How much to order at once: the EOQ trade-off

Decide course — make the call

• Track: Supply Chain & Procurement
• Difficulty: Beginner · 4/8
• Read time: ~18 min, then you make the call
• The concept: EOQ / order-quantity trade-off
• Scored decision — one defensible answer, reasoning shown. You pick the call; every wrong option shows what it costs you. This is a Decide course: you make a judgment, you don’t run code, and it is not a certification.
• ▶ Interactive model — a calculator on this page turns your own numbers into the decision, so you can stress-test the call yourself.

1. Before you start

Every time you buy a part you use over and over, two costs pull in opposite directions. Order a lot at once and you place few orders — but you sit on a big pile of stock, tying up cash and warehouse space. Order a little at a time and your shelves stay lean — but you place many orders, and each order costs money to raise, ship, and receive. The order quantity is the dial between them. The Economic Order Quantity (EOQ) is the setting that makes the two costs add up to the least.

A tiny example: if raising one order costs you $10 and holding one unit for a year costs $2, then ordering in tiny batches buries you in $10 order charges, and ordering a year’s worth at once buries you in holding cost. The cheapest batch is somewhere in between — and there is a formula for it.

Three honest statements before you start:

• This is a Decide course. You read a situation, learn the idea, and make a call. You do not write or run any code.
• The company below, Halden Gearworks, is composite — an invented firm built from ordinary figures so the arithmetic is clean. No number is a claim about any real company.
• This is not a certification. It shows, to you, that you can defend an order-quantity call.

You need only arithmetic and a square root. The hard part is judgment, not maths.

2. The Situation

Halden Gearworks machines industrial gearboxes and buys a steel bearing housing it uses on every unit — 12,000 a year, steadily. The buyer currently orders 3,000 at a time, four times a year, “to keep the paperwork down.” A supplier has just dangled a small price cut for ordering even bigger. The plant manager, eyeing a full stockroom, wants smaller, more frequent orders instead.

Both of them are guessing. The order size that actually costs the least is a number you can compute — and whether the discount is worth taking turns on a second number neither of them has worked out.

3. What you’ll be able to do

After this course you will be able to:

• Compute a part’s Economic Order Quantity from its annual demand, its per-order cost, and its per-unit holding cost — and say what the EOQ is balancing.
• Explain why the total-cost curve is flat near the EOQ, so a rounded, practical order quantity is usually fine — and name how far off you can be before it matters.
• Decide whether a quantity discount is worth ordering above the EOQ, by weighing the price saving against the extra holding cost — and name the number that flips the answer.

4. Prerequisites & time box

Prerequisites: arithmetic and a square root. Helpful but not required: the idea that holding inventory has a cost (covered in section 6). No spreadsheet, no supply-chain background.

Time box: about 18 minutes of reading (measured), plus your own thinking time on the call. That is under the 25-minute cap for a concept course.

Difficulty: 4 / 8 — a new-manager decision: a couple of interacting factors and one real judgment call, where the obvious answer is often the trap.

Free-tier honesty: no signup, no software, requires_gpu: false.

5. The case & where the numbers come from

Halden Gearworks is a composite manufacturer: its figures are ordinary values a machining shop would recognise, chosen for clean arithmetic and not drawn from or claimed about any real firm. The definitions — EOQ, ordering cost, holding (carrying) cost, quantity discount — are standard and cited in section 11. Every figure below is an in-course assumption; every later number is computed from these.

Item	Figure
Annual demand for the bearing housing	12,000 units / year
Ordering cost per order (raise PO, freight, receive, inspect)	$300 / order
Holding cost per unit per year (capital, space, insurance, obsolescence)	$5 / unit / year
Purchase price (base)	$50 / unit
Discount tier	order 2,400+ at once → $49.40 / unit
Current practice	3,000 units, 4 times a year

Holding cost is commonly quoted as a percentage of a unit’s value (roughly 20-30% a year is typical in the carrying-cost literature cited in section 11); here we state Halden’s holding cost directly as $5 a unit so every step is reproducible.

6. The Concepts

The order-quantity trade-off

Two costs move in opposite directions as you change the order size Q.

• Annual ordering cost = (number of orders a year) × (cost per order) = (D ÷ Q) × S, where D is annual demand and S is the cost of one order. Bigger Q → fewer orders → less ordering cost.
• Annual holding cost = (average units on hand) × (holding cost per unit) = (Q ÷ 2) × H. On a steady draw-down, stock sits at Q right after delivery and 0 just before the next, averaging Q ÷ 2. Bigger Q → more stock on the shelf → more holding cost.

