EOQ Calculator
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The Economic Order Quantity (EOQ) Calculator determines the ideal order quantity a business should purchase to minimize total inventory management costs. EOQ identifies the exact equilibrium point where inventory setup/ordering costs equal inventory holding/carrying costs.
By implementing an EOQ inventory model, companies avoid both stockouts and excessive warehousing expenses, freeing up working capital and optimizing supply chain operations across manufacturing, wholesale, and e-commerce retail businesses.
Economic Order Quantity (EOQ) Formula
The classic Economic Order Quantity formula is calculated as the square root of twice the annual demand multiplied by ordering cost, divided by annual holding cost per unit:
EOQ = √[ (2 × D × S) / H ]
Where:
- D (Annual Demand): Total number of units sold or consumed over a 12-month period.
- S (Order / Setup Cost): Fixed cost incurred per order placed (includes shipping, handling, invoice processing, and inspection fees).
- H (Holding / Carrying Cost): Annual cost to store one unit of inventory (includes warehouse rent, insurance, storage, and capital tie-up expenses).
Inventory Cost Trade-Off Matrix
EOQ solves the fundamental tension between order frequency and storage expense. The table below illustrates how order sizing impacts operational supply chain costs:
| Order Quantity Strategy | Ordering Costs | Holding Costs | Total Cost & Risk Impact |
|---|---|---|---|
| Small, Frequent Orders | High (Multiple transaction fees) | Low (Minimal stock in warehouse) | Higher administrative expenses, increased stockout risk during supplier delays. |
| Large, Infrequent Orders | Low (Fewer purchase orders) | High (Heavy warehousing costs) | Capital tied up in stock, higher risk of damage, theft, or inventory obsolescence. |
| EOQ Optimal Point | Balanced | Balanced | Minimum total inventory cost. Maximum working capital efficiency. |
Step-by-Step EOQ Calculation Example
Suppose an e-commerce retailer manages a popular electronics accessory with the following supply parameters:
- Annual Demand (D): 10,000 units
- Order Cost (S): $50 per purchase order
- Holding Cost (H): $4 per unit per year
Step 1: Multiply 2 by Demand and Order Cost
2 × 10,000 × $50 = 1,000,000
Step 2: Divide by Holding Cost per Unit
1,000,000 / 4 = 250,000
Step 3: Take the Square Root
√(250,000) = 500 units
Result: The optimal purchase batch size is 500 units. Placing 20 orders per year (10,000 / 500) minimizes total combined ordering and holding expenses.
Frequently Asked Questions (FAQ)
What are the primary assumptions of the EOQ model?
The standard EOQ model assumes constant consumer demand, fixed ordering and holding costs, instantaneous order delivery, and no bulk quantity discounts from suppliers.
How does holding cost impact EOQ?
Holding cost is inversely related to EOQ. Higher holding costs (such as expensive refrigerated storage or high insurance) reduce the optimal order quantity, forcing smaller, more frequent replenishment batches.
Can EOQ be modified for bulk volume discounts?
Yes. Businesses can calculate total annual costs across different supplier price break tiers to determine if bulk purchasing discounts outweigh the extra carrying costs of larger order sizes.
What is the difference between EOQ and Reorder Point (ROP)?
EOQ answers how much inventory to purchase per batch, whereas Reorder Point (ROP) specifies when to place the order based on lead time and safety stock thresholds.