Quantity Discount EOQ Calculator
Enter annual demand, order cost, carrying rate, supplier price breaks, case pack size, and maximum order size. The calculator tests feasible order quantities in each tier and shows the annual cost of the best option.
Recommended order quantity1,000
- Selected price tier
- Tier 3: 1000 to 5000 units at $9.40 per unit
- Unit price
- $9.40
- Total annual inventory cost
- $95,675.00
- Annual savings from discounts
- $5,906.14
- Purchase cost per year
- $94,000.00
- Ordering cost per year
- $500.00
- Carrying cost per year
- $1,175.00
- Cash required per order
- $9,400.00
- Orders per year
- 10
- Average days between orders
- 36.5
- Average cycle inventory
- 500
Price-tier comparison
| Tier | Best quantity | Unit price | Purchase cost | Ordering cost | Carrying cost | Total annual cost | Difference |
|---|---|---|---|---|---|---|---|
| Tier 1: 1 to 499 units at $10.00 per unit | 499 | $10.00 | $100,000.00 | $1,002.00 | $623.75 | $101,625.75 | $5,950.75 |
| Tier 2: 500 to 999 units at $9.70 per unit | 642 | $9.70 | $97,000.00 | $778.82 | $778.43 | $98,557.24 | $2,882.24 |
| Tier 3: 1000 to 5000 units at $9.40 per unit | 1,000 | $9.40 | $94,000.00 | $500.00 | $1,175.00 | $95,675.00 | $0.00 |
Assumes all-units discounts, constant annual demand, instantaneous replenishment, and no stockouts.
Freight, safety stock, shelf life, financing limits, taxes, and supplier reliability are not modeled unless included in the entered costs or maximum order quantity.
How to use this calculator
- Enter annual demand and the fixed cost of placing one replenishment order.
- Enter the annual carrying rate as a percentage of inventory value.
- Add the base price and two all-units quantity discount tiers from the supplier quote.
- Enter the case-pack multiple and the largest order you can accept.
- Compare the recommended quantity with the tier table before committing cash or space.
How the quantity discount EOQ is calculated
A quantity discount changes the normal EOQ decision because the cheapest annual cost may occur at a price-break minimum rather than at the unconstrained EOQ. This calculator models an all-units discount: once an order reaches a tier minimum, that tier's unit price applies to every unit in the order.
For each tier, the annual cost tested is:
TC(Q) = D × c + (D ÷ Q) × S + (Q ÷ 2) × i × c
- D is annual demand.
- c is the unit price for the tier.
- S is the fixed cost to place one order.
- i is the annual carrying-rate decimal.
- Q is the order quantity.
The unconstrained EOQ for a tier is sqrt((2 × D × S) ÷ (i × c)). The calculator then limits that quantity to the tier's lower and upper bounds, the maximum order quantity, and the entered case-pack multiple. It tests the nearest valid multiples around the EOQ plus the feasible tier endpoints. That matters when a price break is not a case-pack multiple, because the first eligible order might be higher than the supplier's stated threshold.
Why a larger order can win
The total cost includes purchase cost, ordering cost, and carrying cost. A larger order usually reduces ordering cost because fewer orders are placed each year, but it raises average cycle inventory and therefore carrying cost. A discount tier can still win if the lower purchase price is large enough to offset the added inventory and cash tied up in each order.
The table shows the best feasible quantity inside each tier. The winning row is the one with the lowest total annual inventory cost, not necessarily the lowest unit price. The savings row compares that winning cost with the best feasible order quantity if the base price applied to every order size.
What this calculator leaves out
The model assumes known, steady annual demand and instantaneous replenishment without stockouts. It does not calculate safety stock, reorder points, lead-time risk, spoilage, taxes, supplier reliability, or quantity-dependent freight. It also does not model incremental or block pricing; use it only when the quoted tier price applies to every unit in the order.
The recommended quantity is a cost minimum under the inputs. Before placing an order, compare the cash required per order with working-capital limits, shelf life, storage space, and any operational risk not captured in the carrying rate.
Worked example
Suppose annual demand is 10,000 units, each order costs $50, and carrying cost is 25% of item value per year. The supplier charges $10 below 500 units, $9.70 from 500 to 999 units, and $9.40 at 1,000 units or more. Orders can be placed in single units and the maximum order is 5,000 units.
At the base price, the best feasible order is about 632 units and costs about $101,581 per year if the base price applied to every order size. Inside the second tier, the best quantity is 642 units and costs about $98,557 per year. Inside the third tier, the EOQ is below the tier minimum, so the calculator tests the 1,000-unit price break and gets $95,675 per year.
The recommendation is therefore 1,000 units at $9.40 per unit. Purchase cost is $94,000 per year, ordering cost is $500 per year, carrying cost is $1,175 per year, cash required per order is $9,400, and estimated savings versus the base-price-only search are about $5,906 per year.
Common questions
How do quantity discounts change EOQ?
A normal EOQ balances order cost against carrying cost at one unit price. With all-units discounts, the lower purchase price can make a price-break minimum cheaper than the EOQ from the previous tier. The calculator therefore compares the best feasible annual cost inside each tier.
Why can a price-break minimum beat the calculated EOQ?
The EOQ for a discounted tier may be below that tier minimum, so the smallest qualifying order is the first feasible way to get the lower price. If the annual purchase savings are larger than the extra carrying cost, that breakpoint can be the cheapest choice.
What is an all-units quantity discount?
In an all-units discount, the selected tier price applies to every unit in the order. For example, if 1,000 units qualifies for $9.40, all 1,000 units are priced at $9.40. That is different from incremental pricing, where only units above a threshold receive the lower price.
Should carrying cost use the discounted unit price?
Yes for this model. Carrying cost is entered as a percentage of inventory value, so the value of average cycle inventory changes when the unit price changes. Each tier uses its own unit price in the holding-cost term.
How do case-pack sizes affect the optimal order?
Case packs turn the order quantity into a multiple. If a supplier price break is 500 units but cases contain 144 units, the first feasible order that reaches the break is 576 units. The calculator rounds tier bounds to valid multiples before comparing costs.
Does EOQ include safety stock or reorder points?
No. EOQ answers how much to order under steady demand and immediate replenishment assumptions. Safety stock and reorder points answer when to order under lead-time and demand uncertainty, so they should be calculated separately.