Safety Stock Formula for a Late Truck and a Fast Week

Lamp L-14 sells about 8 units a day, and the supplier usually takes 6 days. Last month someone set the buffer at 60 units because the worst day and the worst lead time got multiplied together. Most of those units are still sitting. A safety stock formula should size that buffer from how much demand and lead time actually move, not from the scariest pair of numbers in the file. What is the safety stock formula? Safety stock is the extra units above average demand during lead time. One version subtracts a typical case from a worst case. The service-level version multiplies a z-score by demand variation and the square root of lead time. A late truck puts lead-time variation inside that same square root. How do you calculate safety stock without a z-score? The max-minus-average version needs no statistics. Subtract average daily demand times average lead time from maximum daily demand times maximum lead time. For L-14, treat the inputs as an example. Maximum daily demand is 12 and the average day is 8. Maximum lead time is 9 days against an average lead time of 6. The worst case multiplies 12 by 9 and gets 108. A typical wait is 8 times 6, so 48. Subtract and the buffer is 60 units, which is why this shortcut runs hot. That 60 assumes the busiest day and the slowest truck show up together and then stay that way for the whole wait. I'd use it for a handful of SKUs when you do not have a demand history worth a standard deviation. Past that, it ties up cash the average week never needs. How do you calculate safety stock with a service level? When lead time is steady and demand is the thing that moves, safety stock equals Z times the standard deviation of daily demand times the square root of lead time in days. Z comes from the service level you want during a replenishment cycle. That cycle service level is the chance you do not run out before the PO arrives. It is not the percent of units filled across the whole year. NC State's safety stock tutorial separates those two ideas, and it notes that fill rate usually lands higher than the cycle service level you planned. NIST's normal table lists the z value for a 95 percent cumulative probability as 1.645. The 90 percent value is 1.282. The 99 percent value is 2.326. L-14's daily demand has a standard deviation of 3 units in this example. Lead time is a fixed 6 days. The square root of 6 is about 2.449. Three times 2.449 is about 7.348. At 95 percent, 1.645 times 7.348 is about 12.1. Round up to 13 units, because you cannot stock a fraction of a lamp. The 99 percent case uses 2.326 times that same 7.348, about 17.1, which rounds up to 18 units. On this SKU the step from 95 to 99 percent adds 5 units, not a second pile of 13. What changes when lead time moves around? Ignore a wobbly supplier and the buffer is too small. An MIT manufacturing note combines the two when demand variation and lead-time variation are independent: Z times the square root of lead time times demand variance, plus average demand squared times lead-time variance. Keep the same example lamp. Average demand is 8, and demand variance is 3 squared, which is 9. Lead time of 6 makes the demand piece 6 times 9, or 54. Lead-time standard deviation is 1.5 days, so its variance is 2.25. Average demand squared is 64, and 64 times 2.25 is 144. That 144 is the late-truck piece. Inside the root: 54 plus 144 is 198. The square root of 198 is about 14.07. Times 1.645 is about 23.1. Round up to 24 units. Method on the same lamp Safety stock Worst day times worst lead time, minus the average case 60 Z of 1.645, demand variation only, lead time fixed at 6 days 13 Z of 1.645, demand variation plus a 1.5-day lead-time swing 24 The jump from 13 to 24 is the late truck. If your receipts really do swing by a day and a half, the fixed-lead-time formula will look neat and still stock you out. Where does safety stock sit in the reorder point? Reorder point equals average demand times lead time, plus this buffer. With the 24-unit result, L-14's trigger is 8 times 6 plus 24, which is 72. With the 13-unit result, the trigger is 48 plus 13, which is 61. Those are different buys. Do not paste the 60 from the max method onto a reorder point you also built with a z-score. You would be buffering the same lamp twice, on two different stories. Demand planning in OneChannelAdmin is where that buffer can sit next to the forecast that feeds it. The units themselves are inventory management. A lead time you measure from real receipts is only as good as the purchase orders in order fulfillment. How do you pick a safety stock number? Run one SKU the whole way before you copy a z-score across the catalog. Measure average daily demand and the standard deviation of daily demand from recent history. Skip stockout days if a zero that day means you had nothing to sell. Measure average lead time, and the standard deviation of lead time, from PO date to sellable receipt. Pick a cycle service level. Use NIST's table for Z: 1.282 at 90 percent, 1.645 at 95 percent, 2.326 at 99 percent. If lead time barely moves, multiply Z by the daily demand deviation and by the square root of lead time. If lead time moves, use the combined square root so the late truck is in the buffer. Round up to a whole unit. Add it to average demand times lead time. That sum is the reorder point, not a second safety stock. A items can justify 99 percent. A slow accessory often cannot. The holding cost of 18 versus 13 on L-14 is small. The same gap on a $400 sofa is not. Recalculate the deviation after a rough quarter, not every Monday. One wild week can inflate it and leave you holding that spike for a year. If you drop the week because it was a stockout or a one-off promo, write the reason down, or the next planner puts the week back in. This z-score also assumes the daily noise is roughly bell-shaped. A SKU that sells nothing most days and 30 units once a week will not behave like L-14, even if the average lands near 8. Keep the formula for items that sell on most days. For the lumpy ones, forecast the size of a sale and the gap between sales, then build the buffer from that pattern instead. Questions about the safety stock formula What is the safety stock formula when lead time is fixed? Z times the standard deviation of demand per period, times the square root of lead time. Z is 1.645 for a 95 percent cycle service level on NIST's normal table. Round the result up to a whole unit. What is the safety stock formula when the supplier is late sometimes? Put lead-time variance in the same square root as demand variance. Multiply Z by the square root of lead time times demand variance, plus average demand squared times lead-time variance. Use this when the two kinds of noise are independent. Is safety stock the same as the reorder point? No. Safety stock is only the buffer. The reorder point is average demand during lead time plus that buffer. Ordering at the safety stock number alone reorders too late. Why is the max-minus-average buffer so much larger? It multiplies the busiest day by the slowest lead time, then subtracts the average case. On L-14 that produced 60 units, against 13 units from a 95 percent z-score with a fixed lead time. The max method is a blunt cover when you have little history. Does a higher service level double the buffer? Not as a rule. On this lamp, 95 percent needed 13 units and 99 percent needed 18. Check the arithmetic for the SKU. The z-score rises faster than the service percentage, and the unit impact still depends on your variation. OneChannelAdmin Team writes about safety stock, reorder points, and the units those formulas are supposed to protect.