Financial Management and Business Data Analytics · Inventory Management

EOQ with Quantity Discounts: How to Solve Numericals

Updated 10 October 2026 · Fact-checked

EOQ with quantity discounts finds the cheapest order size when the supplier lowers the price for bigger orders. Compute the EOQ for each price, keep only those that fall inside their own quantity band, add the minimum quantity of each higher band, then compare total costs. Choose the lowest total cost.

Understand EOQ with Quantity Discounts

The basic EOQ model assumes one fixed price. It balances ordering cost, which falls as orders get bigger, against carrying cost, which rises. A supplier discount adds a third force: bigger orders also cut the purchase price.

This means the EOQ alone may no longer be the cheapest order size. A larger order may cost more to carry, but the saving on price can outweigh that. So you cannot trust the formula alone. You must compare total cost at each possible order size.

Total cost has three parts: purchase cost (annual demand × price), ordering cost (number of orders × cost per order) and carrying cost (average stock × carrying cost per unit). In the basic model purchase cost does not change with order size, so it is ignored. With discounts it does change, so it must be included.

Carrying cost can be given in two ways. It may be a fixed rupee amount per unit per year, so EOQ is the same at every price. Or it may be a percentage of the purchase price, so each price gives a different carrying cost and a different EOQ. Read the question carefully for this.

The only order sizes worth testing are the EOQ that is valid in its own price band, and the lowest quantity of each band offering a lower price. The cheapest of these is the best order size.

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. If C is a percentage of price, C = percentage × price of that band.
Carrying cost: Carrying cost = (Q ÷ 2) × C; Assumes steady usage, so average stock is half the order quantity Q.
Ordering cost: Ordering cost = (A ÷ Q) × O; A ÷ Q is the number of orders in a year. It can be a fraction in a calculation.
Purchase cost: Purchase cost = A × price per unit; Use the price of the band that Q falls in.
Total relevant cost: Total cost = A × P + (A ÷ Q) × O + (Q ÷ 2) × C; Compare this for each candidate order size. The lowest total is the best order size.
Validity check: EOQ is valid only if lower limit ≤ EOQ ≤ upper limit of its price band; If the EOQ is below the band, use the band's minimum quantity instead. If it is above the band, ignore it.

How to solve EOQ with Quantity Discounts questions

This method works for any quantity discount question, whether carrying cost is fixed or a percentage of price.

1Write down annual demand, ordering cost per order, carrying cost basis and the full price schedule with quantity bands.
2Calculate the EOQ using the price of the first band, or the fixed carrying cost if given. Round only at the end.
3Check whether this EOQ lies within its own band. If carrying cost is a percentage of price, repeat the EOQ for each band and check each one.
4Build the list of candidates: every valid EOQ, plus the minimum quantity of every band whose price is lower than the price of the band holding the valid EOQ.
5For each candidate, work out purchase cost, ordering cost and carrying cost using that band's price, then add them.
6Present the figures in a neat table-like layout with one line per candidate.
7Choose the order quantity with the lowest total cost and state it clearly with the total cost.
8Add one line of interpretation, for example that the discount saving outweighs the extra carrying cost.

Quickest way: Candidate-list shortcut

When to use it: Use when time is short and the schedule has two or three price bands.

Find the EOQ for each price band, starting with the highest price, which is usually the lowest quantity band.
For each band, check where the EOQ lies. If it is inside the band, it is a candidate. If it is below the band, use the band's lower limit as the candidate. If it is above the band, ignore that band's EOQ.
Keep the lower limit of each cheaper band as a candidate, since a bigger order may earn the lower price.
Compute total cost for each candidate. Calculate purchase cost first, since it is the largest part of the total.
Compare the totals and pick the lowest. Write the answer in the first line of your conclusion.

Common mistakes in EOQ with Quantity Discounts

Leaving out purchase cost when comparing totals.
In the basic EOQ model purchase cost is ignored, so students carry that habit over.
Fix: With discounts the price changes between options, so always include A × price in every total.
Using the EOQ of a band even though it falls outside that band's quantity range.
Students compute the formula and stop without checking validity.
Fix: After every EOQ calculation, compare it with the band limits. If it is too low, use the lower limit of the band instead.
Using the same carrying cost for every band when it is stated as a percentage of price.
The carrying cost per unit is copied from the first calculation.
Fix: Recompute C = percentage × price for each band, and use it in both EOQ and carrying cost.
Calculating carrying cost on the full order quantity instead of Q ÷ 2.
Students forget that stock falls steadily to zero between orders.
Fix: Always use average stock, which is Q ÷ 2, unless the question states otherwise.
Picking the EOQ with the biggest discount without checking totals.
A larger discount feels like a better deal.
Fix: A lower price can still be worse if the extra carrying cost is larger than the saving. Only the total cost comparison decides.
Rounding the EOQ early and carrying rounding errors into the totals.
Students round to a whole number at once.
Fix: Keep full precision while finding EOQ. Round the order quantity only when you use it as a candidate, and say so.

