Atlas/A.02 Inventory & replenishment/Economic order quantity (EOQ)

The economic order quantity

Definition

The economic order quantity, or EOQ, answers the complement of the reorder point: not when to order, but how much. It is the lot size that minimises the total cost of managing a reference, balancing two opposing forces: the cost of placing orders, which pushes toward large, rare orders, and the cost of holding stock, which pushes toward small, frequent ones.

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The least-cost lot
small lot large lot cost
Ordering cost
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Holding cost
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Total cost
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Slide the lot size: total cost is minimal at the EOQ point.

Why it matters

The right lot, neither too much nor too little.

Once you have decided when to order, you still have to decide how much. Ordering large lots reduces the number of orders and their fixed costs (administration, transport, receiving, setup) but inflates average stock and its holding cost. Ordering small and often does the opposite. The EOQ is the point where these two forces balance, where the total cost of managing the reference is lowest.

The business stake is the hidden cost of lots. You easily see the unit purchase price, less easily what it costs, cumulated over the year, to order too often or to carry too much stock. The EOQ puts a figure on this trade-off and avoids the two symmetric excesses: a multitude of costly small orders, and a build-up of oversized lots sleeping in the warehouse.

Its virtue is also its robustness. The total-cost curve is flat around its minimum: straying a little from the EOQ costs almost nothing. That is good news, no need for surgical precision, but also a safeguard: no point refining the EOQ to the gram when you can, at near-equal cost, round to a practical pack size.

Business impact

The EOQ rests on ideal assumptions: stable, known demand, fixed costs, instant replenishment. Reality always departs from them. Taken literally, the formula can recommend lots that are absurd given pack sizes, quantity discounts or shelf life.

The expert lesson: the EOQ is a starting point, not a verdict. You use it to frame the order of magnitude of the right lot, then adjust it to reality, pack sizes, discounts, capacity, expiry. And you exploit the flatness of the curve: since cost varies little around the optimum, you favour a practical lot close to the EOQ rather than the exact EOQ. The formula informs the decision, it does not replace it.

The mechanism

Two opposing costs, one minimum.

Two costs oppose each other. The ordering cost is fixed per order: the more often you order, in small lots, the more it accumulates. Related to annual demand, it equals the number of orders times the unit ordering cost, that is, demand divided by lot size, times that cost. It falls as the lot grows.

The holding cost, on the other hand, grows with lot size. A larger lot means a higher average stock, on the order of half the lot, hence more tied-up capital, more space, more obsolescence risk. It rises in proportion to the lot.

Total cost is the sum of the two: a U-shaped curve. The diagram shows it, with its two components. The minimum, the EOQ, sits where the two costs equalise, and the formula gives it directly. At that exact point, ordering cost and holding cost are exactly equal, an elegant property that helps check a calculation at a glance.

EOQ = √ ( 2 · D · S / H )
D the demand over the period, often the year; S the fixed cost of placing an order; H the cost of holding one unit in stock over the same period. In the numerator, what pushes toward large lots (demand and ordering cost); in the denominator, what pushes toward small lots (holding cost). The square root explains the robustness: doubling demand does not double the lot, it grows by a factor of the square root of two only. At the EOQ point, ordering cost and holding cost are equal.

The traps

Three EOQ errors.

01

Taking the formula literally

The EOQ assumes stable demand and fixed costs. Applied without judgment, it proposes lots incompatible with pack sizes, discounts or expiry. It frames the order of magnitude; the final lot adjusts to reality.

02

Mispricing the two costs

Everything depends on the quality of the ordering cost and the holding cost. An underestimated ordering cost pushes toward lots too small; an underestimated holding cost, obsolescence forgotten, toward lots too large. Wrong inputs give a wrong EOQ, with the confidence of a formula.

03

Ignoring quantity discounts

When the supplier offers a rebate above a threshold, the pure EOQ no longer suffices: you must compare the total cost at the EOQ and the total cost at the discount threshold, discount included. Stopping at the classic EOQ sometimes leaves money on the table.

The rollout

Four steps to a right lot.

Price the two costs properly

Estimate the real cost of placing an order (administration, transport, receiving) and the real holding cost (capital, space, obsolescence, as a percentage of value). These are the two levers; getting them right is the priority.

Compute the order of magnitude

Apply the formula to obtain the reference EOQ. Read it as a benchmark, not an instruction: it gives the right lot scale.

Adjust to reality

Round to a practical pack size close to the EOQ, factor in quantity discounts by comparing total costs, and respect capacity and expiry. The flatness of the curve allows these adjustments at no notable extra cost.

Revise when the economics change

Recompute if demand, ordering cost or holding cost move notably: higher rates, a change of transport, a new storage policy. The EOQ follows the reference's economics.

Neighboring concepts

Read next.

From knowledge to action

Do your lot sizes really minimise total cost?

Between ordering cost and holding cost, many lots are inherited from habit, not from a calculation. Our Inventory & distribution file resets your order quantities on the real economics of each reference.