EOQ with Quantity Discount
Suppliers often cut the unit price if you order in bigger batches. That changes the EOQ question: is the discount worth the extra holding cost? You find the EOQ at each price, bump it up to the minimum order if needed, and pick the option with the lowest total annual cost, including the purchase price.
What you will learn
- Why purchase price must be included in total cost with discounts
- How to calculate EOQ at each price break
- What to do when the EOQ falls below a discount's minimum order
- How to compare total annual cost and pick the best order size
The formulas
- D
- annual demand in units
- S
- cost per order
- i
- annual holding cost rate
- P
- unit price at that price break
- Q
- order quantity being tested
- D × P
- annual purchase cost
Worked example
Annual demand is 10,000 units, each order costs $50, and holding cost is 20% of the unit price per year. The price is $10 per unit, or $9.60 for orders of 1,000 units or more. What order size minimizes total cost?
- At $10: H = $2, EOQ = √(2 × 10,000 × $50 ÷ $2) ≈ 707 units, which qualifies for this price.
- TC at 707 ≈ $100,000 + $707 + $707 ≈ $101,414.
- At $9.60: H = $1.92, EOQ ≈ 722 units, below the 1,000 minimum, so test Q = 1,000.
- TC at 1,000 = $96,000 + (10 × $50) + (500 × $1.92) = $96,000 + $500 + $960 = $97,460.
- Compare: $97,460 is lower than about $101,414.
Answer: Order 1,000 units at $9.60 for a total annual cost of $97,460, about $3,954 less than ordering 707 units at $10 (figures rounded to the nearest dollar).
Common questions
How do you calculate EOQ with quantity discounts?
Calculate the EOQ for each price level. If an EOQ is below that price's minimum order, raise it to the minimum. Then work out total annual cost, including the purchase cost, for each candidate and choose the lowest.
Why include the purchase price in total cost with discounts?
In basic EOQ the unit price is the same for every order size, so it does not affect the decision. With discounts the price depends on order size, so annual purchase cost changes and must be part of the comparison.
What if the EOQ is below the minimum quantity for a discount?
You cannot get the discount at that EOQ, so test the minimum quantity needed to qualify instead. Total cost is lowest as close to the EOQ as allowed, which makes the minimum order size the best feasible choice at that price.
Is it always worth taking the quantity discount?
No. A bigger order raises average inventory and holding cost. If the savings on price and ordering cost are smaller than the extra holding cost, the regular EOQ at the higher price wins. You must compare total costs.