EOQ (Economic Order Quantity) Calculator
This calculator determines the optimal order quantity that minimizes total inventory costs, including ordering costs and holding costs.
Enter the annual demand, ordering cost per order, and holding cost per unit (or as a percentage of unit cost).
Enter Inventory Parameters
Understanding EOQ (Economic Order Quantity)
What is EOQ?
The Economic Order Quantity (EOQ) is the ideal order quantity a company should purchase to minimize inventory costs such as holding costs, shortage costs, and order costs. This production-scheduling model was developed in 1913 by Ford W. Harris.
EOQ Formula
The primary EOQ formula is:
EOQ = √((2 × D × S) / H)
Where:
- D = Annual demand (units)
- S = Ordering cost per order ($)
- H = Holding cost per unit per year ($)
Total Annual Inventory Cost Formula
The total cost includes ordering, holding, and purchase costs:
Total Cost = (D/Q × S) + (Q/2 × H) + (D × P)
Where:
- Q = Order quantity (EOQ when optimized)
- P = Unit cost ($)
Assumptions of EOQ Model
- Demand is constant and known
- Lead time is constant
- Ordering and holding costs are constant
- No quantity discounts available
- No stockouts occur
Example Calculation
EX: A company has annual demand of 10,000 units, ordering cost of $50 per order, and holding cost of $2 per unit/year.
EOQ = √((2 × 10,000 × 50) / 2) = √(1,000,000) = 1,000 units
Total Cost = (10,000/1,000 × 50) + (1,000/2 × 2) + (10,000 × P) = $500 + $1,000 + (P × 10,000)
Real-Life EOQ Examples
Click on an example to see the step-by-step calculation:
Example 1: Retail Store Inventory
Scenario: A clothing store sells 5,000 units of a particular shirt annually.
1. Known Values: Annual Demand (D) = 5,000 units, Ordering Cost (S) = $30 per order, Holding Cost (H) = $1.50 per unit/year.
2. EOQ Calculation: EOQ = √((2 × 5,000 × 30) / 1.50) = √(300,000 / 1.50) = √200,000 ≈ 447 units
3. Number of Orders: 5,000 / 447 ≈ 11.19 orders/year
4. Cycle Time: 365 / 11.19 ≈ 32.6 days between orders
5. Total Cost: (5,000/447 × 30) + (447/2 × 1.50) ≈ $335.57 + $335.25 = $670.82 (excluding purchase cost)
Conclusion: The store should order 447 shirts about 11 times per year.
Example 2: Manufacturing Components
Scenario: A factory needs 20,000 components annually for production.
1. Known Values: D = 20,000, S = $100 per order, H = $5 per unit/year.
2. EOQ Calculation: EOQ = √((2 × 20,000 × 100) / 5) = √(4,000,000 / 5) = √800,000 ≈ 894 units
3. Number of Orders: 20,000 / 894 ≈ 22.37 orders/year
4. Cycle Time: 365 / 22.37 ≈ 16.3 days between orders
5. Total Cost: (20,000/894 × 100) + (894/2 × 5) ≈ $2,237 + $2,235 = $4,472
Conclusion: The factory should order 894 components about 22 times per year.
Example 3: Percentage Holding Cost
Scenario: A retailer sells 8,000 units/year of a product costing $25/unit.
1. Known Values: D = 8,000, S = $40 per order, Holding Cost = 20% of unit cost.
2. Calculate H: H = 20% × $25 = $5 per unit/year
3. EOQ Calculation: EOQ = √((2 × 8,000 × 40) / 5) = √(640,000 / 5) = √128,000 ≈ 358 units
4. Number of Orders: 8,000 / 358 ≈ 22.35 orders/year
5. Total Cost: (8,000/358 × 40) + (358/2 × 5) + (8,000 × 25) ≈ $894 + $895 + $200,000 = $201,789
Conclusion: The optimal order quantity is 358 units with total annual cost of $201,789.
Example 4: Office Supplies
Scenario: An office uses 2,500 reams of paper annually.
1. Known Values: D = 2,500, S = $15 per order, H = $0.75 per ream/year.
2. EOQ Calculation: EOQ = √((2 × 2,500 × 15) / 0.75) = √(75,000 / 0.75) = √100,000 = 316 reams
3. Number of Orders: 2,500 / 316 ≈ 7.91 orders/year
4. Cycle Time: 365 / 7.91 ≈ 46.1 days between orders
5. Total Cost: (2,500/316 × 15) + (316/2 × 0.75) ≈ $118.67 + $118.50 = $237.17
Conclusion: The office should order 316 reams about 8 times per year.
Example 5: High-Value Electronics
Scenario: A store sells 600 high-end cameras annually at $800 each.
1. Known Values: D = 600, S = $75 per order, Holding Cost = 25% of unit cost.
2. Calculate H: H = 25% × $800 = $200 per unit/year
3. EOQ Calculation: EOQ = √((2 × 600 × 75) / 200) = √(90,000 / 200) = √450 ≈ 21 units
4. Number of Orders: 600 / 21 ≈ 28.57 orders/year
5. Total Cost: (600/21 × 75) + (21/2 × 200) + (600 × 800) ≈ $2,142.86 + $2,100 + $480,000 = $484,242.86
Conclusion: For these expensive items, the store should order just 21 cameras at a time.
