EOQ: the economic order quantity

Wholesale buying has two pain points. Buy small batches often and every order carries its own cost: transport, paperwork, receiving. Buy large batches and the goods sit in the warehouse, cash is tied up and space is taken. EOQ (economic order quantity) finds the batch at which the sum of these two costs is lowest.

The formula

EOQ = √(2 × D × S ÷ H).

• D is annual demand, in units.
• S is the cost of placing one order, in so'm: transport, documents, time spent on receiving and checking. It is not the price of the goods, but what the act of ordering costs.
• H is the cost of holding one unit for a year, in so'm. It is usually taken as a share of the unit cost: the price of money, rent, losses and insurance. 15-25 percent is a common assumption, but work out your own figure.

A worked example

A household item (a dinner set): unit cost 12 000 so'm, 18 000 units sold per year. One order costs 150 000 so'm. Holding is 20 percent of cost: H = 12 000 × 0.2 = 2 400 so'm per unit per year.

EOQ = √(2 × 18 000 × 150 000 ÷ 2 400) = √(5 400 000 000 ÷ 2 400) = √2 250 000 = 1 500 units.

So 18 000 ÷ 1 500 = 12 orders a year, roughly one every 30 days. Average stock is half the batch, that is 750 units, or 750 × 12 000 = 9 million so'm.

Why this particular batch

Annual cost has two parts: ordering cost (D ÷ Q × S) and holding cost (Q ÷ 2 × H). Compare three batch sizes:

• 500 units: 36 orders × 150 000 = 5.4 million, holding 250 × 2 400 = 0.6 million. Total 6.0 million so'm.
• 1 500 units: 12 × 150 000 = 1.8 million, holding 750 × 2 400 = 1.8 million. Total 3.6 million so'm.
• 4 500 units: 4 × 150 000 = 0.6 million, holding 2 250 × 2 400 = 5.4 million. Total 6.0 million so'm.

The cheapest option is the point where the two costs are equal. A small batch drowns in ordering cost, a large one in holding cost.

An important detail: near the optimum the curve is level. Order 1 200 units and the total is 3.69 million (only 2.5 percent more); order 1 800 and it is 3.66 million (1.7 percent more). A 20 percent deviation from EOQ raises cost by less than 3 percent. So do not hesitate to round the result to a carton, a pallet or the supplier's minimum batch.

If there is a discount

The supplier offers a 4 percent discount on a batch of 3 000 units: the price falls to 11 520 so'm. Compare the two options on total cost.

• By EOQ: purchases 18 000 × 12 000 = 216 million, plus 3.6 million. Total 219.6 million so'm.
• A 3 000-unit batch: purchases 18 000 × 11 520 = 207.36 million, orders 6 × 150 000 = 0.9 million, holding 1 500 × (11 520 × 0.2) = 3.456 million. Total 211.716 million so'm.

The discount wins about 7.9 million so'm. But the one-off payment is 34.56 million instead of 18 million, and the stock lasts two months. Do not decide without checking cash flow, seasonality and shelf life.

When EOQ does not work

• When demand swings sharply or is seasonal: annual D shows the average, while the real months look different.
• For goods with a short shelf life: the batch must sell before it expires.
• When the batch size is dictated by truck or container capacity, or by a minimum order.
• When S and H are rough estimates. S is often underestimated, because the time of the people at the receiving dock never makes it into the price.

Conclusion

EOQ answers "how much" to order, and the reorder point answers "when": together they work as one system. The formula helps only if demand and costs are right, and it cannot help if the balance is wrong. CountLab verifies balances through stock counts and, with ABC/XYZ analysis, shows which items deserve this calculation first.