EOQ Calculator

EOQ Calculator - Economic Order Quantity

Calculate your optimal order quantity with our free Economic Order Quantity (EOQ) calculator. Minimize inventory costs, reduce waste, and optimize your supply chain management.

What is EOQ?

Economic Order Quantity (EOQ) is a formula used by businesses to determine the optimal order quantity that minimizes total inventory costs. It balances holding costs (costs to store inventory) against ordering costs (costs to place orders) to find the most cost-effective order size. EOQ helps businesses maintain adequate stock levels while reducing unnecessary expenses.

Why Use EOQ?

• Cost Reduction: Minimize total inventory holding and ordering costs
• Cash Flow Optimization: Avoid over-investing in inventory
• Storage Efficiency: Optimize warehouse space utilization
• Stockout Prevention: Maintain adequate inventory levels
• Waste Reduction: Reduce obsolete and expired inventory
• Supplier Negotiation: Plan orders for better pricing terms

How to Calculate EOQ

EOQ Formula

EOQ = √[(2 × D × S) ÷ H]

Where:
D = Annual demand (units per year)
S = Ordering cost per order
H = Holding cost per unit per year

Example:
Annual Demand: 1,000 units
Ordering Cost: $50 per order
Holding Cost: $2 per unit per year

EOQ = √[(2 × 1,000 × 50) ÷ 2]
EOQ = √[100,000 ÷ 2]
EOQ = √50,000
EOQ = 224 units (optimal order quantity)

Understanding the Components

1. Annual Demand (D):

• Total units sold or used per year
• Based on historical sales data
• Adjusted for seasonal variations
• Includes forecasted growth

2. Ordering Cost (S):

• Fixed costs per order regardless of size
• Includes processing, receiving, and inspection
• Accounts for administrative time
• May include shipping if not unit-based

3. Holding Cost (H):

• Cost to store one unit for one year
• Includes warehousing, insurance, and capital costs
• Often expressed as percentage of unit value
• Accounts for obsolescence and spoilage risk

Calculating Holding Costs

Holding Cost Components

Storage Costs:

• Warehouse rent or ownership costs
• Utilities (electricity, climate control)
• Equipment and maintenance
• Handling and labor costs

Capital Costs:

• Opportunity cost of tied-up capital
• Interest on loans used to purchase inventory
• Return you could earn elsewhere

Risk Costs:

• Obsolescence and shrinkage
• Spoilage (for perishables)
• Insurance and taxes

Holding Cost Rate Calculation:

Annual Holding Cost Rate:
- Storage: 3% of inventory value
- Capital cost: 8% (interest rate)
- Risk costs: 4% (obsolescence, insurance)
Total holding cost rate: 15%

If unit cost = $100:
Holding Cost (H) = $100 × 0.15 = $15 per unit per year

EOQ in Practice

Example 1: Retail Store

Scenario:

• Product: Designer jeans
• Annual sales: 2,400 pairs
• Ordering cost: $75 per order
• Holding cost: $8 per pair per year

Calculation:

EOQ = √[(2 × 2,400 × 75) ÷ 8]
EOQ = √[360,000 ÷ 8]
EOQ = √45,000
EOQ = 212 pairs

Orders per year: 2,400 ÷ 212 = 11.3 ≈ 11 orders
Order frequency: Every 33 days

Example 2: Manufacturing

Scenario:

• Component: Steel bolts
• Annual usage: 50,000 units
• Ordering cost: $120 per order
• Unit cost: $0.50
• Holding cost rate: 20%

Calculation:

Holding Cost = $0.50 × 0.20 = $0.10 per unit

EOQ = √[(2 × 50,000 × 120) ÷ 0.10]
EOQ = √[12,000,000 ÷ 0.10]
EOQ = √120,000,000
EOQ = 10,954 units

Orders per year: 50,000 ÷ 10,954 = 4.6 ≈ 5 orders
Order frequency: Every 73 days

Example 3: Restaurant

Scenario:

• Item: Olive oil (cases)
• Annual usage: 500 cases
• Ordering cost: $40 per order
• Case cost: $120
• Holding cost rate: 25% (high spoilage risk)

Calculation:

Holding Cost = $120 × 0.25 = $30 per case

EOQ = √[(2 × 500 × 40) ÷ 30]
EOQ = √[40,000 ÷ 30]
EOQ = √1,333
EOQ = 37 cases

Orders per year: 500 ÷ 37 = 13.5 ≈ 14 orders
Order frequency: Every 26 days

EOQ Assumptions and Limitations

Key Assumptions

The EOQ model assumes:

• Constant demand - Usage rate is steady and predictable
• Fixed costs - Ordering and holding costs remain constant
• No shortages - Stockouts are not acceptable
• Instant delivery - Lead time is constant or negligible
• Fixed price - No quantity discounts available

When EOQ May Not Apply

Consider modifications when:

• Demand is highly seasonal or variable
• Suppliers offer quantity discounts
• Lead times are uncertain
• Storage space is limited
• Items have short shelf lives
• Minimum order quantities apply

Advanced EOQ Concepts

EOQ with Quantity Discounts

When suppliers offer discounts for larger orders, compare the total cost at each discount level:

Total Cost = (D × Unit Price) + (D × S ÷ Q) + (Q × H ÷ 2)

Compare total costs at:
1. EOQ quantity (no discount)
2. Minimum quantity for each discount tier
3. Choose the lowest total cost

Example:
- Normal price: $100, EOQ = 200 units
- Discount: $95 if ordering 500+ units

Calculate total cost at both quantities and choose lower

EOQ with Production Runs (EPQ)

For items you produce rather than purchase:

EPQ = √[(2 × D × S) ÷ H × (P ÷ (P - D))]

Where:
P = Production rate (units per year)
D = Demand rate (units per year)
S = Setup cost per production run
H = Holding cost per unit per year

Use EPQ when production rate exceeds demand rate

Related Calculators

• Reorder Point Calculator - When to place orders based on lead time
• Safety Stock Calculator - Buffer stock for demand uncertainty
• Inventory Turnover Calculator - How efficiently inventory is used