Management Accounting · Accounting for material, labour and overheads

Inventory Control and Economic Order Quantity (EOQ) for ACCA Management Accounting

Updated 11 October 2026 · Fact-checked

Inventory control balances the cost of ordering against the cost of holding stock. The EOQ is the order size that minimises total of these costs: EOQ = √(2 × Co × D ÷ Ch). Reorder level = maximum usage × maximum lead time. Buffer stock covers uncertainty in demand or delivery.

Understand Inventory Control and Economic Order Quantity (EOQ)

Every business that holds inventory faces two opposing costs. Ordering costs rise when you place many small orders: paperwork, delivery, inspection. Holding costs rise when you keep a lot of stock: storage, insurance, theft, obsolescence and the interest lost on money tied up in stock.

The economic order quantity (EOQ) is the order size where total ordering cost plus total holding cost is lowest. At that point annual ordering cost equals annual holding cost. Small orders mean high ordering cost and low holding cost. Large orders mean the reverse.

The EOQ model assumes demand is constant and known, lead time is constant, no stockouts occur, and the purchase price per unit stays the same whatever the order size. Ordering cost per order and holding cost per unit per year are also assumed constant. Real life breaks these assumptions, which is why the EOQ is a guide, not a guarantee.

Stock levels tell you when to order. The reorder level is the stock level at which you place a new order, so that new stock arrives as the old runs out. Buffer stock (safety stock) is the minimum you keep to cover higher than expected demand or late delivery. The maximum stock level and minimum stock level show the upper and lower limits you aim to stay within.

When a supplier offers a bulk discount, the purchase price is no longer the same for all order sizes. So you cannot rely on the EOQ alone. You must compare total annual cost at the EOQ and at each discount threshold.

Key formulas 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. Use consistent time periods.
Reorder level: Reorder level = maximum usage × maximum lead time; This is the usual ACCA definition. If a question gives only average usage and lead time, it may use those instead, so read the wording.
Buffer stock: Buffer stock = reorder level − (average usage × average lead time); The extra stock held to cover usage or lead time above average.
Minimum stock level: Minimum level = reorder level − (average usage × average lead time); Same calculation as the buffer stock formula above.
Maximum stock level: Maximum level = reorder level + reorder quantity − (minimum usage × minimum lead time); The highest stock should reach if usage and lead time are at their lowest.
Average stock: Average stock = EOQ ÷ 2 (with no buffer stock); EOQ ÷ 2 + buffer stock (with buffer); Used to find total annual holding cost.
Total annual inventory cost: Total cost = purchases + ordering costs + holding costs = (D × price) + (D ÷ Q × Co) + (average stock × Ch); Q = order quantity. Use this to compare bulk discount options.

How to solve Inventory Control and Economic Order Quantity (EOQ) questions

Use this order for any inventory control or EOQ question.

1Identify what is asked: an order quantity, a stock level, or a cost comparison.
2List the data: annual demand D, ordering cost Co, holding cost Ch, price, usage rates and lead times.
3Check that units match. If demand is weekly, convert to annual, or convert Ch to the same period.
4For EOQ, apply √(2 × Co × D ÷ Ch). Round only at the end, and check whether the question wants a whole number.
5For stock levels, calculate the reorder level first, then buffer, minimum and maximum levels.
6For bulk discounts, calculate total annual cost at the EOQ and at each discount quantity above it. Include the purchase cost.
7Choose the option with the lowest total cost, provided the EOQ is feasible at its price band.
8Check the answer is sensible: for example, maximum level should be above reorder level.

Quickest way: Fast route for objective test questions

When to use it: Use this for number entry and multiple choice EOQ questions where you have about three minutes.

Write D, Co and Ch on scrap paper straight away.
Calculate 2 × Co × D first, divide by Ch, then take the square root on the calculator.
For multiple choice, estimate: if two options are far apart, a rough square root will often be enough.
For stock levels, calculate maximum usage × maximum lead time before anything else.
For discount questions, only compare total costs. Ignore costs that are the same in every option, but keep the purchase price if it differs.

