Order quantity

A supplier sells at €8.00 a unit, in packs of 24, with a minimum order of 1,000 and €7.80 from 2,400 units. You sell 1,000 a month, an order costs you €60 to place and receive, and holding stock costs 25% of its value a year.

The textbook EOQ is 849 units. The minimum order pushes you to 1,008, and that costs only €25 a year more: the cost curve is flat around the EOQ. The price break is the real decision, and it depends on a word the quote often leaves out. If the lower price applies to all units of an order of 2,400 or more, order 2,400 and save €1,482 a year. If it applies only to the units above 2,400 (incremental), the best order at that price, 2,568, costs €965 a year more than staying at 1,008. Ask the supplier which one they mean.

The tool also gives the price each break has to reach to pay off. Read as all-units, the break pays at €7.92 or less, so the quoted €7.80 has room to spare. Read as incremental, it would pay only at €7.51 or less: that is the number to negotiate with. And the minimum order would cost nothing extra if the supplier took €0.002 a unit off.

The yearly cost of an order size

For an order of Q units: purchase D × p(Q) ÷ Q, ordering D × S ÷ Q, and holding h × p(Q) ÷ 2. D is the yearly demand (12 × the monthly figure), S the cost per order, h the holding rate and p(Q) what the Q units cost under the price breaks. Half an order sits in stock on average, valued at what you paid for it. Without breaks the lowest sum is at the EOQ, √(2 × D × S ÷ (h × price)).

What the supplier allows

Orders are multiples of the pack size and at least the minimum order rounded up to the pack. Your cap, if you set one, is the most months of demand you will take in one order, rounded down to the pack. If the cap is below the minimum order the tool says so and shows the minimum.

Price breaks

All-units: every unit of an order at or above the break costs the break price. Incremental: each band of units costs its own price, so an order just above the break is only slightly cheaper per unit on average. Within one price band the yearly cost is a smooth curve with a single lowest point, so the tool checks the pack multiples either side of that point and the band's edges, for every band, and keeps the cheapest. The tests check this against trying every allowed order.

Break-even prices

For each price break the tool finds, by bisection, the highest break price at which the break's best order still costs no more a year than the best order without that break. For the minimum order it solves the same question for the unit price: the price at which ordering the minimum costs the same as the best order below it. Both are prices to take into a negotiation, not forecasts.

Scrap

If part of what you buy cannot be used, you buy D ÷ (1 − scrap) to end with D good units, and every cost is on the units bought. With 12k good units a year and 2% scrap that is 12,245 bought. The tool shows the cost per good unit as well.

Room to round

The orange band on the chart and the "room to round" line give the order sizes whose yearly cost stays within 1% (and 5%) of the best order's ordering and holding cost. Rounding to a full pallet layer, a pallet or a truck inside that band costs little.

What the tool leaves out

Demand is taken as steady; for the buffer against uneven demand and late deliveries, useSafety stock. No forecasting, no several items sharing one order or one truck, no capacity limits, no expiry write-offs beyond your cap. Freight that changes with the order size (a full truck vs a part load) is not modelled; put an average in the cost per order.

Disclaimer

A planning aid, not advice. Check the result against your supplier's terms and your own costs before you order. Your inputs stay in your browser (in the page address and local storage so you can come back to them); nothing you type is sent to this site. See the privacy notice and Impressum.

What is the EOQ formula?

EOQ = √(2 × D × S ÷ H): D is the annual demand in units, S the cost of placing one order, H the cost of holding one unit for a year (often the unit price × a holding rate). At the EOQ the yearly ordering cost and the yearly holding cost are equal, and their sum is lowest.

What if the supplier has a minimum order quantity above the EOQ?

Order the minimum, rounded up to the pack size. The cost curve is flat near the EOQ, so the minimum usually costs little: in the example on this page the EOQ is 849 units, the minimum order 1,000, and ordering 1,008 costs €25 a year more.

What is the difference between all-units and incremental quantity discounts?

With all-units pricing, an order at or above the break quantity gets the lower price on every unit. With incremental pricing, only the units above the break get it. The same quote can lead to opposite decisions: with a break at 2,400 units from €8.00 to €7.80, all-units pricing makes 2,400 the best order (€1,482 a year cheaper), incremental pricing keeps 1,008 (the best order at the lower price costs €965 a year more).

What holding cost rate should I use?

Your own, if you can build it: the cost of the capital tied up in stock (usually the largest part), plus storage, handling, insurance, shrinkage and obsolescence, each as a share of the stock value a year. Without one, 25% a year is a common textbook planning figure: Heizer and Render’s Operations Management breaks a typical rate down to 26%, 11 points of it capital; MIT’s logistics course uses 25% in its worked examples. The order quantity moves with the square root of the rate, so a rough figure costs little.