EOQ Calculator (Economic Order Quantity)
EOQ Calculator (Economic Order Quantity)
The order size that keeps the yearly cost of ordering and of holding stock as low as possible, how many orders that means a year, and when to reorder.
Economic order quantity
12,000 units a year, $1,500 per order, $40 a unit a year to hold; 7 days’ lead time at 40 units a day
The EOQ (Harris, 1913)
- D
- annual demand in units
- S
- the cost of placing one order
- H
- the cost of holding one unit for a year (or a % of the unit cost × the unit cost)
- Q*
- the order size at which ordering cost (D ÷ Q × S) and holding cost (Q ÷ 2 × H) add up to the least
Worked example
12,000 units a year, $1,500 per order, $40 a unit a year to hold; 7 days' lead time at 40 units a day
Q* = √(2 × 12,000 × 1,500 ÷ 40) = √9,00,000 = 948.7, about 949 units
Orders a year = 12,000 ÷ 948.7 = 12.6, one every 29 days
Ordering cost = 12.65 × 1,500 = $18,974; holding = 948.7 ÷ 2 × 40 = $18,974
Total = $37,947 a year; reorder when stock falls to 7 × 40 = 280 units
Yearly cost of the example at other order sizes
| Order size | Ordering cost | Holding cost | Total |
|---|---|---|---|
| 300 | $60,000 | $6,000 | $66,000 |
| 500 | $36,000 | $10,000 | $46,000 |
| 949 | $18,967 | $18,980 | $37,947 |
| 1,500 | $12,000 | $30,000 | $42,000 |
| 2,000 | $9,000 | $40,000 | $49,000 |
| 3,000 | $6,000 | $60,000 | $66,000 |
Why the EOQ works, and when not to trust it
Every order has a fixed cost — freight booking, paperwork, receiving — so ordering rarely in large lots saves on ordering. But large lots sit on the shelf, and stock costs money to hold: storage, insurance, damage and the interest on the cash tied up. The economic order quantity, first published by Ford W. Harris in 1913, is the order size where the two costs balance. Ordering Q units at a time, you place D ÷ Q orders a year and hold Q ÷ 2 units on average, and the sum of the two costs is lowest at Q = √(2DS ÷ H).
In the example that is about 949 units, 12.6 orders a year, for $37,947 of ordering and holding cost. The curve is flat around the minimum: ordering 500 at a time costs $46,000 and 2,000 at a time $49,000, but ordering 20% more or less than the EOQ adds under 3% ($949 a year at 80% of it). So round the EOQ to a pack or pallet size freely; it is being far off that costs money.
The model rests on assumptions worth checking. Demand is taken as steady and known; the order arrives all at once; the unit price does not change with order size. If a supplier offers a quantity discount, compare the total cost including the purchase price at each price break. The reorder point, daily demand × lead time, only covers average demand; add safety stock if demand or delivery times vary, or you will run out about half the time. Holding cost is the input most often underestimated, because the cost of capital is easy to forget.
For how long cash is tied up in stock and receivables, see the cash conversion cycle calculator; for the margin each unit brings in, the contribution margin calculator; for liquidity, the current ratio calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
What is the EOQ formula?
EOQ = √(2 × annual demand × cost per order ÷ holding cost per unit per year). It is the order size at which yearly ordering and holding costs are equal and their total is smallest.
How do I work out the holding cost?
Add up a year’s storage, insurance, spoilage and the interest on the money in stock, per unit. Many businesses use a percentage of the unit cost; choose that option on the page.
What is the reorder point?
The stock level at which to place the next order: daily demand × supplier lead time, plus any safety stock. 40 units a day and a 7-day lead time give 280 units.
Does EOQ work with quantity discounts?
Not directly. The basic model assumes one unit price; with discounts, compare total cost including the purchase price at the EOQ and at each price break.
Related calculators
References
- Harris FW. How Many Parts to Make at Once. Factory, The Magazine of Management 1913;10(2):135–136, 152. Reprinted in Operations Research 1990;38(6):947–950 — the origin of the economic order quantity, Q = √(2DS ÷ H).
- Heizer J, Render B, Munson C. Operations Management: Sustainability and Supply Chain Management. Pearson. Chapter on inventory management: the basic EOQ model, its assumptions (known, constant demand; instant receipt; no quantity discounts), total annual ordering and holding cost, and the reorder point = daily demand × lead time (plus any safety stock).