Economic order quantity (EOQ): what it is and how to calculate it

Economic order quantity (EOQ): what it is and how to calculate it

Buying merchandise looks like a common-sense decision: you order when you run low, and that is it. But any shop owner who has tried both extremes knows it is not that simple. If you order small amounts often, freight, wasted time and paperwork eat the profit of every purchase. If you order a large amount all at once, your money stays frozen in boxes that take up space, cost money to store and can be damaged or expire before they sell. Between those two extremes there is an optimal quantity to order: the economic order quantity, known by its initials in English as EOQ.

This article explains what EOQ is, what the formula looks like, how to calculate it with a worked example and, above all, when it makes sense to use it and when it does not in a real business. You do not need to be an accountant or master complicated spreadsheets: with a calculator and the data of a single product you reach the number.

The buying dilemma: not too little, not too much

Behind every purchase there are two costs that almost nobody adds up. The first is the ordering cost: everything it costs to place an order, regardless of its size. Every time you order merchandise you pay freight or shipping, you lose time getting quotes and calling the supplier, and someone has to receive, count, check and put away what arrived. In practice, this includes:

• Freight, shipping or surcharges for small orders.
• The time the owner or manager spends quoting, negotiating and placing the order.
• Receiving: unloading, checking quantities, inspecting for damage and storing the goods.
• Paperwork: purchase order, invoice, payment and recording the receipt in inventory.

The second is the holding cost: everything it costs to keep merchandise in stock. This includes the space the boxes occupy, the invested money that is no longer available for other things, and the risk that the product gets damaged, expires, gets lost or becomes obsolete:

• Space: shelving, a warehouse or the back corner you could use for something else.
• Frozen capital: every dollar in inventory is a dollar that is not in the bank or buying what sells fastest.
• Shrinkage risk: expiries, dents, humidity, theft and products that go out of fashion.
• Insurance, security and upkeep: whatever it costs to look after what is stored.

Here is the catch: these two costs move in opposite directions. If you order in very small lots, you pay a lot in ordering costs, because you place many orders a year, but very little in holding costs, because you barely hold inventory. If you order in huge lots, you pay little in ordering costs, because you place few orders, but a lot in holding costs. At some point in between, the sum of the two is as low as it can get. That point is the EOQ.

What is the economic order quantity

The economic order quantity is the number of units it makes sense to order every time you buy a product so that the sum of ordering cost and holding cost is as low as possible. It does not tell you when to order; that job belongs to the reorder point. It tells you how much to order: the size of the lot.

For example, if a product's EOQ is 200 units, the rule would be: every time you must buy, order 200 units, not 80 out of urgency or 600 to make the trip worthwhile. The formula was proposed by Ford W. Harris in 1913, and more than a century later it is still the basis of many companies' purchasing systems. Its popularity comes from being simple and from giving a numeric answer to a question that is usually solved by gut feeling.

The EOQ formula

The EOQ formula looks like this:

EOQ = square root of (2 × D × S ÷ H)

Where:

• D = annual demand for the product, in units, that is, what you sell or consume in a year.
• S = ordering cost: what each order costs in money.
• H = holding cost per unit per year, in money.

Annual demand comes from your sales history or from what you used last year. The ordering cost (S) is estimated by adding freight and time: if each order costs $15 in shipping and half an hour of work you value at $5, then S is $20. The holding cost (H) is almost always calculated as a percentage of the unit cost: common practice ranges between 20% and 30% per year. If a unit costs you $8 and you use 25%, H is $2 per unit per year. Do not look for accounting-level precision in S and H: look for a reasonable order of magnitude, because EOQ tolerates errors in these figures.

Why does the formula have the 2? Because on average you only keep half the lot in stock: if you order 200 units and sell them at an even pace, the average inventory is 100. That is the quantity you actually pay to hold.

Worked example: how much to order in a grocery store

Let us use a concrete case. A grocery store sells 2,000 packs of a fast-moving detergent a year. Each order to the distributor costs $20 including freight, time and paperwork. Keeping one pack in storage for a year costs $2, counting space, capital and shrinkage risk. How many packs should it order on each purchase?

