EOQ with quantity discounts.

EOQ when the supplier offers price breaks

The plain economic order quantity formula assumes one price. Real quotes rarely work that way: 1 to 1,000 units at one price, 1,001 to 5,000 at a lower one, and so on. Then the right question is not "what is the EOQ" but "which tier is cheapest once ordering and holding costs are counted". This page answers that by running the EOQ calculation inside each tier and comparing the totals, so a lower unit price is weighed against the cash and shelf space a bigger order ties up.

It is the buy-side companion to the single-price EOQ calculator, which says outright that it ignores discounts. For a one-off purchase rather than a repeating order, use the supplier price-break calculator.

Worked example

A shop uses 10,000 units a year. An order costs $40.00 to place and receive. Holding costs 10% of the unit price a year. The supplier charges $50.00 for 1 to 1,000 units, $45.00 for 1,001 to 5,000 and $40.00 from 5,001.

• Tier at $50.00: holding is $5.00 a unit, EOQ is 400 units, total cost is $502,000.00. This matches the 400-unit, $502,000 example in the Wikipedia article.
• Tier at $45.00: holding is $4.50, EOQ is 421.6, below the 1,001 minimum, so the order is 1,001 units and the total is $452,651.85.
• Tier at $40.00: holding is $4.00, EOQ is 447.2, below the 5,001 minimum, so the order is 5,001 units. Goods $400,000.00, ordering $79.98, holding $10,002.00, total $410,081.98.

Second check, using the inputs on an MIT OpenCourseWare slide (2,000 units a year, $500 per order, holding 25% of price, $50.00 base price, 2% off at 500 or more; the slide does not print the answer). Tier at $50.00: EOQ 400, total $105,000.00. Tier at $49.00: EOQ 404.1 is below 500, so the order is 500 units and the total is $103,062.50. The discount tier wins, and the calculator takes the break quantity exactly as the slide's algorithm says to when the discounted EOQ falls short.

The deepest discount wins by $42,569.87 a year over the middle tier. The holding rate and order cost here are example inputs, not market figures.

How it is calculated

For each tier with price P and minimum m: holding cost h = holding rate x P (or your fixed dollar figure); EOQ = sqrt(2 x D x S / h); if that is below m, the order size is m; if it reaches the next tier's minimum, the tier is skipped, because the next tier is cheaper per unit and is tested on its own. Total cost T = P x D + S x D / Q + h x Q / 2, the formula in the Wikipedia article, where D is annual demand, S the fixed cost per order and Q the order size. The tier with the lowest T is shown.

The model assumes constant demand, full delivery when stock reaches zero, a fixed cost per order and an all-units discount, where "an order of 1 to 1000 units costs $50 each" and higher quantities reprice every unit (Wikipedia's wording). The article says algorithms are needed for the optimum but does not spell one out; the tier-by-tier comparison here is this site's implementation of its total-cost formula. Incremental (marginal) discounts, where only the extra units get the lower price, are not modelled; see the price-break calculator.

What this does not cover

• Incremental discounts where each price applies only to the units in its band.
• Minimum order sizes, case packs and pallet quantities. Round the result to what you can really buy.
• Shelf life, obsolescence and storage limits, which can make a large tier a bad buy even when it is cheapest on paper.
• Stockouts, price changes during the year and lead times. Use the reorder point calculator for timing.

Sources

Opened and read on 2026-10-26 (figures and wording as of that date):

• Economic order quantity, Wikipedia: total cost formula, assumptions, the all-units discount definition and the 400-unit, $502,000 example.
• Extensions to EOQ, MIT OpenCourseWare ESD.260 (Chris Caplice, MIT Center for Transportation & Logistics): definitions of all-units and incremental discounts and the all-units algorithm (compare the total cost at the EOQ with the total cost at the break quantity).