly the one more likely to run out.

You hold more than the average so that you do not run out even if more sells than expected between placing an order and receiving it. How much extra you need depends on how much sales fluctuate, how many days delivery takes, when you place orders, and how far you tolerate stockouts. The size of the average does not appear in the safety stock formula, except when the delivery date varies.

flowchart TB
        accTitle: Four factors that determine safety stock
        accDescr: Shows that safety stock is determined by four factors: demand variability, lead time and its variability, the ordering policy, and the target service level.
        A["Demand variability"] --> SS["Safety stock"]
        B["Lead time"] --> SS
        C["Ordering policy"] --> SS
        D["Service level"] --> SS

Figure 1: Safety stock is determined by four things: demand variability, lead time, ordering policy and service level.

In the diagram a solid line marks a relation that always holds and a dashed line marks a conditional one (the conditions are given per relation on the detail page). The full list of relations (10 in total, with evidence and certainty) and the definitions of the main concepts are collected on the knowledge map detail page (in Japanese). Data: JSON-LD / Turtle

Safety stock and the reorder point

Consider a policy in which you watch the inventory level and place an order when it falls to a set level. The inventory level that triggers this order is called the reorder point. The time from placing an order to receiving the goods is the lead time, and the demand that goes out during that time is called lead-time demand¹.

The reorder point is the average lead-time demand plus the safety stock. Put another way, safety stock is what remains after subtracting the average lead-time demand from the reorder point: a margin for when more sells than average¹².

flowchart TB
        accTitle: One cycle of a reorder point policy
        accDescr: Shows one cycle in which an order is placed when inventory falls to the reorder point, inventory keeps falling during the lead time, and inventory recovers when the goods arrive, and that the reorder point consists of average demand and safety stock.
        A["Inventory falls"] --> B["Falls to the reorder point"]
        B --> C["Place an order"]
        C --> D["Lead time (until delivery)"]
        D --> E["Goods arrive and inventory recovers"]
        E --> A
        B -.-> F["Reorder point = average lead-time demand + safety stock"]

Figure 2: The reorder point is made up of what sells at the average rate until delivery and a margin (safety stock) for when more than average sells.

If sales during the lead time match the average, the safety stock is what remains on hand when the goods arrive. Even if more than average sells, there is no stockout as long as the difference fits within the safety stock. Deciding how much safety stock to hold means deciding “how much more than average you prepare for.”

Expressing demand variability with the standard deviation

How much sales fluctuate can be expressed as the standard deviation of past sales. The standard deviation is a value that shows how far data is spread out from its average. In Excel you can calculate it with the STDEV.S function, which treats the data you pass as a sample and divides by n−1³.

A standard deviation computed from daily sales is the fluctuation for one day. If the lead time is 9 days, what you need is the fluctuation of 9 days of demand. When each day’s demand can be treated as independent of the others, the variability (variance) of L days of demand is L times that of one day, and the standard deviation is √L times as large².

flowchart TB
        accTitle: Deriving the lead-time standard deviation from the daily standard deviation
        accDescr: Shows the flow of computing the one-day standard deviation from daily sales and multiplying by the square root of the number of lead-time days to get the standard deviation of lead-time demand.
        A["Daily sales"] --> B["One-day standard deviation (STDEV.S)"]
        B --> C["Multiply by √lead time (days)"]
        C --> D["Standard deviation of lead-time demand"]

Figure 3: The fluctuation of lead-time demand is the one-day standard deviation multiplied by the square root of the number of lead-time days.

The fluctuation over 9 days is not 9 times the one-day figure but 3 times (√9). This is because high and low days offset each other, so even when the lead time gets longer, safety stock does not grow in proportion to the number of days. This offsetting, however, assumes that each day’s demand is independent.

Service level and the safety factor

Cycle service level

The service level puts a number on how far you want to avoid stockouts. A commonly used one is the cycle service level, which is the probability that no stockout occurs within one replenishment cycle²¹. At 95%, a stockout can occur during the lead time in roughly 1 out of 20 replenishments.

