Safety stock & reorder points

An inventory norm is a standing rule for one item at one location: reorder coffee beans when 26 kg are left, or keep about 10 days of shampoo at the Pune warehouse. Every norm answers two everyday questions:

1. When do I reorder? Early enough that new stock lands before the shelf runs dry.
2. How much extra do I keep for surprises? Busy days happen, and trucks run late.

Picture a café that uses about 4 kg of coffee beans a day. Its supplier takes 5 days to deliver, so the café burns through roughly 20 kg while an order is on its way. It has to reorder before stock falls to 20 kg, and it needs a cushion on top for the days when customers drink more or the truck turns up late. That cushion is safety stock.

Norms matter because they decide how much cash sits on shelves and how often customers hear “sorry, we’re out”. Set them too high and money gets stuck in stock that may go stale. Set them too low and you lose sales.

Step 1: demand during the wait

If you sell $d$ units a day and the supplier takes $L$ days, you expect to use $d \times L$ while you wait. In a perfectly predictable world, that would be the whole reorder point:

For the café, $4 \times 5 = 20$ kg.

Step 2: a buffer for demand that wobbles

Daily demand is never exactly 4 kg. If a typical day strays from the average by $\sigma_d$, then demand over $L$ independent days strays by $\sigma_d\sqrt{L}$, not $\sigma_d \times L$, because good and bad days partly cancel. To cover that wobble at a chosen service level, multiply by $z$, the number of standard deviations of protection:

Step 3: a buffer for a supplier who runs late

When the delivery time itself varies by $\sigma_L$ days, the two kinds of uncertainty combine:

Say the café’s truck usually takes 5 days but sometimes 4, 6 or 7, so $\sigma_L = 1$ day. Then $5 \times 1.5^2 + 4^2 \times 1^2 = 11.25 + 16 = 27.25$. Its square root is 5.22 kg, and safety stock rises to $1.645 \times 5.22 \approx 8.6$ kg. One day of delivery uncertainty moves the reorder point from 25.5 kg to about 28.6 kg.

Step 4: say it in days of supply

Managers usually talk in days rather than kilograms, so divide by average daily demand:

• Safety stock: $8.6 \div 4 \approx 2.2$ days of supply.
• Average stock on hand is about half an order plus the buffer. With the café’s usual order of 77.5 kg, that is $77.5 \div 2 + 8.6 \approx 47$ kg, roughly 12 days of supply.

A norm like “keep 12 days” is easy to communicate, but it should come out of this calculation. A blanket number copied across every item ignores how differently each one behaves.

Why the square root of lead time

Expected demand adds up day by day: five days of 4 kg is 20 kg. Uncertainty does not add that way. Variances add, and the standard deviation is the square root of the variance:

So doubling the lead time multiplies the buffer by about 1.41, not 2. This assumes days are independent. If demand runs in streaks, where one busy day tends to follow another, the real variability is larger and the square-root rule understates the buffer.

A faster supplier is not always the better one

Compare two suppliers for the café, both at 95% service ($z = 1.645$, $\sigma_d = 1.5$ kg, $d = 4$ kg a day, orders of 77.5 kg):

Supplier B is two days faster, yet the café ends up holding about 19% more stock on average. The reason is the $d^{2}\sigma_L^{2}$ term: delivery uncertainty is multiplied by demand. At a factory using 1,000 units a day, a single day of delivery variation is worth 1,000 units of uncertainty on its own. Reliability, not just speed, is what lets you hold less.

The service-level trap

Service is not free, and it gets expensive quickly:

Each extra point of service near 100% needs more buffer than the one before. That is why companies set different targets for different items: perhaps 98–99% for a critical spare part, 95% for a regular component and 90% for a cheap, slow-moving item. Inventory segmentation (ABC-XYZ) is how those targets get assigned.

Use forecast error, not raw demand variability

The formulas use $\sigma_d$, the variability of demand. But most companies forecast, so what really hurts is how wrong the forecast is. In practice $\sigma$ should be the standard deviation of forecast error over the lead time (the RMSE, if the forecast is unbiased). A better forecast shrinks the buffer, and a biased forecast quietly breaks it. This is where forecast accuracy and inventory meet.

Reorder on inventory position, not on what is on the shelf

Suppose the café orders 77.5 kg at 26 kg, and two days later the shelf shows 18 kg. A system that only looks at stock on hand sees 18 < 26 and orders again, even though 77.5 kg is already on the way. The fix is to compare the reorder point with inventory position:

Here that is $18 + 77.5 = 95.5$ kg, well above 26, so nothing new is ordered. Duplicate orders right after a large purchase are a classic sign that a system is checking the shelf instead of the position.

How companies actually set norms

Most companies move through three stages:

1. Rules of thumb. “Two weeks of stock for everything”, kept in spreadsheets. Easy to explain and wrong for most items.
2. Statistical safety stock per item and location. The formulas on this page, recalculated every planning cycle, usually inside the ERP or a planning tool. In SAP, for example, the results typically end up as the safety stock and reorder point in the material master’s planning data.
3. Multi-echelon optimization. Buffers sized across plant, warehouse and store together, so the network holds less in total than each site would on its own. Planning platforms such as SAP IBP, o9, Kinaxis and Blue Yonder sell this as inventory optimization.