Every week, someone in a company makes a decision that looks trivial and yet, added up over a year, moves thousands of euros: how much to order at a time. Ordering a lot at once reduces the number of orders, but fills the warehouse and ties up capital. Ordering little and often keeps inventory low, but multiplies the cost of each order. Between these two extremes there is a balance point — and there is a formula, nearly a century old, that calculates it.
That formula is the economic order quantity, best known by its acronym EOQ. It is one of the oldest and most useful models in inventory management: it takes two costs that pull in opposite directions and finds the batch size that minimises their sum. Despite its age, it remains the right starting point for deciding how much to order of an item with reasonably stable demand.
This article explains the logic behind the EOQ, presents the formula and a worked example step by step, and — just as important — shows where the model helps and where it misleads. Because using a formula without understanding its assumptions is a fast way to make wrong decisions with a false sense of rigour.
The dilemma: order a lot or a little at a time
Picture an item with steady demand throughout the year. If you order it in large quantities, a few times a year, you save on everything it costs to place an order — administrative processing, transport, receiving and inspection. In return, you are left with a lot of idle inventory, which takes up space, risks deteriorating or becoming obsolete and, above all, locks up money that could be elsewhere.
If you do the opposite — small, frequent orders — average inventory falls and with it the cost of holding it, but the cost of ordering soars, because you pay those fixed costs over and over. The EOQ exists precisely to arbitrate this dilemma with numbers, rather than settling it by habit or intuition.
The two costs that oppose each other
The whole logic of the EOQ rests on separating and quantifying two types of cost:
- Ordering cost (S): the fixed cost of placing an order, regardless of its size — administrative time, transport, receiving. The more orders per year, the higher this total cost.
- Holding cost (H): the cost of keeping one unit in inventory for a year — tied-up capital, space, insurance, risk of obsolescence. The larger the average inventory, the higher this cost.
There is also a third element, annual demand (D), which is not itself a cost but the scale of the problem. The EOQ combines these three values to find the batch that minimises the sum of ordering cost and holding cost. Note that the cost of the product itself does not enter the formula: since annual demand is the same regardless of batch size, the total cost of buying the items does not change — what changes is how much you spend ordering and storing them.
The EOQ formula
The economic order quantity is calculated with the Wilson formula:
EOQ = √((2 × D × S) / H)
Where D is annual demand (in units), S the cost of placing an order and H the cost of keeping one unit in inventory for a year. The result is the number of units to order each time that minimises total ordering and holding costs. The square root is not arbitrary: it comes from setting the two cost curves equal, and it is why doubling demand does not double the batch — it only raises it by about 41%.
A worked example
Consider a distribution company selling an item with stable annual demand of 12,000 units. Each order costs 60 € to process (S) and keeping one unit in inventory for a year costs 3 € (H). Applying the formula:
EOQ = √((2 × 12000 × 60) / 3) = √480000 ≈ 693 units
The result says the most economical batch is about 693 units. With demand of 12,000 units a year, that corresponds to roughly 17 orders a year, or one order every 21 days. It is worth checking the costs at that point: the annual ordering cost is 17.3 × 60 ≈ 1,039 €, and the annual holding cost is (693 / 2) × 3 ≈ 1,039 €. It is no coincidence that they are equal — at the EOQ optimum, the two costs balance exactly, and their sum, about 2,078 € a year, is the lowest possible.
To see that it really is the minimum, compare it with habit-based alternatives. Ordering 1,000 units at a time (once a month) would give 720 € of ordering cost plus 1,500 € of holding, a total of 2,220 €. Ordering 2,000 at a time would give 360 € plus 3,000 €, that is 3,360 €. Both worse than the EOQ's 2,078 €.
What the EOQ reveals about costs
There is a subtle lesson hidden in this example. The difference between the EOQ (2,078 €) and the monthly order (2,220 €) is just 142 € a year — about 7%. This happens because the total cost curve is quite flat near the optimum: getting the batch wrong by 30% or 40% costs little.
This robustness is good practical news. It means you do not need perfect data nor to recalculate the EOQ every week; an approximate value, rounded to a round number or to a multiple of the shipping case, captures almost all the benefit. The EOQ is more useful as a compass — to find the right order of magnitude — than as a magic number to follow to the unit.
When the EOQ helps and when it misleads
The basic model rests on assumptions worth keeping in mind, because when they fail the formula can point the wrong way:
- Constant, known demand. The EOQ assumes steady demand. For seasonal or very irregular items, the single value loses meaning.
- No quantity discounts. If the supplier lowers the unit price above a certain volume, it may pay to order more than the EOQ — there is a variant of the model for that case.
- Stable costs. If ordering or holding costs vary a lot, the EOQ stops being a fixed target.
- Immediate replenishment, no stockouts. The basic model ignores lead time and demand variability — which are exactly what the reorder point and safety stock address.
None of this invalidates the EOQ; it just defines its place. It is an excellent starting point for items with stable demand and a poor substitute for common sense for everything else.
EOQ, reorder point and safety stock
It is important not to confuse two different questions. The EOQ answers how much to order at a time. It says nothing about when to order — that is the job of the reorder point, which accounts for lead time and demand during that lead time, usually with a safety stock cushion to absorb variability.
In practice, the two work together: the EOQ sets the batch size and the reorder point sets the trigger moment. A good inventory policy combines both — deciding how much to order with the EOQ and when to order with the reorder point — instead of treating each item as an isolated case solved by eye.
Common mistakes when applying the EOQ
A few frequent stumbles when taking the formula into the field:
- Mixing time units. Demand and holding cost must be on the same time base, usually annual. Using annual demand with a monthly holding cost gives a meaningless result.
- Forgetting the true holding cost. Many companies underestimate H by counting only space, ignoring tied-up capital, insurance and obsolescence. Too low an H pushes the EOQ toward batches that are too large.
- Treating the result as exact. The EOQ gives an order of magnitude, not a verdict. Round to practical values.
- Applying it to the wrong items. For very irregular demand or extremely low-turnover items, other methods serve better.
In practice
The economic order quantity is one of those models that are worth less for the number they produce and more for the question they force you to ask: how much does it actually cost to order and store this item? Just by answering that honestly, many companies discover they are ordering by habit, not by calculation.
Use the EOQ as a compass for items with stable demand, feed it with realistic ordering and holding costs, and combine it with a reorder point to decide the timing. Do not chase the last unit — the curve is flat near the optimum — but avoid the extremes, because it is there, in huge or tiny batches, that money is lost without anyone noticing.