If lead-time demand is treated as following a normal distribution, the cycle service level determines a safety factor k, and the safety stock is k multiplied by the standard deviation of lead-time demand². The normal distribution spreads symmetrically around its mean, and the one with mean 0 and standard deviation 1 is called the standard normal distribution⁴. k is the point at which the cumulative probability of the standard normal distribution equals the cycle service level, and in Excel it can be found with the NORM.S.INV function⁵.

flowchart TB
        accTitle: Deriving safety stock from the cycle service level
        accDescr: Shows the flow of finding the safety factor from the target cycle service level with NORM.S.INV, multiplying by the standard deviation of lead-time demand to get the safety stock, and adding average demand to get the reorder point.
        A["Target cycle service level"] --> B["Safety factor k (NORM.S.INV)"]
        B --> C["Safety stock = k × lead-time standard deviation"]
        C --> D["Reorder point = average lead-time demand + safety stock"]

Figure 4: Find the safety factor from the target service level and multiply by the standard deviation to get the safety stock.

The safety factors for common service levels, computed with NORM.S.INV, are as follows (to four decimal places).

Raising the level by 3 points from 95% to 98% increases k by about 0.41, while raising it just 1 point from 98% to 99% increases it by about 0.27. The higher the target, the more safety stock each additional point costs. Inventory balloons as you approach 100%, so rather than setting every item uniformly to 99%, one option is to set higher levels for items where a stockout has a bigger impact.

How it differs from the fill rate

There is another service level measure called the fill rate. It is the share of demand filled immediately from stock¹². While the cycle service level counts “whether a stockout occurred,” the fill rate counts “how much was short.”

The two values can differ greatly. In an example from University of Iowa lecture material, with an order quantity of 500 units and lead-time demand averaging 150 units with a standard deviation of 50, a safety factor of 0.9 is enough to reach a 99% fill rate target. The cycle service level in that case is 81.6%, so a stockout occurs with 18.4% probability on each replenishment¹. The fill rate is computed as 1 minus the expected shortage divided by the order quantity, so with a large order quantity a stockout is small as a proportion even when it happens².

flowchart TB
        accTitle: Difference between cycle service level and fill rate
        accDescr: Shows that the cycle service level is the probability that no stockout occurs in one replenishment cycle and the fill rate is the share of demand filled from stock, and that the two can differ greatly for the same inventory.
        S["The same safety stock"] --> C["Cycle service level"]
        S --> F["Fill rate"]
        C -.-> C2["Probability of no stockout in one cycle"]
        F -.-> F2["Share of demand filled from stock"]

Figure 5: Even with the same inventory, the service level value changes greatly depending on whether you count the number of stockouts or the quantity short.

When you say “a 95% service level,” decide first which measure the 95% refers to. The worked examples in this article use the cycle service level, whose formula is simpler.

A worked example in Excel

From here on, the calculation uses fictitious numbers. Item A sells 20 units a day on average, the standard deviation of daily sales is 6 units, and the lead time is 9 days and never varies. The target is a 95% cycle service level.

B2:B61 is assumed to hold daily sales for the past 60 days. The “Result” column shows the values when the average and standard deviation come out at exactly 20 and 6. The safety stock is about 30 units and the reorder point about 210 units. If you order when inventory (including quantities already ordered but not yet received) falls to 210 units, the probability of a stockout before the goods arrive 9 days later is about 5%.

flowchart TB
        accTitle: Steps in the worked example
        accDescr: Shows the steps of finding the average and standard deviation from the past 60 days of sales, finding the safety factor from the service level, multiplying by the square root of the lead time to get the safety stock, and adding average demand to get the reorder point.
        A["Past 60 days of sales"] --> B["Average 20, standard deviation 6"]
        B --> C["9-day standard deviation = 6 × 3 = 18"]
        D["95% → k = 1.6449"] --> E["Safety stock = 1.6449 × 18 ≈ 30"]
        C --> E
        E --> F["Reorder point = 20 × 9 + 30 ≈ 210"]

Figure 6: Calculate the safety stock and reorder point in turn from four values: average, standard deviation, lead time and service level.

