Cost and Management Accounting · Material Cost

Economic Order Quantity and Ordering Costs

Updated 4 October 2026 · Fact-checked

Economic Order Quantity (EOQ) is the order size that makes total ordering cost plus carrying cost lowest. Use EOQ = √(2 × A × O ÷ C), where A is annual demand, O is cost per order and C is carrying cost per unit per year. With discounts, compare total cost at each price.

Understand Economic Order Quantity and Ordering Costs

Every time you buy material, you face two opposing costs. Ordering more often raises the ordering cost: the cost of placing and receiving each order, such as purchase department expenses, transport, inspection and paperwork. Ordering in large lots raises the carrying cost: interest on money locked in stock, storage, insurance, obsolescence and pilferage.

Ordering cost falls as order size rises, because you place fewer orders. Carrying cost rises as order size rises, because the average stock held is higher. The EOQ is the order size where these two costs are equal, and that is where their total is lowest.

The model assumes demand is known and steady, the price is constant, the ordering cost per order is fixed, the carrying cost per unit is fixed and there are no stock-outs. Average stock is taken as half of the order quantity. That is why carrying cost = (Q ÷ 2) × C.

When a supplier offers a quantity discount, the price changes with order size. Then the plain EOQ is not enough. The purchase cost itself now differs between options, so you must compare the total cost (purchase + ordering + carrying) at each possible order size and pick the lowest.

Key rules to remember

Economic Order Quantity: EOQ = √(2 × A × O ÷ C); A = annual consumption in units, O = ordering cost per order, C = carrying cost per unit per year.
Carrying cost per unit: C = Purchase price per unit × carrying cost % (+ any fixed storage cost per unit); If carrying cost is given as a percentage, it applies to the price. Under discounts, C changes with the price.
Total ordering cost: (A ÷ Q) × O; A ÷ Q is the number of orders a year.
Total carrying cost: (Q ÷ 2) × C; Uses average stock of Q ÷ 2.
Total inventory cost with discount: Total cost = A × Price + (A ÷ Q) × O + (Q ÷ 2) × C; Compute for each price band's quantity and choose the minimum.
Number of orders and cycle: Orders per year = A ÷ EOQ; Days between orders = days in year ÷ orders; Often asked as a follow-up part.

How to solve Economic Order Quantity and Ordering Costs questions

Use this order for any EOQ or discount question. It keeps the working clean and earns step marks.

1Write down A (annual demand), O (cost per order) and C (carrying cost per unit per year). Convert monthly or weekly data into annual figures.
2If carrying cost is a percentage, convert it into rupees per unit using the price. Check that you use the right price.
3Compute EOQ = √(2AO ÷ C) and show the substitution.
4Find number of orders (A ÷ EOQ) and, if asked, ordering cost and carrying cost at EOQ. They should be equal.
5If discounts exist, work out the EOQ for each band at that band's price and compare it with the band's range. If a band's EOQ lies inside the band, use it. If it is below the band minimum, use the minimum quantity of that band. If it is above the band's upper limit, that band is not feasible.
6Prepare a table of total cost (purchase + ordering + carrying) for each eligible quantity.
7Choose the lowest total cost and state the order size clearly. Add the saving or extra cost if the question asks.

Quickest way: Fast EOQ with a total-cost table

When to use it: Use it for numerical questions and for MCQs where you must pick an order size or a cost.

Compute EOQ first. For MCQs, test each option's square: EOQ² = 2AO ÷ C, and pick the option that matches.
At EOQ, ordering cost equals carrying cost, so total relevant cost = 2 × carrying cost = √(2AOC). This saves one calculation.
Test the EOQ of each band. If it lies within the band, use it. If it is below the band minimum, use the band's minimum quantity. If it is above the band's upper limit, drop that band. Compare total costs across all feasible quantities.
The purchase cost A × Price is large, so a discount often wins even when the quantity is above EOQ. Still, confirm by calculation.
In the written answer, draw a small table with columns: quantity, price, purchase cost, ordering cost, carrying cost, total. Label each line.

Common mistakes in Economic Order Quantity and Ordering Costs

Using monthly demand directly in the formula.
The question gives monthly usage and the student forgets the formula needs annual demand.
Fix: Convert to annual first, and check that C is also per year.
Taking carrying cost percentage on the wrong base.
Students apply the percentage to total annual purchases or forget it applies per unit price.
Fix: Carrying cost per unit = price × percentage. Under discounts, recompute it using the discounted price.
Dividing Q by 2 for ordering cost or forgetting it for carrying cost.
The average stock logic is mixed up with the number of orders.
Fix: Ordering cost uses A ÷ Q orders. Carrying cost uses Q ÷ 2 average stock.
Ignoring purchase cost when comparing discount offers.
Students compare only ordering and carrying costs, as in plain EOQ.
Fix: With different prices, always include A × Price in each total.
Accepting an EOQ that lies outside its price band.
The EOQ is computed at one price and applied to another band without checking.
Fix: Recalculate EOQ at each band's price and check it against the band. If it is below the band minimum, use the minimum quantity. If it is above the band's upper limit, treat that band as not feasible.
Not rounding sensibly.
Students leave EOQ as a decimal or round a number of orders incorrectly.
Fix: Round EOQ to a practical whole unit if asked, and state the number of orders as given by A ÷ EOQ.

