What is EOQ (economic order quantity)?

The economic order quantity (EOQ) is the order size that makes the yearly cost of ordering plus the yearly cost of holding stock as low as it can be. Order often in small lots and you pay the cost of placing and receiving many orders; order rarely in big lots and you pay to keep a lot of stock. The EOQ is the balance point:

EOQ = √(2 × D × S ÷ H)

D is the yearly demand in units, S the cost of one order (placing it, receiving it, paying the invoice) and H the cost of holding one unit for a year, usually the unit price times a holding rate.

Example. 12,000 units a year, €60 an order, a €8.00 unit held at 25% a year (H = €2.00): EOQ = √(2 × 12,000 × 60 ÷ 2) = 849 units, about 14.1 orders a year. At the EOQ the two costs are equal: €849 a year of ordering and €849 of holding.

The cost is flat near the EOQ. Ordering x times the EOQ costs ½(x + 1/x) times the minimum ordering plus holding cost: 25% more than the EOQ costs 2.5% more, twice the EOQ 25% more. So rounding to a pack, a pallet or a supplier’s minimum near the EOQ costs little, and a rough holding rate does little harm: the EOQ moves only with the square root of it.

What it assumes. Steady, known demand; one item; a fixed cost per order; any quantity allowed; one price. Real suppliers add a minimum order quantity, pack sizes and price breaks, and demand is not steady, which is what safety stock is for. What a supplier’s minimum and a price break do to the EOQ, in numbers: EOQ vs minimum order quantity. Order quantity starts from the EOQ and then applies the supplier’s rules (this example).

Sources

• Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135–136. Reprinted in Operations Research, 38(6), 947–950 (1990).
• Caplice, C. (2006). ESD.260 Logistics Systems, Lecture 7: Inventory Management I, slides 22–27. MIT OpenCourseWare.