Like item B at the start, if the average is the same 20 units but the standard deviation is three times larger at 18 units, the safety stock is also three times larger, about 89 units. Conversely, if almost the same number sells every day and the standard deviation is 2 units, a safety stock of about 10 units is enough. Even with the same average, the safety stock needed differs greatly from item to item.

When the lead time varies

So far the lead time has been a constant 9 days every time. In practice, the number of days until delivery can vary because of the supplier. When the lead time varies with a mean of μ_L days and a standard deviation of σ_L days, the standard deviation of lead-time demand is found with the following formula¹.

Standard deviation of lead-time demand = √( μ_L × σ_d² + μ_d² × σ_L² )
  μ_d: average daily demand   σ_d: standard deviation of daily demand
  μ_L: average lead time (days)   σ_L: standard deviation of lead time (days)

The first term comes from demand fluctuation and the second from fluctuation in the delivery date. For item A in the worked example, if the lead time varies with a mean of 9 days and a standard deviation of 2 days, this is √(9 × 36 + 400 × 4) = √1924 ≈ 43.9. The safety stock is 1.6449 × 43.9 ≈ 72 units, more than twice the roughly 30 units when the lead time is constant.

flowchart TB
        accTitle: How lead-time variability adds to safety stock
        accDescr: Shows that the variability of lead-time demand consists of a part from demand fluctuation and a part from delivery-date fluctuation, and that safety stock is the combined standard deviation multiplied by the safety factor.
        A["Demand fluctuation (μ_L × σ_d²)"] --> C["Standard deviation of lead-time demand"]
        B["Delivery-date fluctuation (μ_d² × σ_L²)"] --> C
        C --> D["Safety stock = k × standard deviation"]

Figure 7: When the delivery date varies, safety stock needs a margin for that on top of demand fluctuation.

The lecture material points out that a long lead time with no variability can sometimes require less safety stock than a lead time that is shorter on average but varies a lot¹. When comparing suppliers, record and compare not only the average number of days but also how much the delivery date varies.

When you order on fixed days

There is also a policy of checking inventory and ordering at fixed intervals, such as ordering every Monday. Each time, the order quantity is set to bring inventory back up to a certain level (the order-up-to level). With this policy you need to cover demand for R + L days: the interval R until the next order plus the lead time L until delivery⁶.

flowchart TB
        accTitle: Coverage period under a reorder point policy and a periodic review policy
        accDescr: Shows that under a reorder point policy safety stock covers demand over the lead time, while under a periodic review policy it covers demand over the order interval plus the lead time.
        A["Reorder point policy"] --> A2["Coverage period = lead time L"]
        B["Periodic review policy"] --> B2["Coverage period = order interval R + lead time L"]
        A2 --> S["Safety stock = k × standard deviation over that period"]
        B2 --> S

Figure 8: When you order on fixed days, the period until the next order day is also part of the period whose fluctuation you must cover.

If item A in the worked example is switched to ordering every 7 days, the coverage period is 7 + 9 = 16 days. The 16-day standard deviation is 6 × √16 = 24 units, and the safety stock is 1.6449 × 24 ≈ 39.5 units. It is more than the roughly 30 units under the reorder point policy because inventory is not checked between order days, so safety stock also has to absorb the fluctuation over that period. The order-up-to level is 20 × 16 + 39.5 ≈ 360 units. At each order, you order this level minus the inventory position (inventory on hand plus quantities ordered but not yet received, minus backorders)⁶.

