Financial Management and Business Data Analytics · Inventory Management

Economic Order Quantity (EOQ) Model: Formula and Numericals

Updated 10 October 2026 · Fact-checked

Economic Order Quantity is the order size that gives the lowest total of ordering cost and carrying cost. Use EOQ = √(2AO ÷ C), where A is annual demand, O is cost per order and C is carrying cost per unit per year. Then find the number of orders as A ÷ EOQ.

Understand Economic Order Quantity (EOQ) Model

Every firm that holds stock faces two opposing costs. Each time you place an order, you pay an ordering cost: purchase paperwork, transport, inspection. Each unit you keep in the store costs you a carrying cost: storage, insurance, obsolescence and interest on money locked up.

If you order in large lots, you place few orders, so ordering cost is low. But average stock is high, so carrying cost is high. If you order in small lots, carrying cost falls but ordering cost rises. The Economic Order Quantity (EOQ) is the lot size where the total of the two costs is the lowest.

At EOQ, total ordering cost equals total carrying cost. This is the key check for every numerical. Average stock is half the order size (Q ÷ 2), because stock falls steadily from Q to zero and is then refilled.

The basic model rests on assumptions: demand is known and constant, lead time is fixed, the whole order arrives at once, there are no stock-outs, the price per unit stays the same (no quantity discounts), and ordering and carrying costs behave as stated. Real life breaks several of these, so the model gives a guide, not an exact answer. Safety stock, reorder level and discounts are handled in related topics.

Key rules to remember

Economic Order Quantity: EOQ = √(2 × A × O ÷ C); A = annual demand in units, O = ordering cost per order, C = carrying cost per unit per year. Keep A and C on the same unit and the same year.
Carrying cost per unit: C = carrying cost % × purchase price per unit; Use this when carrying cost is given as a percentage of price. If it is given in rupees per unit per year, use it directly.
Number of orders per year: N = A ÷ EOQ; If the answer is not a whole number in the question, state it as it is unless asked to round.
Time between orders: Days between orders = number of days in year ÷ N; Use 360 or 365 days as the question states. If nothing is stated, say which one you use.
Total ordering cost: (A ÷ Q) × O; Q is the order size.
Total carrying cost: (Q ÷ 2) × C; Based on average stock of Q ÷ 2, with no safety stock.
Total relevant cost at EOQ: Total relevant cost = √(2 × A × O × C) = EOQ × C; At EOQ ordering cost equals carrying cost, so each is half of this total.
Total inventory cost: Total cost = purchase cost (A × P) + ordering cost + carrying cost; Purchase cost is the same for every order size when there is no discount, so it does not change the EOQ.

How to solve Economic Order Quantity (EOQ) Model questions

Follow the same order every time. It protects you from unit mix-ups and gives step marks even if an arithmetic slip occurs.

1List the data: annual demand (A), cost per order (O), purchase price per unit and carrying cost. Convert monthly or weekly demand into a yearly figure.
2Find carrying cost per unit per year (C). If it is a percentage, multiply it by the unit price.
3Write the formula EOQ = √(2AO ÷ C), put in the values and compute 2AO ÷ C before taking the square root.
4Find the number of orders as A ÷ EOQ and the gap between orders as days in the year ÷ number of orders.
5Calculate ordering cost (N × O) and carrying cost (EOQ ÷ 2 × C). Check that they are equal.
6Add purchase cost only if the question asks for total inventory cost or compares policies.
7If another order size is proposed, compute its total relevant cost the same way and state the saving or extra cost.
8Write the final answer with units and a one-line conclusion.

Quickest way: Square-root shortcut and equal-cost check

When to use it: Use it in the MCQ section or when you need a fast written answer with limited time.

Compute 2 × A × O first, then divide by C. Simplify by cancelling zeros before the square root.
Test your result by squaring it: EOQ × EOQ should equal 2AO ÷ C.
Get total relevant cost as EOQ × C. You do not need to compute both costs separately.
If demand becomes 4 times, EOQ doubles, because EOQ moves with the square root of demand.
EOQ varies with √A and √O, and inversely with √C. If ordering cost becomes 4 times, EOQ doubles. If carrying cost becomes 4 times, EOQ halves.
For MCQs, test each option by checking whether ordering cost equals carrying cost at that quantity. The option where they are equal is the EOQ.

Common mistakes in Economic Order Quantity (EOQ) Model

Using carrying cost percentage as the rupee value of C.
The question says 20% and students put 20 or 0.20 into the formula directly.
Fix: Multiply the percentage by the purchase price first. 20% of ₹25 gives C = ₹5 per unit per year.
Mixing monthly demand with yearly carrying cost.
A and C must be for the same period, but the question may give monthly usage.
Fix: Convert demand to an annual figure before starting, or convert C to a monthly figure, but never mix the two.
Forgetting to take the square root, or taking it before dividing.
Rushing through a long expression.
Fix: Work out 2AO ÷ C as one number, write it down, then take the root. Check by squaring.
Using the full order size instead of half for carrying cost.
Students forget that average stock is Q ÷ 2.
Fix: Always write carrying cost as (Q ÷ 2) × C. At EOQ, it should match ordering cost.
Adding purchase cost when finding EOQ.
Students think total cost must include purchase price in the formula.
Fix: Purchase cost does not affect EOQ in the basic model. Add it only to get total inventory cost, and use price only to find C.
Not stating the days used for time between orders.
Questions use 360 or 365 days, and students pick one without saying so.
Fix: Use the number of days the question gives. If none is given, write your assumption in the answer.

