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Economic Order Quantity (EOQ

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### Operations Research: The Trade-Off at the Heart of EOQ Developed in 1913 by Ford Whitman Harris, the **Economic Order Quantity (EOQ)** model solves the fundamental inventory trade-off: 1.

Reviewed by Noman Khan · MBA
Last updated:
Editorial Guidelines

⚙ Input Values

📊 Results

Primary EOQ & Reorder Point Summary
EOQ: 698 units/order ➔ Reorder Point: 680 units (Min Cost: $2,234/yr across 17.2 orders)
Economic Order Quantity (Optimal EOQ in Units)
698 units / purchase order
Reorder Point (ROP in Units Trigger)
680 units (Reorder Trigger)
Total Minimum Annual Inventory Cost ($)
$2,234 / year (Minimum Total Cost)
Optimal Number of Orders Placed per Year
17.2 orders / year
Order Cycle Interval (Days Between Orders)
Every 17.5 days (17 operating days)
Annual Ordering Costs ($)
$1,117 / year
Annual Holding / Storage Costs ($)
$1,117 / year
✦ Supply Chain Operations & Inventory Optimization Diagnostic
Inventory Optimization Analysis (Harris EOQ Model): For annual demand of 12,000 units with $65.00/order setup cost and $3.20/unit/year holding cost: [1] Economic Order Quantity (EOQ) is 698 units per batch (raw: 698.2 units). [2] Order Frequency: Placing 17.2 orders/year (every 17.5 operating days). [3] Cost Equilibrium: Annual Ordering Cost is $1,117 and Annual Holding Cost is $1,117, achieving the mathematical minimum Total Inventory Cost of $2,234/year. [4] Reorder Trigger: Place a new purchase order whenever stock drops to 680 units (480 units lead time demand + 200 units safety buffer).
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📐 Formula

Ford W. Harris Economic Order Quantity (EOQ) & supply chain equations: Order Quantity (EOQ) = √((2 × D × S ÷ H)) : D = Annual Demand (Units), S = Order Cost (\/order), H = Holding Cost (\/unit/yr) Orders Placed = (D ÷ EOQ) Cycle Interval (Days) = Operating Work DaysAnnual Orders Ordering Cost = ((D ÷ EOQ)) × S, Annual Holding Cost = ( EOQ2) × H Minimum Inventory Cost (TIC) = √(2 × D × S × H) Point (ROP) = (Daily Demand × Lead Time Days) + Safety Stock

💡 Practical Example

✅

For example, managing a warehouse with 12,000 units of annual demand, a $65.00 fixed cost per purchase order, a $3.20/unit/year carrying holding cost, 12 days supplier lead time, 200 units of safety stock, and 300 operating days per year: \(65)}{3.20}} = \sqrt{487,500} = \mathbf{698.21\text{ units (700 units billed)}}\). The business places \ (every 17.5 days). Daily demand is \, giving a Reorder Point (ROP) of \((40 \times 12) + 200 = \mathbf{680\text{ units}}\) at a minimum total inventory cost of $2,234.28/year.

📖 About Economic Order Quantity (EOQ

Operations Research: The Trade-Off at the Heart of EOQ

Developed in 1913 by Ford Whitman Harris, the Economic Order Quantity (EOQ) model solves the fundamental inventory trade-off:

  • Ordering Too Frequently (Small batch sizes): Minimizes holding/warehousing costs, but skyrockets administrative ordering fees and shipping costs.
  • Ordering Infrequently (Large batch sizes): Lowers ordering fees, but ties up working capital and drives up warehouse storage, insurance, and spoilage costs.
  • The EOQ Minimum: At the exact EOQ point, Annual Ordering Costs equal Annual Holding Costs, achieving the mathematically optimal lowest total cost.

How to Use This Calculator

Enter your Annual Product Demand (D in Units / Year) (e.g. 12000), Fixed Cost per Purchase Order (S in - Admin, freight, setup) (e.g. 65.0), Annual Holding / Carrying Cost per Unit (H in / unit / year) (e.g. 3.20 (Storage, insurance, obsolescence)), Supplier Delivery Lead Time (Days) (e.g. 12), Safety Stock Buffer (Units) [Optional] (e.g. 200), and Operating Business Days per Year (e.g. 300 (or 365)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Ford W. Harris Economic Order Quantity (EOQ) & supply chain equations: Order Quantity (EOQ) = √((2 × D × S) / (H)): D = Annual Demand (Units), S = Order Cost (\/order), H = Holding Cost (\/unit/yr) Orders Placed = (D) / (EOQ) Cycle Interval (Days) = (Operating Work Days) / (Annual Orders) Ordering Cost = ((D) / (EOQ)) × S, Annual Holding Cost = ((EOQ) / (2)) × H Minimum Inventory Cost (TIC) = √(2 × D × S × H) Point (ROP) = (Daily Demand × Lead Time Days) + Safety Stock

Worked Example

For example, managing a warehouse with 12,000 units of annual demand, a 65.00 fixed cost per purchase order, a 3.20/unit/year carrying holding cost, 12 days supplier lead time, 200 units of safety stock, and 300 operating days per year: 65)3.20 = √(487,500) = 698.21 units (700 units billed). The business places \ (every 17.5 days). Daily demand is giving a Reorder Point (ROP) of (40 × 12) + 200 = 680 units at a minimum total inventory cost of 2,234.28/year.

Understanding Your Result

Optimal inventory management balances holding costs (typically 20–30% of inventory value annually: storage, insurance, obsolescence, capital cost) against ordering costs. EOQ minimizes the total of these two cost types. Safety stock protects against demand variability and lead time variability — the standard formula uses service level z-scores: 95% service level z=1.645, 99% z=2.

  • Days inventory outstanding (DIO) benchmark: retail 30–60 days, manufacturing 50–80 days, distribution 20–40 days. Below industry average DIO is generally better.

💡 Methodological Standards & Calculation Accuracy

  • All calculations are performed client-side in your browser using verified, standards-compliant mathematical algorithms.
  • Results are provided for educational and informational analysis; verify critical applications with certified domain specialists.
  • Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
  • Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Sources: NIST Standards · ISO International Standards

Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.

❓ Frequently Asked Questions

What is Economic Order Quantity (EOQ)?
EOQ is the ideal order quantity a company should purchase for its inventory to minimize the total combined costs of ordering, receiving, and holding stock.

What is the Reorder Point (ROP)?
The Reorder Point is the specific inventory level that triggers a new purchase order, calculated as: ROP = + Safety Stock.

Why do holding costs and ordering costs balance at EOQ?
Because holding cost increases linearly with batch size while ordering cost decreases hyperbolically; setting the derivative of total cost to zero proves they are exactly equal at the minimum cost point.

What costs are included in holding / carrying costs?
Holding costs include physical warehouse storage rent, inventory insurance, taxes, material handling labor, depreciation, obsolescence, and the opportunity cost of capital (interest).

What is safety stock?
Safety stock is an extra buffer of inventory held to protect against unexpected supplier delivery delays or sudden spikes in consumer demand.

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