For Halden, D = 12,000, S = $300, H = $5. Take the buyer’s current Q = 3,000:

• Ordering cost = (12,000 ÷ 3,000) × $300 = 4 × $300 = $1,200.
• Holding cost = (3,000 ÷ 2) × $5 = 1,500 × $5 = $7,500.
• Total relevant cost = $1,200 + $7,500 = $8,700 a year.

The buyer optimised the wrong cost: ordering four times a year is cheap on paperwork but leaves 1,500 housings sitting on the shelf on average. The purchase price of the part ($50) is the same however you slice the orders, so it drops out of this decision — only ordering and holding costs change with Q. (Price comes back the moment a discount is on the table; see below.)

The EOQ formula

The total relevant cost (D ÷ Q)×S + (Q ÷ 2)×H is smallest when the two terms are equal. Solving that gives the Economic Order Quantity:

EOQ = sqrt( 2 · D · S / H )

For Halden: EOQ = sqrt( 2 × 12,000 × $300 / $5 ) = sqrt( 7,200,000 / 5 ) = sqrt( 1,440,000 ) = 1,200 units. Check it by rebuilding the two costs at Q = 1,200:

• Orders a year = 12,000 ÷ 1,200 = 10; ordering cost = 10 × $300 = $3,000.
• Holding cost = (1,200 ÷ 2) × $5 = 600 × $5 = $3,000.
• Total relevant cost = $6,000 a year.

At the EOQ the ordering cost and the holding cost are equal ($3,000 each) — that balance is the whole idea, and it is why the formula works. Moving from the buyer’s 3,000-unit habit to the 1,200-unit EOQ cuts the relevant cost from $8,700 to $6,000 — about $2,700 a year saved, with no change to the part, the price, or the demand.

(An interactive calculator sits here — enter demand, ordering cost, holding cost, and a discount tier, and it returns the EOQ, the cost at the EOQ, and whether the discount is worth ordering bigger.)

Why the total-cost curve is flat near the EOQ

The EOQ sits at the bottom of a shallow bowl, not a sharp spike — so being near it is almost as cheap as being on it. Halden’s EOQ is 1,200, at $6,000 a year. Watch what a round, practical quantity costs:

• Q = 1,000 (round pallet quantity): orders = 12; ordering = 12 × $300 = $3,600; holding = 500 × $5 = $2,500; total = $6,100 — just $100 (1.7%) above the EOQ.
• Q = 1,500: orders = 8; ordering = $2,400; holding = 750 × $5 = $3,750; total = $6,150 — $150 (2.5%) above the EOQ.

Being off the EOQ by ±25% costs under 3%. That is the practical payoff of the formula: you do not need to order exactly 1,200. Round to a convenient truck-load, pallet, or box multiple and you leave almost nothing on the table. The costly mistakes are the big ones — Halden’s 3,000-unit habit, at $8,700, is 45% over — not the small rounding. So the honest advice is “order roughly the EOQ,” which is why a slightly “wrong” round quantity is usually the right business answer.

When a quantity discount shifts the call

The flat bowl assumes the price per unit is fixed. A quantity discount breaks that assumption: buy in a big enough batch and the unit price drops, so now the purchase cost changes with Q too, and it can swamp the ordering-and-holding trade-off. To judge a discount, compare the two things it moves:

Halden’s supplier offers $49.40 instead of $50 if each order is at least 2,400 units (double the EOQ).

• Purchase saving: $0.60 off × 12,000 units a year = $7,200 a year. This is real money the EOQ calculation never saw, because at a single price the purchase cost was the same at any Q.
• Extra ordering + holding cost of moving from Q = 1,200 to Q = 2,400: at 2,400, orders = 12,000 ÷ 2,400 = 5, so ordering = 5 × $300 = $1,500 and holding = 1,200 × $5 = $6,000, a total of $7,500 — versus $6,000 at the EOQ. Extra cost = $1,500 a year.
• Net: $7,200 saved − $1,500 extra = +$5,700 a year. Take the discount.

