Inventory and the cost of holding it
What holding stock really costs, how to size safety stock for a service level, why lead time matters so much, and the bullwhip effect in numbers.
Key takeaways
- Stock on a shelf is cash that is not earning anything. Each unit held costs a share of its value every year.
- Safety stock grows only with the square root of lead time, but stock in transit grows in full proportion to it.
- Cost of capital: the cash tied up could repay debt or be invested. Illustrative: 10 percent a year.
- Storage and handling: warehouse space, staff, equipment. Illustrative: 6 percent.
- Insurance and any taxes on stock. Illustrative: 1 percent.
Key idea
Stock on a shelf is cash that is not earning anything. Each unit held costs a share of its value every year. Safety stock grows with how unpredictable demand is and with the square root of lead time, and the last few points of service level are the most expensive.
The toolkit lesson explained what safety stock and service level are. Here you size them. You will need one new idea: the standard deviation, a measure of how much daily demand usually moves around its average. If a shop sells 400 units on an average day but most days fall between about 280 and 520, the standard deviation is about 120 units.
What holding stock costs
The parts of holding cost, with an illustrative yearly rate
- Cost of capital: the cash tied up could repay debt or be invested. Illustrative: 10 percent a year.
- Storage and handling: warehouse space, staff, equipment. Illustrative: 6 percent.
- Insurance and any taxes on stock. Illustrative: 1 percent.
- Shrink and obsolescence: theft, damage, expiry, and stock that goes out of fashion or out of date. Illustrative: 8 percent, and much higher for fashion or electronics.
- Together these give an illustrative holding cost of 25 percent of the stock's value a year. Ask the company for its own figure; it varies a lot by product.
Sizing safety stock
When lead time is fixed, a common formula is: safety stock = z x standard deviation of daily demand x square root of lead time in days. The z number comes from the service level the company wants, meaning the chance that it does not run out before the next delivery arrives. The reorder point is the stock level that triggers a new order: average demand during the lead time plus the safety stock.
| Chance of not running out in a cycle | z number |
|---|---|
| 90 percent | 1.28 |
| 95 percent | 1.65 |
| 98 percent | 2.05 |
| 99 percent | 2.33 |
| 99.9 percent | 3.09 |
So-what
Going from 95 to 99 percent raises safety stock by about 40 percent; going to 99.9 percent nearly doubles it.
Worked case
Safety stock for a spare part in Dubai
The prompt
A fictional distributor in Dubai sells an air-conditioner part. It sells 400 units a day on average, with a standard deviation of 120 units a day. It buys from a factory in China with a lead time of 25 days by sea. Each unit costs AED 150 and the holding cost is 25 percent a year. How much safety stock does it need for 95 and for 99 percent service, what does the extra reliability cost, and what would a supplier with a 9-day lead time save?
The structure
- Safety stock = z x daily standard deviation x square root of lead time
- Variation over the lead time
- Safety stock at 95 and 99 percent
- Holding cost of the difference
- Key: Effect of a shorter lead time
Working it through
1. Variation over 25 days
The square root of 25 is 5.
Standard deviation over the lead time (units):120 × 5 = 6002. Safety stock at 95 percent
z is 1.65.
Safety stock at 95 percent (units):1.65 × 600 = 9903. Safety stock at 99 percent
z is 2.33.
Safety stock at 99 percent (units):2.33 × 600 = 1,3984. Cost of the extra reliability
The extra units, times AED 150, times 25 percent a year.
Extra holding cost for 99 percent (AED a year):(1,398 - 990) × 150 × 0.25 = 15,3005. Reorder point at 95 percent
25 days of average demand plus safety stock.
Reorder point at 95 percent (units):400 × 25 + 990 = 10,9906. Safety stock with a 9-day lead time
The square root of 9 is 3.
Safety stock at 95 percent, 9-day lead time (units):1.65 × 120 × 3 = 5947. Stock in transit saved
16 fewer days on the water at 400 units a day, valued at AED 150 and 25 percent a year.
Holding cost saved on goods in transit (AED a year):(25 - 9) × 400 × 150 × 0.25 = 240,000
The recommendation
The distributor should stay at 95 percent service unless customers will pay for more, and should seriously price a nearer supplier. First, moving from 95 to 99 percent needs 408 more units, costing about AED 15,300 a year. Second, a 9-day supplier would cut safety stock from 990 to 594 units and, much more important, remove 6,400 units from the sea, saving about AED 240,000 a year in holding cost. The risk is that a nearer supplier charges more per unit, so compare the full landed cost. As a next step, ask for quotes from suppliers in India or the Gulf and compare landed cost per unit.
Safety stock grows only with the square root of lead time, but stock in transit grows in full proportion to it. Cutting the time goods spend on the way often frees more cash than any clever safety stock formula.
The bullwhip effect in numbers
Here is how a small rise in shopper sales becomes a large jump at the factory. A shop in Jakarta sells 10,000 cases of a soft drink a week and keeps two weeks of sales in stock. Each week it orders what it sold plus whatever it needs to reach its stock target. One week sales rise 10 percent to 11,000. The target rises to 22,000, so the shop orders 11,000 plus 2,000: 13,000, which is 30 percent more than usual. The distributor uses the same rule on the orders it receives. It sees 13,000 instead of 10,000, raises its target from 20,000 to 26,000, and orders 13,000 plus 6,000: 19,000, which is 90 percent more than usual. A 10 percent change in drinking became a 90 percent change in factory orders.
Bar chart: One week's change in demand at each step (percent). Values in percent change. Shopper sales: 10; Shop orders to the distributor: 30; Distributor orders to the factory: 90.
So-what
Each step that forecasts from the orders it receives multiplies the swing.
A shop keeps three weeks of sales in stock and orders what it sold plus the change in its stock target. Weekly sales rise from 5,000 to 5,500 units. How many units does it order that week?
"Factory orders swing far more than end sales, which points to the bullwhip effect. I would ask for point-of-sale data from the shops and check whether each step is ordering from the orders it receives rather than from real sales."
Lead time falls from 36 days to 9 days. Demand and service level stay the same. What happens to safety stock?
A company holds AED 10 million of stock and its holding cost is 25 percent a year. What does the stock cost to hold each year?
Sources for this lesson (2)
- Recognized public explanations of case-interview concepts and terms
- MIT Sloan Management Review, "The Bullwhip Effect in Supply Chains" (1997)
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