Example 6: Bulk Food Ingredients
Scenario: A bakery uses 12,000 kg of flour annually.
1. Known Values: D = 12,000 kg, S = $60 per order, H = $0.80 per kg/year.
2. EOQ Calculation: EOQ = √((2 × 12,000 × 60) / 0.80) = √(1,440,000 / 0.80) = √1,800,000 ≈ 1,342 kg
3. Number of Orders: 12,000 / 1,342 ≈ 8.94 orders/year
4. Cycle Time: 365 / 8.94 ≈ 40.8 days between orders
5. Total Cost: (12,000/1,342 × 60) + (1,342/2 × 0.80) ≈ $536.51 + $536.80 = $1,073.31
Conclusion: The bakery should order 1,342 kg of flour about 9 times per year.
Example 7: Automotive Parts
Scenario: A car manufacturer needs 50,000 spark plugs annually.
1. Known Values: D = 50,000, S = $200 per order, H = $1.25 per unit/year.
2. EOQ Calculation: EOQ = √((2 × 50,000 × 200) / 1.25) = √(20,000,000 / 1.25) = √16,000,000 = 4,000 units
3. Number of Orders: 50,000 / 4,000 = 12.5 orders/year
4. Cycle Time: 365 / 12.5 = 29.2 days between orders
5. Total Cost: (50,000/4,000 × 200) + (4,000/2 × 1.25) = $2,500 + $2,500 = $5,000
Conclusion: The manufacturer should order 4,000 spark plugs about 12-13 times per year.
Example 8: Pharmaceutical Supplies
Scenario: A hospital uses 3,000 boxes of gloves monthly (36,000 annually).
1. Known Values: D = 36,000, S = $25 per order, H = $0.50 per box/year.
2. EOQ Calculation: EOQ = √((2 × 36,000 × 25) / 0.50) = √(1,800,000 / 0.50) = √3,600,000 ≈ 1,897 boxes
3. Number of Orders: 36,000 / 1,897 ≈ 18.97 orders/year
4. Cycle Time: 365 / 18.97 ≈ 19.2 days between orders
5. Total Cost: (36,000/1,897 × 25) + (1,897/2 × 0.50) ≈ $474.43 + $474.25 = $948.68
Conclusion: The hospital should order 1,897 boxes about 19 times per year.
Example 9: Low-Demand Item
Scenario: A specialty store sells 150 custom-made items annually.
1. Known Values: D = 150, S = $40 per order, H = $8 per unit/year.
2. EOQ Calculation: EOQ = √((2 × 150 × 40) / 8) = √(12,000 / 8) = √1,500 ≈ 39 units
3. Number of Orders: 150 / 39 ≈ 3.85 orders/year
4. Cycle Time: 365 / 3.85 ≈ 94.8 days between orders
5. Total Cost: (150/39 × 40) + (39/2 × 8) ≈ $153.85 + $156 = $309.85
Conclusion: For this low-demand item, ordering 39 units about 4 times per year is optimal.
Example 10: Seasonal Product
Scenario: A seasonal product has annual demand of 4,000 units concentrated in 6 months.
1. Known Values: D = 4,000, S = $35 per order, H = $1.20 per unit/year.
2. EOQ Calculation: EOQ = √((2 × 4,000 × 35) / 1.20) = √(280,000 / 1.20) ≈ √233,333 ≈ 483 units
3. Number of Orders: 4,000 / 483 ≈ 8.28 orders/year
4. Cycle Time: 182.5 (6 months) / 8.28 ≈ 22 days between orders during season
5. Total Cost: (4,000/483 × 35) + (483/2 × 1.20) ≈ $289.86 + $289.80 = $579.66
Conclusion: During the 6-month season, orders of 483 units should be placed about every 22 days.
Frequently Asked Questions about EOQ
1. What is the main purpose of the EOQ model?
The EOQ model helps businesses determine the optimal order quantity that minimizes total inventory costs, balancing ordering costs and holding costs.
2. What are the limitations of the EOQ model?
EOQ assumes constant demand, fixed ordering and holding costs, no quantity discounts, and immediate delivery. These assumptions may not hold in real-world scenarios.
3. How does holding cost affect EOQ?
Higher holding costs lead to smaller EOQ (to minimize inventory), while lower holding costs allow larger orders. The relationship is inverse square root.
4. How does ordering cost affect EOQ?
Higher ordering costs lead to larger EOQ (to reduce order frequency), while lower ordering costs allow smaller, more frequent orders.
5. What if my supplier offers quantity discounts?
The basic EOQ model doesn't account for discounts. You'd need to calculate total costs at different price breaks and compare with EOQ results.
6. How do I calculate holding cost as a percentage?
If given as a percentage (e.g., 20%), multiply by the unit cost: H = (Percentage/100) × Unit Cost.
7. What's the difference between EOQ and reorder point?
EOQ determines how much to order, while reorder point determines when to order based on lead time demand and safety stock.
8. Can EOQ be used for manufacturing?
Yes, in manufacturing it's called Economic Production Quantity (EPQ), which accounts for production rates while minimizing setup and holding costs.
9. How often should I recalculate EOQ?
Recalculate when demand patterns change significantly, or when ordering/holding costs change by more than 10-15%.
10. What if my EOQ isn't a whole number?
Round to the nearest whole number for practical ordering. The cost curve is relatively flat near EOQ, so small deviations have minimal impact.
