Financial Management · Management of inventories, accounts receivable, accounts payable and cash

Inventory Management and Economic Order Quantity (EOQ)

Updated 11 October 2026 · Fact-checked

Economic order quantity (EOQ) is the order size that minimises the total of ordering and holding costs for an item with steady demand. Use EOQ = √(2 × Co × D ÷ Ch). Set the reorder level from usage during the lead time. With bulk discounts, compare total annual costs, including purchase price, at each order size.

Understand Inventory Management and Economic Order Quantity

Inventory ties up cash. Hold too little and you risk stock-outs, lost sales and stopped production. Hold too much and you pay to store, insure and finance it, and it may become obsolete. Inventory management looks for the balance.

The EOQ model looks at two costs that pull in opposite directions. Ordering costs (placing the order, delivery handling, inspection) are incurred per order, so larger and fewer orders cut them. Holding costs (storage, insurance, obsolescence, and the finance cost of cash tied up) are incurred per unit held, so smaller and more frequent orders cut them. EOQ is the quantity where total of the two is lowest. At that point, annual ordering cost equals annual holding cost.

The model assumes demand is constant and known, the lead time is known, there are no stock-outs, and the price per unit does not change with order size. Real firms rarely meet all of these. That is why EOQ is a guide, not a rule. The reorder level deals with timing: it is the stock level at which you place the next order so that stock arrives as the last unit is used. A buffer stock can be added to cover uncertainty in demand or lead time.

If a supplier offers a bulk discount, the EOQ is no longer automatically best. A larger order saves on price and ordering costs but raises holding costs. You must compare total annual costs, including purchases, at the EOQ and at each discount quantity.

Just-in-time (JIT) takes a different view. Instead of finding the best order size, it tries to cut inventory close to zero by receiving goods only when needed. It needs reliable suppliers, short lead times and a smooth production process. EOQ accepts inventory as a cost to be balanced; JIT treats holding inventory as waste to be removed.

Key rules to remember

Economic order quantity: EOQ = √(2 × Co × D ÷ Ch); Co = cost per order, D = annual demand in units, Ch = holding cost per unit per year. D and Ch must use the same time period (annual).
Total annual ordering and holding cost: Total cost = (D ÷ Q) × Co + (Q ÷ 2) × Ch; Q is the order size. Average stock is Q ÷ 2 because stock falls steadily from Q to zero.
Total annual cost including purchases: Total cost = D × P + (D ÷ Q) × Co + (Q ÷ 2) × Ch; P is the price per unit at that order size. Use this form for bulk discount decisions.
EOQ cost balance: At EOQ: (D ÷ Q) × Co = (Q ÷ 2) × Ch; A quick check on your answer. If the two costs differ at EOQ, something is wrong.
Reorder level (no buffer): Reorder level = usage per period × lead time; With uncertain demand or lead time, many questions use maximum usage × maximum lead time.
Reorder level with buffer stock: Reorder level = average usage × average lead time + buffer stock; Use whichever approach the question's data points to.

How to solve Inventory Management and Economic Order Quantity questions

Use this method for any EOQ, reorder level or discount question.

1Read the data and list D, Co, Ch and P. Check units: convert monthly or weekly figures to annual so D and Ch match.
2Identify what the holding cost is. If it is a percentage of price, work out the cost per unit per year. Note whether it changes under a discount.
3Calculate EOQ = √(2 × Co × D ÷ Ch). Keep the full figure for the next steps, round only at the end.
4Calculate the number of orders (D ÷ Q) and the annual ordering and holding costs if asked. Check they are equal at EOQ.
5For the reorder level, multiply usage by lead time. Add buffer stock if given, or use maximum usage and maximum lead time if the question gives ranges.
6For a bulk discount, calculate total annual cost (purchases + ordering + holding) at the EOQ and at each discount quantity. Use the discount quantity itself, not the EOQ, when the EOQ is below the threshold.
7Choose the lowest total cost, state the order quantity and the saving, and comment on any assumptions.

Quickest way: Compare totals at the EOQ and at the threshold

When to use it: Use this in Section B or C when a supplier offers a discount for orders above a set size.

Work out the EOQ at the normal price.
If the EOQ already meets the discount threshold, order the EOQ (check holding cost if it is a percentage of price).
If not, calculate total cost at the EOQ and at the threshold quantity only. Other quantities above the threshold cost more in holding with no further saving.
Write down the three cost lines each time: purchases, ordering, holding. This keeps working clear for method marks.
Pick the lower total and state the saving.