We plug the numbers into the formula: 2 × 2,000 × 20 = 80,000; divided by 2 gives 40,000; the square root of 40,000 is 200. The EOQ is 200 packs. With that lot size it places 2,000 ÷ 200 = 10 orders a year, that is, roughly one order every five weeks.

The total annual cost has two parts: the ordering cost, which is the number of orders times the cost of each one (10 × $20 = $200), and the holding cost, which is the average inventory times the unit cost (100 × $2 = $200). Both halves come out equal, and that is no coincidence: at the EOQ, ordering cost and holding cost balance out.

The following table shows what happens if you order a different quantity than the EOQ. Watch the last column: any other lot size costs more.

(Figures rounded to the nearest dollar. Total cost is calculated as (D ÷ Q) × S + (Q ÷ 2) × H.)

The takeaway from the table is practical: if today you buy in lots of 100, you spend $500 a year on this single product; with lots of 200 you would spend $400. That is $100 a year in savings on one item, without changing supplier or price. Multiplied across the products you buy often, EOQ pays for the time it took to calculate it.

How to use the result in practice

EOQ gives you a number, but the real storeroom has boxes, pack sizes and supplier minimums. Before adopting it, make these four adjustments:

• Round sensibly. If the EOQ comes out at 200 but the supplier sells in cases of 24, order 192 or 216, that is, 8 cases or 9 cases. The cost difference between 192 and 216 is tiny; what matters is stopping arbitrary quantities.
• Turn the lot into a rhythm. With 10 orders a year, schedule the purchase for roughly every five weeks. A fixed routine avoids urgent orders, which are always expensive.
• Compare it with what you do today. Calculate the total cost with your current lot and with the EOQ. The difference is the saving you are leaving on the table; use it to convince yourself, and whoever does the buying, to change the habit.
• Review it with the supplier. If the supplier requires a minimum order above the EOQ, you will have to order that minimum and accept the extra cost, or negotiate: many suppliers lower the freight or improve the price when the buyer commits to steady quantities.

Also, EOQ is not calculated once. Recalculate it at least once a year and every time demand, the product price or the freight rate changes. And if you do not have the annual demand figure at hand yet, this is the moment to start recording receipts and issues for every product: without that history, no formula works.

When EOQ does not apply well

EOQ is a model and, like every model, it rests on assumptions that are not always true. Know its limits so you do not apply it blindly:

• It assumes constant demand. If your business is seasonal, like gifts in December, school supplies in January or a high season during vacations, the calculation with average annual demand is off in each period. In that case, calculate the EOQ per season, using that season's demand.
• It ignores volume discounts. If the supplier lowers the price from a certain volume, ordering more than the EOQ can make sense. The correct way to decide is to compare the discount saving against the extra holding cost; EOQ gives you the baseline for that calculation.
• It does not work the same with perishable or fashion products. If the optimal lot takes longer to sell than the product lasts, or than its season lasts, the limit is the expiry date, not the formula. For food, cosmetics and fashion, use EOQ only when the time it takes to consume the lot is shorter than its useful life.
• It ignores supplier delays and emergencies. EOQ assumes the order arrives when you need it. In practice, combine it with a minimum or safety stock to cover delays and unexpected sales peaks.

None of these limitations invalidates the formula: they simply remind you that the result is a starting point for deciding with numbers, not an automatic command.

The idea to take home

The economic order quantity answers in a single operation the question every business asks: how much do I buy each time? Ordering too much freezes your money on shelves; ordering too little multiplies your freight and your time. EOQ finds the balance between the two and, on the way, gives you a number against which to check every purchase order.

The calculation is the easy part; the hard part is keeping information up to date so the decision repeats month after month with real data. An inventory and stock-record software such as Kardex Tauro helps you record receipts and issues for every product, so that when it is time to review how much to buy you know exactly how much you have and how much you have sold. The formula tells you how much to order; the orderly record tells you the basis on which to decide it.