Common mistakes in Inventory Control and Economic Order Quantity (EOQ)

Using monthly demand with an annual holding cost
The question gives data in mixed periods and students plug numbers in without checking.
Fix: Convert everything to a year before using the formula.
Forgetting purchase cost in bulk discount comparisons
Students are used to ordering and holding costs only, which are the only costs in the basic EOQ.
Fix: When price changes with order size, include D × price in every total cost.
Using the average rather than the maximum for reorder level
Students mix up the reorder level formula with the buffer stock formula.
Fix: Reorder level uses maximum usage and maximum lead time. Averages appear only in the buffer calculation.
Ignoring buffer stock in average stock for holding costs
Students remember EOQ ÷ 2 and forget that the buffer is always held.
Fix: Add buffer stock to EOQ ÷ 2 when a buffer is given.
Choosing the discount quantity without checking the EOQ
A discount looks attractive, so students skip the comparison.
Fix: Calculate total cost at the EOQ and at each threshold. The cheapest total wins.
Putting the holding cost as a percentage of price into the formula as a percentage
Ch is given as, for example, 10% of unit cost.
Fix: Convert it to a money amount per unit per year first, then use it in the formula.

Worked examples

Example 1

A company uses 18,000 units of a component a year. Each order costs $90. Holding one unit for a year costs $5. Calculate the EOQ and the total annual ordering and holding cost at the EOQ.

Show the solution

EOQ = √(2 × 90 × 18,000 ÷ 5).
2 × 90 × 18,000 = 3,240,000.
3,240,000 ÷ 5 = 648,000.
√648,000 = 804.98, so about 805 units.
Orders per year = 18,000 ÷ 805 = 22.36, about 22.4 orders. Ordering cost ≈ 22.36 × $90 = $2,012.
Average stock = 805 ÷ 2 = 402.5 units. Holding cost ≈ 402.5 × $5 = $2,012.
The two costs are equal, as expected at the EOQ. Total ≈ $4,025.

Answer: EOQ is about 805 units. Total ordering and holding cost is about $4,025 a year.

Example 2

A firm uses 10,000 units a year. Order cost is $50. Holding cost is $2 per unit per year. The price is $20 per unit for orders under 2,000 units and $19.50 per unit for orders of 2,000 units or more. Which order quantity minimises total annual cost?

Show the solution

EOQ = √(2 × 50 × 10,000 ÷ 2) = √500,000 = 707.1 units. This is below 2,000, so it is at the $20 price.
Cost at 707 units: purchases = 10,000 × $20 = $200,000.
Ordering = 10,000 ÷ 707.1 × $50 = $707.
Holding = 707.1 ÷ 2 × $2 = $707.
Total at EOQ = $200,000 + $707 + $707 = $201,414.
Cost at 2,000 units: purchases = 10,000 × $19.50 = $195,000.
Ordering = 10,000 ÷ 2,000 × $50 = 5 × $50 = $250.
Holding = 2,000 ÷ 2 × $2 = $2,000.
Total at 2,000 = $195,000 + $250 + $2,000 = $197,250.
$197,250 is lower than $201,414.

Answer: Order 2,000 units at a time. Total annual cost is $197,250, which is $4,164 below the cost at the EOQ.

Exam tips

Number entry questions often need rounding. Check whether the answer should be to the nearest whole unit or dollar.
Read whether holding cost is given per unit per year or as a percentage of price. Convert before using the formula.
In bulk discount questions, always compute the EOQ first. If it is already at or above a discount threshold, that discount applies and no comparison is needed for lower prices.
For multiple response questions on EOQ assumptions, remember the key ones: constant demand, constant lead time, no stockouts, and constant price per unit.
Write the formula before the numbers. It stops you putting values in the wrong place under time pressure.

Practice questions from Accounting for material, labour and overheads

Inventory Control and Economic Order Quantity (EOQ) in other exams

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

Inventory Control and Economic Order Quantity (EOQ): frequently asked questions

What is the EOQ formula in ACCA MA?

EOQ = √(2 × Co × D ÷ Ch). Co is the cost of placing one order, D is annual demand and Ch is the holding cost per unit per year. It gives the order size with the lowest combined ordering and holding cost.

How do I calculate the reorder level and buffer stock?

Reorder level = maximum usage × maximum lead time. Buffer stock = reorder level − (average usage × average lead time). Always check which figures the question gives you.

How do bulk discounts change the EOQ answer?

With a discount, the purchase price differs by order size, so it affects total cost. Calculate total annual cost, including purchases, at the EOQ and at each discount threshold. Choose the lowest total.

Why do ordering and holding costs equal each other at the EOQ?

Ordering cost falls as order size rises, while holding cost rises. Total cost is lowest where the two lines cross. This only applies to the basic EOQ model without discounts.