Worked examples

Example 1

Annual demand for a material is 7,200 units. Ordering cost is ₹500 per order. Purchase price is ₹50 per unit and carrying cost is 20% of the price per year. Find the EOQ, the number of orders a year and the total ordering and carrying cost at EOQ.

Show the solution

A = 7,200 units; O = ₹500; C = 20% × ₹50 = ₹10 per unit per year.
EOQ = √(2 × 7,200 × 500 ÷ 10) = √(7,200,000 ÷ 10) = √720,000 = 848.53 units.
√720,000 = 848.53, so EOQ is about 849 units.
Orders per year = 7,200 ÷ 848.53 = 8.4853 orders, about 8.5 orders.
Ordering cost = 8.4853 × ₹500 = ₹4,242.64, about ₹4,243. (If you round orders to 8.49 first, you get about ₹4,245, so keep the exact figure.)
Carrying cost = (848.53 ÷ 2) × ₹10 = 424.26 × ₹10 = ₹4,242.64, about ₹4,243. The two are equal.
Total ordering and carrying cost = ₹8,485.28, about ₹8,485, which equals √(2 × 7,200 × 500 × 10) = √72,000,000 = ₹8,485.28.

Answer: EOQ ≈ 849 units; about 8.5 orders a year; ordering cost ≈ ₹4,243 and carrying cost ≈ ₹4,243; total ≈ ₹8,485.

Example 2

A firm uses 4,000 units a year. Ordering cost is ₹100 per order. Carrying cost is ₹2 per unit per year. The supplier charges ₹10 per unit for orders below 1,000 units and ₹9.50 per unit for orders of 1,000 units or more. Which order size should the firm choose?

Show the solution

A = 4,000; O = ₹100; C = ₹2 per unit per year (fixed, not linked to price).
EOQ = √(2 × 4,000 × 100 ÷ 2) = √400,000 = 632.46, about 632 units. This lies in the ₹10 band (below 1,000).
Option 1: Q = 632.46 at ₹10. Purchase = 4,000 × 10 = ₹40,000. Ordering = (4,000 ÷ 632.46) × 100 = ₹632.46. Carrying = (632.46 ÷ 2) × 2 = ₹632.46. Total = 40,000 + 632.46 + 632.46 = ₹41,264.92.
Option 2: Q = 1,000 at ₹9.50. Purchase = 4,000 × 9.50 = ₹38,000. Ordering = (4,000 ÷ 1,000) × 100 = ₹400. Carrying = (1,000 ÷ 2) × 2 = ₹1,000. Total = ₹39,400.
Compare: ₹39,400 is lower than ₹41,264.92, so the discount is worth taking.
Saving = 41,264.92 − 39,400 = ₹1,864.92 (about ₹1,865).

Answer: Order 1,000 units at a time at ₹9.50. Total annual cost is ₹39,400 against ₹41,265 at EOQ, a saving of about ₹1,865.

Exam tips

Write the formula and the substituted values before the answer. Step marks depend on this.
For discount questions, always show a total-cost table. It makes the comparison obvious to the examiner.
Read how carrying cost is given: a rupee amount per unit or a percentage of price. This decides whether C changes with the discount.
In MCQs, use the fact that ordering cost equals carrying cost at EOQ to check your answer quickly.
State the final decision in a sentence, with the order size and the cost saving.

Practice questions from Material Cost

Economic Order Quantity and Ordering Costs 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 and Ordering Costs: frequently asked questions

What is the difference between ordering cost and carrying cost?

Ordering cost is the cost of placing and receiving an order, such as paperwork, transport and inspection. Carrying cost is the cost of holding stock, such as storage, insurance, interest and obsolescence. Ordering cost falls as order size rises, while carrying cost rises.

How do I use the EOQ formula with a quantity discount?

Find the EOQ and check which price band it lies in. Then calculate total cost (purchase, ordering and carrying) at the EOQ and at the minimum quantity of each cheaper band. Choose the lowest total cost.

Why is average stock taken as Q ÷ 2?

The model assumes stock falls steadily from Q to zero before the next order arrives. The average of Q and zero is Q ÷ 2, so carrying cost is charged on half of the order quantity.

Is purchase cost relevant in EOQ?

In plain EOQ with one fixed price, purchase cost is the same for any order size, so it does not affect the decision. With quantity discounts the price differs, so purchase cost must be included in the comparison.