Economic Order Quantity (EOQ

Operations Research & Lot Sizing: The Wilson EOQ Tradeoff

First derived by Ford Whitman Harris in 1913 and popularized by R. H. Wilson, the EOQ model finds the exact order size that minimizes total inventory management costs by balancing two opposing forces:

• Ordering Costs (Slope Downward): Large order batches reduce the number of purchase orders placed per year, cutting PO processing and receiving fees.

• Holding Costs (Slope Upward): Large batches increase average inventory held in the warehouse, escalating capital interest, warehouse rent, shrinkage, and insurance.

• The Exact Minimum Point: Total inventory cost is minimized at the exact intersection where Annual Ordering Cost = Annual Holding Cost.

How to Use This Calculator

Enter your Annual Demand Volume (D [Units / year]) (e.g. 12,000), Fixed Cost per Purchase Order (S [ / order]) (e.g. 85 (85 PO processing, shipping & receiving cost)), Unit Purchase Price / Manufacturing Cost (C [ / unit]) (e.g. 35 (35.00 per unit)), Annual Holding / Carrying Cost Rate (I [% of unit cost]) (e.g. 20 (20% annual carrying cost rate)), and Operating Business Days per Year (e.g. 250 (250 business days or 365 calendar days)). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Ford W. Harris / Wilson Economic Order Quantity (EOQ) equations:

Unit Holding Cost (H) = Unit Purchase Cost (C) × Holding Cost Rate (I \%) = C × I

Economic Order Quantity (Q^*) = √((2 × D × S) / (H))

Annual Ordering Cost = ((D) / (Q^*)) × S

Annual Holding Cost = ((Q^*) / (2)) × H

Total Variable Inventory Cost (TC) = ((D) / (Q^)) S + ((Q^) / (2)) H = √(2DSH)

Orders per Year (N) = (D) / (Q^*), Order Interval (Days) = (Operating Days) / (N)

Worked Example

For example, managing a product with fixed purchase order cost unit cost and a \ across 250 business days: Economic Order Quantity is 85)7.00 = 540 units/order. Annual ordering cost is \1,888.89 and holding cost is \1,890.00, delivering a Total Annual Variable Inventory Cost of \3,778.89/year with 22.2 orders per year (placed every 11.3 business days).

Understanding Your Result

For financial decisions, validate your result against your specific tax situation, current interest rate environment, and applicable regulations — these change frequently and vary by jurisdiction. A calculated estimate is a useful starting point; for decisions involving significant capital (more than one month's income), consult a certified financial planner (CFP) or CPA. Financial projections beyond 3–5 years carry increasing uncertainty — model a conservative, base, and optimistic scenario to understand the range of outcomes.