Why firms hold inventory, and what it costs
Inventory is a buffer between supply and demand. Firms hold it to meet customer demand quickly, to smooth uneven production, to protect against late deliveries and to take advantage of bulk prices. But stock ties up cash and space, so the aim is the right amount, not the most or the least.
| Cost | What it includes | Behavior as order size rises |
|---|---|---|
| Ordering (setup) cost | Placing the order, receiving and inspecting, or machine setup for production | Total falls, because fewer orders are placed |
| Holding (carrying) cost | Storage, insurance, shrinkage, obsolescence and the cost of money tied up, often 15 to 30 percent of item value a year | Total rises, because average stock is larger |
| Stockout cost | Lost sales, expediting, and damaged customer goodwill | Falls as safety stock rises |
| Purchase cost | Price paid for the goods | May fall with quantity discounts |
The core trade-off is between ordering and holding costs, and the economic order quantity finds the point where their sum is smallest.
The economic order quantity model
The basic EOQ model assumes constant, known demand, a fixed ordering cost per order, a fixed holding cost per unit per year, instant replenishment, and no shortages or discounts. The formula is:
EOQ = square root of (2 x D x S / H)
where D is annual demand in units, S is the ordering cost per order and H is the holding cost per unit per year. If your question gives holding cost as a percentage of price, first convert it to dollars per unit.
EOQ for a distributor (hypothetical)
Annual demand D = 12,000 units. Ordering cost S = $50 per order. Holding cost H = $4 per unit per year.
EOQ = square root of (2 x 12,000 x 50 / 4) = square root of 300,000 = about 548 units.
Orders per year = 12,000 / 548 = about 21.9. Time between orders = 300 working days / 21.9 = about 13.7 days.
Annual ordering cost = 21.9 x $50 = about $1,095. Annual holding cost = (548 / 2) x $4 = $1,096. The two are nearly equal, which is the signature of the EOQ. Total = about $2,191.
Now compare with other order sizes to see why the EOQ is the minimum.
| Order size Q | Orders per year | Ordering cost | Holding cost (Q/2 x $4) | Total |
|---|---|---|---|---|
| 300 | 40 | $2,000 | $600 | $2,600 |
| 548 (EOQ) | 21.9 | $1,095 | $1,096 | $2,191 |
| 1,000 | 12 | $600 | $2,000 | $2,600 |
A total cost curve is flat near the minimum, so being a little off the EOQ costs little, which is why firms often round to practical quantities such as full pallets.
Reorder point and safety stock
EOQ says how much to order. The reorder point says when. If demand is constant and the lead time is known, the reorder point is demand during lead time.
Daily demand d = 12,000 / 300 = 40 units. Lead time L = 6 days. Reorder point = 40 x 6 = 240 units.
In practice demand varies, so firms add safety stock to protect against a stockout during the lead time. For normally distributed demand, safety stock = z x standard deviation of demand during lead time, where z comes from the service level.
Safety stock (hypothetical)
Daily demand has a standard deviation of 8 units. Lead time is 6 days, so the standard deviation of demand over the lead time is 8 x square root of 6 = 8 x 2.449 = 19.6 units.
For a 95 percent cycle service level, z = 1.65. Safety stock = 1.65 x 19.6 = about 32 units.
Reorder point = 240 + 32 = 272 units.
| Service level | z value | Safety stock (std dev 19.6) |
|---|---|---|
| 90 percent | 1.28 | about 25 units |
| 95 percent | 1.65 | about 32 units |
| 99 percent | 2.33 | about 46 units |
Notice how the safety stock needed rises quickly as the target service level approaches 100 percent. This is a useful point for discussion questions on the cost of high service levels.
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Get an instant quoteQuantity discounts
When the supplier offers a lower price for larger orders, the purchase cost matters and you must compare total costs: purchase plus ordering plus holding. Holding cost is usually a percentage of price, so it falls when the price falls.
Quantity discount (hypothetical)
Price is $20 per unit for orders under 1,000 and $19 per unit for orders of 1,000 or more. D = 12,000, S = $50, holding cost = 20 percent of price.
At $20: H = $4, EOQ = 548 (feasible). Purchase = 12,000 x $20 = $240,000. Ordering plus holding = $2,191. Total = $242,191.
At $19: H = $3.80. The EOQ is square root of (2 x 12,000 x 50 / 3.8) = 562, which is below 1,000, so it is not allowed at this price. The lowest feasible quantity is 1,000. Purchase = 12,000 x $19 = $228,000. Ordering = 12 x $50 = $600. Holding = (1,000 / 2) x $3.80 = $1,900. Total = $230,500.
The discount saves $11,691 a year, so order 1,000 at a time.
- Calculate EOQ at each price If the EOQ is not in the price range, use the lowest quantity that qualifies.
- Compare total costs Include the purchase cost; it often dominates.
- Check real-world limits Storage space, cash flow and the risk of obsolescence can outweigh a discount.
ABC analysis and inventory turnover
Not every item deserves the same control. ABC analysis ranks items by annual usage value (units times unit cost) and splits them into classes.
| Class | Typical share of items | Typical share of value | Control approach |
|---|---|---|---|
| A | About 10 to 20 percent | About 70 to 80 percent | Tight control, frequent reviews, accurate records, careful forecasting |
| B | About 30 percent | About 15 to 20 percent | Moderate control, periodic review |
| C | About 50 percent | About 5 to 10 percent | Simple controls, larger safety stock, bulk ordering |
Inventory turnover measures how often stock is sold and replaced. Turnover = cost of goods sold / average inventory. With COGS of $600,000 and average inventory of $100,000, turnover is 6 times a year. Days of inventory = 365 / 6 = about 61 days. Higher turnover generally means less cash tied up, but extremely high turnover may signal stockouts, so compare with similar firms.
Assumptions, limits and other approaches
Many assignments ask you to evaluate the model, not just apply it. Good points to make are listed below.
- Constant demand is rare. Seasonal or trending demand needs a forecast and a periodic review system. See our guide to forecasting methods.
- Costs are hard to estimate. Ordering and holding costs are approximations, but the flat total cost curve makes the EOQ forgiving of errors.
- Just-in-time (JIT) aims to cut ordering costs and lead times so small, frequent orders become economical, which reduces inventory. It depends on reliable suppliers and is exposed to disruption.
- Continuous and periodic review. Continuous review (reorder point) places an order when stock reaches a level. Periodic review orders at fixed intervals to bring stock up to a target.
- Vendor-managed inventory and technology such as barcodes and real-time tracking improve accuracy and reduce stockouts.
- Check units Annual demand with annual holding cost; do not mix days and years.
- Round sensibly Orders are whole units; state your rounding.
- Show the formula first Then substitute numbers, then give the answer with units.
- Sense-check At the EOQ, annual ordering and holding costs should be about equal.
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