Inventory

Economic order quantity.

Enter yearly demand, what each order costs you and what it costs to hold one unit for a year. See the order size that minimises the two combined.

EOQ = square root of (2 x annual demand x cost per order / holding cost per unit per year). For 1,200 units a year, $50.00 per order and $5.00 to hold a unit for a year, the EOQ is 154.9 units, ordered 7.75 times a year.

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Your numbers

Your numbers
$
$
Needed to turn a holding rate into dollars; also used for the purchase cost line.
%
Work yours out with the inventory carrying cost calculator.
$
Shows how much more a year you pay than at the EOQ.

Result

Worked example

A shop sells 1,200 units a year. Each order costs $50.00 to place and receive, a unit costs $20.00, and holding stock costs 25% of unit cost a year, which is $5.00 per unit. EOQ = sqrt(2 x 1,200 x 50 / 5) = sqrt(24,000) = 154.9 units. That means 7.75 orders a year, one about every 47 days. Ordering costs $387.30 and holding costs $387.30: the two are equal at the EOQ, for $774.60 in total. Ordering 300 at a time instead means 4 orders and $950.00, which is $175.40 a year more.

As a cross-check, the Wikipedia article on EOQ works an example with 10,000 units of yearly demand, $40.00 per order and an effective holding cost of $5.00 ($4.00 plus 2% interest on a $50.00 unit) and gets 400 units; this calculator returns the same 400.

How it works

Q* = sqrt(2DS / h), where D is annual demand, S is the fixed cost of one order and h is the holding cost per unit per year. Total yearly ordering plus holding cost is (D / Q) x S + (Q / 2) x h: ordering cost falls as Q grows, holding cost rises, and the sum is lowest where they are equal.

The model assumes demand is steady, each order arrives in full when stock reaches zero, there is a fixed cost per order and a cost per unit held. It ignores quantity discounts, stockouts, minimum order sizes and shelf life. The purchase cost line (demand x unit cost) is shown so you can compare a supplier's discount tiers by adding it to ordering plus holding cost at each tier's order size. EOQ says how much to order; the reorder point calculator says when.

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Sources

FAQ

What is the EOQ formula?

EOQ = sqrt(2DS / h), where D is annual demand in units, S is the fixed cost per order and h is the holding cost per unit per year. Wikipedia writes the order cost as K; it is the same quantity.

What should I include in cost per order?

Everything that does not change with order size: placing the order, supplier or freight minimums that are fixed per shipment, receiving and put-away time, and invoice processing. Do not include the price of the goods.

How do I set the holding cost?

Either as dollars per unit per year or as a percentage of unit cost. The percentage should cover capital cost, storage, insurance, taxes and spoilage or obsolescence. The inventory carrying cost calculator on this site adds those up for your business.

Does EOQ handle volume discounts?

No. EOQ finds the cheapest order size for a single price. To test a discount tier, add the purchase cost at that tier to ordering plus holding cost at the tier minimum order size and compare totals.

How is EOQ different from the reorder point?

EOQ is how much to order each time. The reorder point is when to place the order, based on lead time, demand and safety stock. You normally need both.

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