Worked examples

Example 1

A firm needs 8,000 units a year. Ordering cost is ₹400 per order. Carrying cost is 20% of the purchase price per unit per year. The supplier's prices are: ₹50 per unit for orders below 1,000 units; ₹48 per unit for 1,000 to 1,999 units; ₹47 per unit for 2,000 units and above. Find the best order quantity.

Show the solution

Price ₹50: C = 20% × 50 = ₹10. EOQ = √(2 × 8,000 × 400 ÷ 10) = √6,40,000 = 800 units. 800 lies within the ₹50 band (below 1,000 units), so it is valid.
Price ₹48: C = ₹9.60. EOQ = √(64,00,000 ÷ 9.6) ≈ 816.5 units. This is below 1,000, so it is not valid. Use 1,000 units.
Price ₹47: C = ₹9.40. EOQ = √(64,00,000 ÷ 9.4) ≈ 825 units. This is below 2,000, so it is not valid. Use 2,000 units.
Candidate 800 units at ₹50: purchase = 8,000 × 50 = ₹4,00,000. Ordering = (8,000 ÷ 800) × 400 = 10 × 400 = ₹4,000. Carrying = (800 ÷ 2) × 10 = ₹4,000. Total = ₹4,08,000.
Candidate 1,000 units at ₹48: purchase = ₹3,84,000. Ordering = 8 × 400 = ₹3,200. Carrying = 500 × 9.60 = ₹4,800. Total = ₹3,92,000.
Candidate 2,000 units at ₹47: purchase = ₹3,76,000. Ordering = 4 × 400 = ₹1,600. Carrying = 1,000 × 9.40 = ₹9,400. Total = ₹3,87,000.
The lowest total cost is ₹3,87,000.

Answer: Order 2,000 units each time at ₹47 per unit. Total annual cost is ₹3,87,000, which is ₹21,000 less than ordering the EOQ of 800 units.

Example 2

A company uses 4,800 units a year. Ordering cost is ₹150 per order and carrying cost is ₹4 per unit per year, whatever the price. The supplier charges ₹40 per unit for orders below 1,000 units and ₹38 per unit for orders of 1,000 units or more. Decide whether the company should take the discount.

Show the solution

Carrying cost is fixed, so the EOQ is the same for both prices. EOQ = √(2 × 4,800 × 150 ÷ 4) = √3,60,000 = 600 units.
600 units is below 1,000, so it is valid at ₹40. At ₹38 the EOQ is not valid, so the candidate is 1,000 units.
At 600 units and ₹40: purchase = 4,800 × 40 = ₹1,92,000. Ordering = (4,800 ÷ 600) × 150 = 8 × 150 = ₹1,200. Carrying = 300 × 4 = ₹1,200. Total = ₹1,94,400.
At 1,000 units and ₹38: purchase = 4,800 × 38 = ₹1,82,400. Ordering = (4,800 ÷ 1,000) × 150 = 4.8 × 150 = ₹720. Carrying = 500 × 4 = ₹2,000. Total = ₹1,85,120.
Saving by taking the discount = 1,94,400 − 1,85,120 = ₹9,280.

Answer: Take the discount and order 1,000 units each time. Total annual cost falls from ₹1,94,400 to ₹1,85,120, a saving of ₹9,280.

Exam tips

Draw a small layout with columns for order quantity, price, purchase cost, ordering cost, carrying cost and total. It earns step marks and keeps you organised.
Read the carrying cost line twice. A fixed rupee amount means one EOQ. A percentage of price means a different EOQ for each band.
Always write the validity check for each EOQ in one line. Examiners look for it.
For MCQs, compute total cost for every candidate. Purchase cost is the largest component, but do not choose on price alone.
End with a clear decision statement in rupees: order quantity, total cost and saving over the plain EOQ.

Practice questions from Inventory Management

EOQ with Quantity Discounts in other exams

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

EOQ with Quantity Discounts: frequently asked questions

Do I include purchase cost in EOQ with quantity discounts?

Yes. In the basic model the price is the same at every order size, so purchase cost is left out. With discounts the price changes by order size, so it must be part of the total cost for each option.

What if the EOQ falls below the minimum quantity for a discount?

Then the EOQ is not valid for that band. The only order size worth testing in that band is its minimum quantity. Work out the total cost at that quantity and compare it with the other options.

Why does carrying cost sometimes change with the price band?

When carrying cost is given as a percentage of purchase price, a lower price means a lower cost per unit to hold stock. So you must work out the rupee carrying cost for each band. If a fixed rupee amount is given, it stays the same.

Is the lowest price always the best choice?

No. A bigger order cuts the price but raises the stock you hold, which raises carrying cost. The best choice is the quantity with the lowest total cost, which you find only by comparing totals.