The formula worked on one part number, and the trap that catches it whenever the lead time is longer than the order cycle.
The reorder point is expected demand over the lead time plus safety stock: ROP = d × L + z × σLT. For part AF-7, which sells 1,840 units a week on a six-week lead time, that is 11,040 + 7,547 = 18,587 units at a 98 per cent cycle service level. Because the lead time is longer than the order cycle, the 18,587 must be compared with stock on hand plus stock on order, never with stock on hand alone.
Worked in full in Supply Chain Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A reorder point answers one question: at what level of stock do we place the next order so that, with the agreed probability, it arrives before the shelf is empty? Everything in it comes from four numbers about demand and the supplier, plus one decision about service.
| Input | Value |
|---|---|
| Mean weekly demand d | 1,840 units |
| Standard deviation of weekly demand σd | 462 units |
| Mean lead time L | 6 weeks |
| Standard deviation of lead time σL | 1.9 weeks |
| Cycle service level voted by the board | 98% |
| z at 98% | 2.0537 |
| Economic order quantity Q | 4,384.5 units |
=B2*B4+NORM.S.INV(B6)*SQRT(B4*B3^2+B2^2*B5^2) with d, σd, L, σL and the service level in B2 to B6The second term of the variance is nearly ten times the first. On this part the supplier's lead time, not the market, creates nine tenths of the uncertainty, which is why the safety stock is so large relative to weekly demand. The full derivation of that buffer is in how to calculate safety stock when lead time varies.
Set 18,587 against what the warehouse can physically hold of this part. AF-7 is bought in batches of 4,384.5 units, one every 2.38 weeks. Just after a delivery the shelf holds, on average, the safety stock plus one batch, about 11,931 units. On average it holds 9,739, worth 278,534 EUR. The reorder point is 6,655 units higher than that typical peak.
That is not an error in the formula. The lead time of six weeks covers 2.52 order cycles, so at any moment two or three orders are already on the way. The reorder point is a target for the inventory position: stock on hand, plus open purchase orders, less any backorders.
| Line | Monday A | Monday B |
|---|---|---|
| Stock on hand | 9,200 | 9,200 |
| Open purchase orders | 8,770 | 13,155 |
| Inventory position | 17,970 | 22,355 |
| Reorder point | 18,587 | 18,587 |
| Decision | Order | Wait |
Both Mondays show the same 9,200 units on the shelf. On Monday A two batches are open and the position sits 617 units below the trigger, so a third order goes out. On Monday B three batches are already open and the position is 3,768 units above it. A planner reading only the shelf would order on both days, and on almost any day, because the shelf practically never reaches 18,587.
The rule of thumb: if d × L is larger than Q, the reorder point will exceed anything the shelf can hold, and a system that triggers on stock on hand will order at every review. Check which quantity your ERP compares with the reorder point before trusting the parameter.
| Cycle service level | z | SS, σL 1.9 wk | ROP, σL 1.9 wk | SS, σL 0.5 wk | ROP, σL 0.5 wk |
|---|---|---|---|---|---|
| 90.0% | 1.28 | 4,709 | 15,749 | 1,869 | 12,909 |
| 95.0% | 1.64 | 6,044 | 17,084 | 2,399 | 13,439 |
| 98.0% | 2.05 | 7,547 | 18,587 | 2,995 | 14,035 |
| 99.0% | 2.33 | 8,548 | 19,588 | 3,393 | 14,433 |
| 99.5% | 2.58 | 9,465 | 20,505 | 3,757 | 14,797 |
Raising the service level from 98 to 99.5 per cent adds 1,918 units to the reorder point. Making the supplier regular, taking the lead-time spread from 1.9 weeks to 0.5, removes about 4,551. The board argues about the first column; the money sits in the second.
If the part is reviewed weekly rather than continuously, the lead time in the formula becomes the review period plus the lead time. The order-up-to level is then 1,840 × 7 = 12,880 plus a safety stock of 7,606, or 20,486 units. The weekly review costs only 59 extra units of buffer, because it lengthens the exposure to demand noise, which is the small part of the variance.
Comparing the trigger with stock on hand. Covered above, and the most expensive of the three because it is invisible in the parameter file: the reorder point looks right and the stock still doubles.
Mixing time units. Demand per week, lead time in days and a standard deviation measured per month cannot go into the same formula. Type AF-7's lead time as 42 days against weekly demand and the reorder point becomes 86,733 units, 68,146 too many, which would pull about 1,948,990 EUR of extra stock into the pipeline before anyone noticed. Convert everything to one grain first, as the AF-7 case does in weeks.
Dropping the lead-time term. With demand variance only, the reorder point falls to 13,364 and the board's 98 per cent becomes about 73.6 per cent in practice: some 5.8 stock-outs a year across 21.8 order cycles, against 0.4. Why the variances must be added, and what each source contributes, is the subject of the safety stock article linked above.
The free workbook for this case, on the Supply Chain Management companion page, carries AF-7's demand, lead time and service level table with every input in a blue cell, so the reorder point can be rebuilt for your own part number.
With the inventory position: stock on hand plus open purchase orders, less backorders. For part AF-7 the reorder point is 18,587 units but stock on hand never exceeds about 11,931, because 2.52 orders are in transit on average. Compared with stock on hand, the trigger would fire at every review and the stock would balloon.
Safety stock is the buffer; the reorder point is the trigger. The reorder point adds the expected demand over the lead time to the safety stock. For AF-7 the expected demand over six weeks is 11,040 units and the safety stock 7,547, so the reorder point is 18,587. Only the 7,547 is expected to be on the shelf when the order lands.
Replace the lead time with the review period plus the lead time. Reviewing AF-7 weekly, demand over seven weeks is 12,880 units and the safety stock rises to 7,606, so the order-up-to level is 20,486. The weekly review adds only 59 units of buffer because nine tenths of the uncertainty comes from the supplier's lead time, not from demand.
This article is one calculation from Supply Chain Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: business operations: cost, contracts, pricing and supply chain → · All 681 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.