Here the discount wins comfortably, because a small price cut applied to every unit outweighs the extra holding on a bigger pile. But the call flips when the balance changes. If Halden’s holding cost were far higher — say $25 a unit instead of $5, because the housings were bulky and prone to rust — the 2,400-unit pile would cost so much to hold that the extra holding (about $18,000 a year) would dwarf the $7,200 price saving, and Halden should stay at its EOQ. The same flip happens if the discount shrinks to a few cents. The lesson: a discount is worth taking only when the price saving beats the extra holding it forces — run both numbers, do not take the headline price on faith.

7. Your Call

You have seen how the EOQ balances ordering against holding, why the cost curve is flat near it, and when a discount is worth ordering bigger. Now a different one lands on your desk.

Brightwater Bottling runs a beverage line and buys a printed can-end it uses on every can — 30,000 a year, steadily. Raising and receiving one order costs $150, and holding one can-end for a year costs $4. So far this is the same EOQ concept as Halden’s. But there are two new wrinkles: Brightwater’s supplier will only accept orders of 2,500 units or more (a minimum order quantity), and Brightwater’s stockroom can physically hold at most 2,000 can-ends at any one time. Your job is a go/no-go feasibility-and-cost call on that supplier, not a discount comparison.

How this differs from the taught case (the transfer): this is a different company and sector (a beverage bottler, not Halden’s gearbox machining), the figures are different so the arithmetic must be redone, and there is an added constraint — a supplier minimum order quantity colliding with a hard storage limit — that turns an order-sizing exercise into a feasibility call. The core concept is the same: the EOQ order-quantity trade-off, and how far off the EOQ you can afford to be.

8. Self-check

Before you write the memo, make sure you can say each of these in one line:

• What two costs does the EOQ balance, and which way does each move as the order size grows?
• Why does rounding the EOQ to a convenient quantity cost almost nothing, and when does that stop being true?
• What is the two-number test for whether a quantity discount is worth ordering above the EOQ?

If any is fuzzy, reread section 6 — the trade-off, the formula, the flat curve, and the discount test are the whole course.

9. Stretch

Push the decision further on your own:

• Back at Halden: the supplier now offers $48.80 (a bigger cut) for orders of 4,000+. Redo the two-number test. Does the deeper discount survive the much larger holding cost of a 4,000-unit pile, and what is the net?
• The EOQ formula assumes a per-order cost S that does not change. If Halden could halve S to $150 by automating its purchase orders, what happens to the EOQ, and to the annual cost — and would that investment change whether the discount is worth taking? (The genuinely harder one: recompute the EOQ with S = $150, then rerun the discount test.)
• Write the one sentence you would say to a buyer who insists “fewer, bigger orders are always cheaper because they cut paperwork.”

10. Ship it — your decision memo

Write a one-page memo to Brightwater’s operations lead. State the call (do not accept the supplier’s 2,500-unit minimum as-is: the 1,500-unit EOQ is the low-cost order size, and a 2,500-unit order cannot be stored under the 2,000 cap — so renegotiate the minimum, add storage, or change supplier). Show the arithmetic (EOQ = sqrt(2 × 30,000 × 150 / 4) = 1,500; cost at EOQ $6,000; cost at 2,500 about $6,800; storage cap 2,000). Name what you rejected (“the $800 penalty is small, just order it”) and why (the cap makes it physically impossible, not merely costly). Name the one thing that would change your mind (more storage or a lower minimum, after which the modest cost penalty — or a real discount — decides it). Keep it to a single page an operations lead grasps in two minutes. This memo is your own argued claim — not a credential.

11. Sources

Halden Gearworks and Brightwater Bottling, and every figure attached to them, are composite and illustrative — constructed for clean teaching arithmetic, not drawn from or claimed about any real company. The concept definitions used to reason about them are standard; references below.

Concept / claim	Source (publisher)	URL	Accessed
EOQ = sqrt(2·D·S/H); balances ordering and holding cost	Wikipedia — Economic order quantity	https://en.wikipedia.org/wiki/Economic_order_quantity	2026-07-19
Holding (carrying) cost and its typical size as a percentage of unit value	Wikipedia — Carrying cost	https://en.wikipedia.org/wiki/Carrying_cost	2026-07-19
Quantity discount for ordering in larger volumes	Wikipedia — Discounts and allowances	https://en.wikipedia.org/wiki/Discounts_and_allowances	2026-07-19

Next up

Finished this call? Continue the Supply Chain & Procurement track:

The cheapest quote isn’t the cheapest supplier: total cost of ownership →  ·  Browse all courses