The (R, S) policy worked on one stocked part: the protection interval, the order-up-to level, the order placed at each review, and why the review period costs less buffer than textbooks suggest when the supplier is unreliable.
In a periodic review system the safety stock must cover demand over the review period plus the lead time, not the lead time alone: SS = z × √((R + L) × σd² + d² × σL²). For part AF-7 in Supply Chain Management, reviewed every two weeks with a six-week lead time, that is 7,665 units, and an order-up-to level of 22,385. Because most of AF-7's uncertainty is the supplier's lead time, the review period adds only 1.6 per cent to the buffer.
Worked in full in Supply Chain Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Under continuous review, an order goes out the moment the inventory position touches the reorder point, so the only exposure is the lead time. Under periodic review, stock is checked every R weeks and topped up to a fixed level S. An order placed today arrives after L weeks, but the next chance to order is R weeks away, so today's order has to carry the part until the delivery that follows the next review. The protection interval is R + L.
Only the demand term stretches with it. The lead-time term, d² × σL², is the spread of a single delivery date and does not grow because you review less often.
Aldermere Filtration's part AF-7, the book's fictional case.
| Input | Value |
|---|---|
| Mean weekly demand d, units | 1,840 |
| Standard deviation of weekly demand σd | 462 |
| Mean lead time L, weeks | 6 |
| Standard deviation of lead time σL, weeks | 1.9 |
| Review period R, weeks | 2 |
| Cycle service level; z | 98%; 2.0537 |
| Holding cost per unit a year; cost per order, EUR | 3.8324; 385 |
Step 1: the variance over the protection interval of 8 weeks.
Demand part = 8 × 462² = 1,707,552
Lead-time part = 1,840² × 1.9² = 12,222,016
σR+L = √13,929,568 = 3,732.2 units
Step 2: safety stock and the order-up-to level.
SS = 2.0537 × 3,732.2 = 7,665
S = 1,840 × 8 + 7,665 = 14,720 + 7,665 = 22,385
Excel: =d*(R+L)+NORM.S.INV(CSL)*SQRT((R+L)*sd^2+d^2*sL^2)
Step 3: the order at each review. Order S minus the inventory position, which is stock on hand plus stock on order less backorders. If the position at a review is 15,000, the order is 22,385 − 15,000 = 7,385. On average the orders equal demand over the review period, 3,680, but each one varies with what was sold.
Step 4: compare with continuous review. The same part under a reorder point policy needs σL over 6 weeks only, 3,674.6, so a safety stock of 7,547 and a reorder point of 18,587, as worked in how to calculate a reorder point with safety stock. Periodic review costs 118 more units, 1.6 per cent.
Average stock under (R, S) is half the average order plus safety stock: 1,840 + 7,665 = 9,505 units. Holding that, plus 26 orders a year, costs 46,437, against 45,725 for continuous review at the EOQ. The longer the review, the fewer the orders but the more stock.
| R, weeks | σ over R + L | Safety stock | Order-up-to S | Orders a year | Holding + ordering, EUR | SS vs continuous |
|---|---|---|---|---|---|---|
| 1 | 3,704 | 7,606 | 20,486 | 52.0 | 52,695 | +0.8% |
| 2 | 3,732 | 7,665 | 22,385 | 26.0 | 46,437 | +1.6% |
| 3 | 3,761 | 7,724 | 24,284 | 17.3 | 46,851 | +2.3% |
| 4 | 3,789 | 7,782 | 26,182 | 13.0 | 48,931 | +3.1% |
| 8 | 3,900 | 8,010 | 33,770 | 6.5 | 61,405 | +6.1% |
The cheapest review period sits next to the economic order interval, the EOQ of 4,384.5 units divided by weekly demand, or 2.38 weeks. Two weeks is the practical choice. The safety stock barely moves with R because 87.7 per cent of the variance over the protection interval is the supplier's lead time.
Then the whole buffer is demand variance, it scales with √(R + L), and the review period matters much more.
| R, weeks | Safety stock | vs continuous (2,324) |
|---|---|---|
| 1 | 2,510 | +8.0% |
| 2 | 2,684 | +15.5% |
| 4 | 3,000 | +29.1% |
| 8 | 3,550 | +52.8% |
The textbook warning that periodic review needs a lot more safety stock is true for a reliable supplier. For an unreliable one the lead-time term swamps it, and the choice between the two policies can be made on administrative grounds: grouped orders, fixed delivery days, fewer reviews.
The common mistake is to reuse the reorder point formula and set S to demand over the lead time plus safety stock, leaving R out of the mean. For AF-7 that gives an order-up-to level of 18,705, 3,680 units short, and the service actually delivered falls from 98 per cent to 85.7. The lesser mistake is to leave R out of the standard deviation only: S becomes 22,267 and service slips to 97.8 per cent. Both terms of the protection interval belong in both parts of the formula. The demand and lead-time inputs, and the share of variance that comes from the supplier, are live in the free workbooks for part AF-7; the lead-time term itself is derived in how to calculate safety stock when lead time varies.
Continuous review orders a fixed quantity the moment stock falls to the reorder point, so the buffer only covers the lead time. Periodic review looks at stock every R periods and orders up to a level S, so the buffer must cover R plus the lead time. On an illustrative part with a 6-week lead time, a 2-week review needs 7,665 units against 7,547.
The order-up-to level minus the inventory position, which is stock on hand plus stock on order less backorders. For an illustrative part selling 1,840 a week, with a 2-week review and a 6-week lead time, S is 14,720 of expected demand plus 7,665 of safety stock, or 22,385. With a position of 15,000 at the review, the order is 7,385; on average orders equal two weeks of demand, 3,680.
Close to the economic order interval, EOQ divided by demand. On an illustrative part with an EOQ of 4,384.5 units and 1,840 a week that is 2.38 weeks. Holding plus ordering cost is 46,437 a year at a 2-week review, 46,851 at 3 weeks and 52,695 at one week, so the cost is flat around the optimum and steep below it.
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.
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