Common mistakes in Inventory Management and Economic Order Quantity

Using Q instead of Q ÷ 2 for holding cost.
Students forget that stock falls from Q to zero, so average stock is half the order size.
Fix: Always write (Q ÷ 2) × Ch. Then check that ordering cost equals holding cost at EOQ.
Mixing time periods, such as monthly demand with annual holding cost.
Data is often given in weeks or months while holding cost is per year.
Fix: Convert everything to annual figures before using the formula, and say so in your working.
Leaving out purchase cost in a bulk discount comparison.
The EOQ formula only uses ordering and holding costs, so students carry that habit over.
Fix: When prices differ, include D × P in every total. Otherwise the discount never shows up.
Using the EOQ when the discount threshold is higher, or ordering a quantity above the threshold.
Students treat the discount quantity as a range and look for a new optimum.
Fix: Compare the EOQ with the exact threshold quantity. Ordering more than the threshold only raises holding cost.
Confusing the reorder level with the order quantity.
Both are numbers of units, and both come from the same question.
Fix: EOQ says how much to order. The reorder level says when to order. Reorder level depends on usage and lead time, not on cost.
Treating EOQ as precise and ignoring its assumptions in discussion parts.
The calculation looks exact, so students forget the model is simplified.
Fix: State that demand and lead time may vary, prices may change, and that buffer stock or JIT may suit better in some businesses.

Worked examples

Example 1

A company uses 20,000 units of a component a year, spread evenly over 50 weeks. Each order costs $45 to place. Holding one unit for a year costs $5. (a) Calculate the EOQ. (b) Calculate the total annual ordering and holding cost at the EOQ. (c) Usage can reach 500 units a week and the lead time can reach 3 weeks. Calculate the reorder level using maximum figures. (d) If instead average usage and a 2-week lead time apply, with a buffer stock of 150 units, calculate the reorder level.

Show the solution

(a) EOQ = √(2 × 45 × 20,000 ÷ 5) = √(1,800,000 ÷ 5) = √360,000 = 600 units.
(b) Orders per year = 20,000 ÷ 600 = 33.33. Ordering cost = 33.33 × $45 = $1,500.
Holding cost = (600 ÷ 2) × $5 = 300 × $5 = $1,500. The two are equal, as expected. Total = $3,000.
(c) Reorder level = maximum usage × maximum lead time = 500 × 3 = 1,500 units.
(d) Average usage = 20,000 ÷ 50 = 400 units a week. Usage in lead time = 400 × 2 = 800 units. Add buffer stock: 800 + 150 = 950 units.

Answer: (a) EOQ = 600 units. (b) Total ordering and holding cost = $3,000 ($1,500 each). (c) Reorder level = 1,500 units. (d) Reorder level = 950 units.

Example 2

Using the data above, the component costs $12 per unit. The supplier offers a 2% discount on the whole order if each order is at least 1,000 units. Holding cost stays at $5 per unit per year. Should the company take the discount?

Show the solution

EOQ at normal price is 600 units, which is below 1,000, so compare 600 with 1,000.
At 600 units: purchases = 20,000 × $12 = $240,000. Ordering = 33.33 × $45 = $1,500. Holding = 300 × $5 = $1,500. Total = $243,000.
Discounted price = $12 × 0.98 = $11.76.
At 1,000 units: purchases = 20,000 × $11.76 = $235,200. Orders = 20,000 ÷ 1,000 = 20, so ordering = 20 × $45 = $900. Holding = (1,000 ÷ 2) × $5 = $2,500. Total = $238,600.
Saving from taking the discount = $243,000 − $238,600 = $4,400.

Answer: Yes. Order 1,000 units at a time. Total annual cost falls from $243,000 to $238,600, a saving of $4,400. This assumes the holding cost per unit does not change and that there is storage space and no risk of obsolescence.

Exam tips

Write the formula and substitute each figure on its own line. Method marks in Section C depend on clear working.
In objective test questions, check units first. A monthly demand figure in an annual formula is the most common trap, and answers are marked all or nothing.
For discount questions, set out a small table of purchases, ordering and holding costs for each quantity. It stops you missing a cost line.
Expect short discussion parts: compare EOQ with JIT, list EOQ assumptions, or explain why buffer stock is held. Give two or three specific points, not a general statement.
If the holding cost is a percentage of price, recalculate it for the discounted price before comparing.

Practice questions from Management of inventories, accounts receivable, accounts payable and cash

Inventory Management and Economic Order Quantity in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Inventory Management and Economic Order Quantity: frequently asked questions

What is the EOQ formula in ACCA FM?

EOQ = √(2 × Co × D ÷ Ch), where Co is the cost per order, D is annual demand and Ch is the annual holding cost per unit. It gives the order size that minimises ordering plus holding costs. The formula is given in the exam formulae sheet, but you still need to apply it correctly.

How do I calculate the reorder level?

Multiply usage per period by the lead time. If the question gives maximum usage and maximum lead time, use those. If it gives averages and a buffer stock, work out average usage during lead time and add the buffer.

How do bulk discounts change the EOQ?

They do not change the formula, but they change the decision. You compare total annual cost, including purchases, at the EOQ and at the discount quantity. The lower total wins, even if the order size is larger than the EOQ.

What is the difference between JIT and EOQ?

EOQ finds the cost-minimising order size while accepting that inventory is held. JIT aims to hold almost no inventory by receiving goods only when needed. JIT needs reliable suppliers, short lead times and stable production, while EOQ assumes steady demand and known lead time.