The ratio built from the bottom up on one stocked part, so you can see which decision, the order size, the service level or the supplier's reliability, actually sets the number.
Inventory turnover is cost of goods sold divided by average inventory at cost. For part AF-7 in Supply Chain Management, a year's cost of goods is 2,736,448 and the average stock is 278,534, so turnover is 9.82 times a year, or 37.2 days of inventory. Built from the bottom up, the ratio shows that 77.5 per cent of that stock is safety stock, which is why the supplier's reliability moves turnover far more than the order size does.
Worked in full in Supply Chain Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The accounting version is a top-down ratio: cost of goods sold for the period over the average of the inventory balances. It is the right number for a balance sheet, but it says nothing about why the stock is there. For a stocked item the average inventory has exactly two parts:
Average inventory = Q ÷ 2 + safety stock. Divide the year's cost of goods by its value at cost and you have the turnover, with each decision behind it in plain view.
Aldermere Filtration stocks part AF-7. The figures are the book's fictional case.
| Input | Value |
|---|---|
| Mean weekly demand, units | 1,840 |
| Standard deviation of weekly demand | 462 |
| Mean lead time, weeks; standard deviation | 6; 1.9 |
| Purchase cost delivered, EUR | 28.60 |
| Selling price, EUR | 47.50 |
| Holding rate a year; cost per order, EUR | 13.4%; 385 |
| Cycle service level | 98% |
Step 1: cost of goods sold. 1,840 a week for 52 weeks is 95,680 units, at 28.60 each.
COGS = 95,680 × 28.60 = 2,736,448
Step 2: cycle stock. The order quantity is the EOQ, worked in how to calculate the economic order quantity: 4,384.5 units, so cycle stock averages 2,192.3.
Step 3: safety stock. With lead time varying, the standard deviation of demand over the lead time is √(6 × 462² + 1,840² × 1.9²) = 3,674.6 units, and at 98 per cent (z = 2.0537) the safety stock is 7,546.7 units. The derivation is in how to calculate safety stock when lead time varies.
Step 4: average inventory and the ratio.
Average inventory = 2,192.3 + 7,546.7 = 9,739.0 units × 28.60 = 278,534
Turnover = 2,736,448 ÷ 278,534 = 9.82
Days of inventory = 365 ÷ 9.82 = 37.2; weeks of cover = 52 ÷ 9.82 = 5.29
Excel: =D*Cost/((Q/2+z*SQRT(L*sd^2+d^2*sL^2))*Cost)
Of the 9,739 units on hand on average, 7,547 are safety stock, 77.5 per cent, and only 22.5 per cent is cycle stock. If the part needed no buffer at all, turnover would be 43.6 and days of inventory 8.4. The 9.82 is therefore mostly a statement about uncertainty, and the book's variance split shows where it comes from: about nine-tenths of the variance of demand over the lead time is the supplier's lead time, not the market.
| Case | Safety stock | Cycle stock | Average stock | Turnover | Days | Cash vs base |
|---|---|---|---|---|---|---|
| Base | 7,547 | 2,192 | 278,534 | 9.82 | 37.2 | 0 |
| Lead-time sd 1.0 week | 4,436 | 2,192 | 189,580 | 14.43 | 25.3 | +88,954 |
| Lead-time sd 0.5 week | 2,995 | 2,192 | 148,363 | 18.44 | 19.8 | +130,171 |
| Lead time fixed | 2,324 | 2,192 | 129,169 | 21.18 | 17.2 | +149,365 |
| Mean lead time 4 weeks | 7,426 | 2,192 | 275,095 | 9.95 | 36.7 | +3,439 |
| Service level 95% | 6,044 | 2,192 | 235,562 | 11.62 | 31.4 | +42,972 |
| Service level 99.5% | 9,465 | 2,192 | 333,401 | 8.21 | 44.5 | −54,867 |
| Order quantity 2 × EOQ | 7,547 | 4,385 | 341,233 | 8.02 | 45.5 | −62,698 |
| Four regional depots | 8,553 | 4,385 | 370,019 | 7.40 | 49.4 | −91,485 |
Two results stand out. A more reliable supplier is the strongest lever: taking the lead-time standard deviation from 1.9 to 0.5 weeks nearly doubles turnover, to 18.44, and frees 130,171 of cash, worth 17,443 a year at the 13.4 per cent holding rate. A shorter average lead time with the same unreliability barely helps: four weeks instead of six moves turnover from 9.82 to 9.95, because the variability term dominates the safety stock. Dispersing the stock across four depots does the opposite of pooling and drops turnover to 7.40.
The common mistake is to divide sales by inventory. Inventory is carried at cost, so the numerator must be cost too. On AF-7 the sales-based ratio is 4,544,800 ÷ 278,534 = 16.32, 66 per cent higher than the true 9.82, simply because the part sells at 1.66 times its cost. The second mistake is to measure stock on a single date. Just after a receipt AF-7 holds 11,931 units and the ratio reads 8.02; just before one it holds the 7,547 of safety stock and reads 12.68. Use an average over the cycle, or a monthly average over the year. The service level table, the variance split and the four-depot comparison are all in the free workbooks for part AF-7, with the inputs in blue cells.
Cost of goods sold, because inventory is carried at cost. Dividing sales by inventory at cost mixes a selling price with a cost and inflates the ratio by the mark-up. On an illustrative part selling at 47.50 and costing 28.60, the correct turnover is 9.82; the sales-based figure is 16.32, 66 per cent higher, with nothing about the stock having changed.
Divide the days in the period by the turnover: 365 divided by 9.82 is 37.2 days of inventory on hand for an illustrative stocked part, or 5.29 weeks of cover on a 52-week year. The same figure is cost of goods sold per day divided into average inventory at cost: 278,534 over 7,497 a day.
Attack the largest component of average stock. On an illustrative part, safety stock is 77.5 per cent of it and is driven mostly by the supplier's lead-time variability. Halving that variability to 1.0 week raises turnover from 9.82 to 14.43; halving the order quantity instead only reaches 11.07, and doubles the number of orders placed.
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 1340 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.