Items this formula does not fit

The formulas so far assume that demand follows a normal distribution and can be treated as independent from day to day. If you apply them to items that do not fit these assumptions, the safety stock may come out too large or too small.

flowchart TB
        accTitle: What to check before applying the formula
        accDescr: Shows checking, for each item, whether it has intermittent demand with many days without sales, whether it has seasonality or a trend, and whether it is a new item with no history, and not using the basic formula as is when one of these applies.
        A["Check the item"] --> B["Many days without sales (intermittent demand)"]
        A --> C["Has seasonality or a trend"]
        A --> D["New item with no sales history"]
        A --> E["None of these"]
        B -.-> B2["Normal distribution assumption fits poorly"]
        C -.-> C2["Use the variability of forecast error"]
        D -.-> D2["Variability cannot be measured"]
        E -.-> E2["Use the basic formula"]

Figure 9: Before applying the formula, check whether the shape of demand fits its assumptions.

Items with many days without sales

Some items, such as repair parts, go many days without selling and then sell in batches when they do. Such demand is called intermittent demand, and it is characterized by many periods of zero demand⁷. With intermittent demand, how to represent the distribution of lead-time demand is the hard part of inventory management, and there is research showing that the normal distribution can be used only when demand variability (the coefficient of variation) is small⁷. For such items, methods that fit other distributions, such as the gamma, Poisson and negative binomial distributions, have been studied⁷.

Items with seasonality or a trend

For items that sell in summer or grow year by year, the standard deviation of daily sales also includes the predictable changes due to the season or trend. MIT lecture material explains that the standard deviation used to compute safety stock is technically the root mean square error (RMSE) of the forecast over the lead time, and that substituting the standard deviation of demand amounts to treating the forecast as the average². If seasonality and trends are built into the forecast, use the variability of the difference between forecast and actual rather than sales themselves.

New items with no sales history

A new item has no past sales, so the standard deviation cannot be calculated. The amount has to be decided outside the calculation, for example by referring to the history of similar items. Once history accumulates, recalculate with the formulas in this article.

Checking the chosen safety stock in operation

A calculated safety stock stops fitting when the underlying numbers (average, standard deviation, lead time) change. When the sales trend changes, or when you change suppliers or shipping methods, it is time to recalculate.

Also check whether the service level you targeted is actually being achieved. For the cycle service level, record for each item the share of replenishment cycles in which a stockout occurred. Items with more stockouts than targeted may have underlying numbers that no longer match reality, or may be items that do not fit the formula’s assumptions (normal distribution, independence). The advantage of deciding with a formula is that, instead of nudging a “multiple of the average” up and down, you can investigate which number is off.

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References

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Frequently Asked Questions

Questions commonly asked at the time of consultation about the topic of this article.

How many times average demand should I keep in stock?

A multiplier alone cannot decide it. Safety stock depends on demand variability (standard deviation), the lead time from ordering to delivery, the ordering policy, and how strongly you want to avoid stockouts (the service level). Even for items with the same average, if the variability is three times larger, the safety stock is three times larger too.

What is the basic safety stock formula?

When you consider only demand variability and the lead time can be treated as constant, safety stock = safety factor × standard deviation of daily demand × √lead time (in days). The reorder point is the average demand during the lead time plus the safety stock. The safety factor is derived from the cycle service level using the normal distribution; for 95% it is about 1.645.

Does a 95% service level mean 95% of orders can be filled?

A 95% cycle service level means a 95% probability that no stockout occurs within one replenishment cycle. It is a different measure from the share of ordered quantity shipped from stock (the fill rate), and the two can differ greatly for the same inventory. Decide first which one you are targeting.

Are there items this formula does not work for?

For items with intermittent demand, which sell on few days with long runs of days without sales, the assumption that demand follows a normal distribution fits poorly. For items with clear seasonality or trends, use the deviation of forecasts from actuals (forecast error) rather than the variability of demand itself. For new items with no sales history, the variability cannot be measured.

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Go Komura

Representative of KomuraSoft LLC

Focused on Windows software development, technical consulting, and bug investigation, with particular strength in projects where existing assets remain and in investigating failures whose cause is hard to see.