Worked examples

Example 1

Bharat Auto Components uses 14,400 units of a part every year. Each order costs ₹250 to place. The purchase price is ₹25 per unit and carrying cost is 20% of the purchase price. Calculate (a) EOQ, (b) number of orders per year, (c) total ordering and carrying cost at EOQ, and (d) the extra cost if the firm orders 1,800 units each time.

Show the solution

Carrying cost per unit C = 20% × ₹25 = ₹5 per year.
EOQ = √(2 × 14,400 × 250 ÷ 5) = √(72,00,000 ÷ 5) = √14,40,000 = 1,200 units.
Number of orders = 14,400 ÷ 1,200 = 12 orders a year (one every month).
Ordering cost at EOQ = 12 × ₹250 = ₹3,000.
Carrying cost at EOQ = (1,200 ÷ 2) × ₹5 = 600 × ₹5 = ₹3,000. Both are equal, so the EOQ is verified. Total relevant cost = ₹6,000.
For Q = 1,800: orders = 14,400 ÷ 1,800 = 8. Ordering cost = 8 × ₹250 = ₹2,000. Carrying cost = (1,800 ÷ 2) × ₹5 = 900 × ₹5 = ₹4,500. Total = ₹6,500.
Extra cost = ₹6,500 − ₹6,000 = ₹500.

Answer: EOQ = 1,200 units; 12 orders a year; total ordering plus carrying cost at EOQ = ₹6,000 (₹3,000 each); ordering 1,800 units at a time costs ₹500 more a year.

Example 2

Kaveri Stores sells 9,000 units of an item a year. Ordering cost is ₹200 per order. The item costs ₹50 and carrying cost is 20% of cost. Using a 360-day year, find (a) EOQ, (b) number of orders and days between orders, (c) total relevant cost, and (d) the new EOQ if annual demand rises to 36,000 units.

Show the solution

C = 20% × ₹50 = ₹10 per unit per year.
EOQ = √(2 × 9,000 × 200 ÷ 10) = √(36,00,000 ÷ 10) = √3,60,000 = 600 units.
Number of orders = 9,000 ÷ 600 = 15 orders.
Days between orders = 360 ÷ 15 = 24 days.
Ordering cost = 15 × ₹200 = ₹3,000. Carrying cost = (600 ÷ 2) × ₹10 = 300 × ₹10 = ₹3,000. Total relevant cost = ₹6,000. Shortcut check: EOQ × C = 600 × ₹10 = ₹6,000.
New EOQ for A = 36,000: √(2 × 36,000 × 200 ÷ 10) = √(1,44,00,000 ÷ 10) = √14,40,000 = 1,200 units.
Demand became 4 times, but EOQ only doubled (600 to 1,200), because EOQ depends on the square root of demand.

Answer: EOQ = 600 units; 15 orders a year, one every 24 days; total relevant cost = ₹6,000; at 36,000 units of demand the EOQ becomes 1,200 units.

Exam tips

In the MCQ section, questions are short: a direct EOQ, a number of orders, or a total cost. Do the 2AO ÷ C step mentally and test your answer by squaring.
In written answers, show the formula, the substitution and the check that ordering cost equals carrying cost. These are separate step marks.
Read the carrying cost line twice. It may be a percentage of price, a rupee amount per unit, or a monthly figure.
When asked to compare the firm's current policy with EOQ, compute total relevant cost for both and state the saving in rupees.
Be ready to write the assumptions and limitations in two or three lines each. Mention constant demand, fixed lead time, no discounts, no stock-outs and the difficulty of estimating costs.

Practice questions from Inventory Management

Economic Order Quantity (EOQ) Model in other exams

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

Economic Order Quantity (EOQ) Model: frequently asked questions

What is the formula for EOQ in CMA Intermediate?

EOQ = √(2AO ÷ C). A is annual demand in units, O is ordering cost per order and C is carrying cost per unit per year. Always bring all three to a yearly basis.

What are the main assumptions of the EOQ model?

Demand is known and constant, lead time is fixed, and each order arrives in one lot. There are no stock-outs, and the price does not change with order size. Ordering cost per order and carrying cost per unit are taken as constant.

What are the limitations of the EOQ model?

Real demand and lead times vary, so a fixed formula can be inaccurate. It ignores quantity discounts and safety stock in its basic form. Costs such as ordering and carrying are also hard to measure exactly.

Does purchase price change the EOQ?

Only through carrying cost when it is stated as a percentage of price. The price itself is not a term in the formula. In the basic model, it is added only when total inventory cost is asked.

How do I find the timing of orders?

First find the number of orders as annual demand ÷ EOQ. Then divide the days in the year, 360 or 365 as given, by the number of orders. This gives the gap between two orders.