How Quantity Discounts Affect Your EOQ

The Challenge of Bulk Discounts

The standard Economic Order Quantity (EOQ) formula assumes that the purchase price per unit remains constant, regardless of how many units you order. However, in the real world, suppliers frequently offer quantity discounts (e.g., "$10 per unit for 1-99 units, $9 per unit for 100+ units").

When discounts are introduced, the standard EOQ formula is no longer sufficient on its own.

Why Standard EOQ Fails Here

If you only use the standard EOQ, you might calculate an optimal order size of 80 units. But what if ordering 100 units drops the price significantly? The savings on the purchase price might outweigh the increased holding costs of storing those extra 20 units.

How to Calculate EOQ with Quantity Discounts

To find the true optimal order quantity when discounts are available, you must follow a multi-step process:

1. Calculate the EOQ for each price tier. Use the standard EOQ formula, but remember that your holding cost (H) might change if it's calculated as a percentage of the unit cost.
2. Adjust invalid EOQs. If the calculated EOQ for a specific price tier does not fall within the required quantity range for that discount, adjust it to the lowest possible quantity that qualifies for the discount.
3. Calculate the Total Annual Cost for each valid/adjusted EOQ. This is the crucial step. The total cost must now include the actual purchase cost of the goods.
   • Total Cost = Annual Purchase Cost + Annual Ordering Cost + Annual Holding Cost
4. Select the lowest total cost. Compare the total costs calculated in step 3. The order quantity that yields the absolute lowest total cost is your optimal order size.

The Trade-off

Taking a quantity discount always increases your holding costs (because you are ordering more at once). The mathematical goal is to ensure that the savings from the lower purchase price and the lower annual ordering costs are greater than the spike in holding costs.