Economic Order Quantity (EOQ)
Find the sweet spot between order placement fees and inventory warehousing carrying costs.
Total units required or sold during the year
Fixed administrative, shipping, and handling charge per purchase order
Warehouse storage, shrinkage, obsolescence, and working capital interest
The EOQ Principle
Results
Ford W. Harris mathematical inventory optimization model.
How Economic Order Quantity is calculated
The Economic Order Quantity (EOQ) formula, formulated by Ford W. Harris in 1913, identifies the exact purchase order size that minimizes total annual inventory costs by balancing fixed purchase order setup fees against ongoing storage carrying costs.
D = Annual demand in units
S = Fixed setup/ordering fee per order
H = Annual carrying cost per unit
Annual Ordering Cost = N × S
Annual Holding Cost = (EOQ ÷ 2) × H
Total Cost = Ordering Cost + Holding Cost
The Equilibrium Principle: At the mathematical minimum of the total cost curve, Annual Ordering Cost exactly equals Annual Holding Cost.
Step-by-step worked example
Consider a distribution facility operating with the default baseline parameters: an annual demand of 10,000 units, a fixed procurement cost of ₹500 per purchase order, and an annual holding cost of ₹25 per unit per year:
| Calculation Step | Formula | Substitution & Computation | Verified Result |
|---|---|---|---|
| 1. Numerator (2 × D × S) | 2 × Annual Demand × Order Cost | 2 × 10,000 × ₹500 | ₹1,00,00,000 |
| 2. Cost Ratio | (2 × D × S) ÷ H | ₹1,00,00,000 ÷ 25 | 400,000 |
| 3. Optimal EOQ | √400,000 | Exact square root | 632.46 Units (632 Units) |
| 4. Order Frequency | D ÷ EOQ | 10,000 ÷ 632.46 | 15.81 Orders / Year |
| 5. Cycle Time (Days) | 365 ÷ Orders / Year | 365 ÷ 15.81 | 23.08 Days (~23 Days) |
| 6. Annual Ordering Cost | 15.81 × ₹500 | 15.81139 × 500 | ₹7,906 |
| 7. Annual Holding Cost | (632.46 ÷ 2) × ₹25 | 316.23 × 25 | ₹7,906 |
| 8. Minimized Total Cost | Ordering + Holding | ₹7,906 + ₹7,906 | ₹15,811 / Year |
Cost Trade-off Matrix: Batch Size Sensitivity
Ordering too little wastes money on repetitive purchase orders and delivery charges; ordering too much clogs warehouse capacity and burns working capital in carrying charges:
| Batch Policy | Order Size | Orders / Year | Annual Ordering | Annual Holding | Total Inventory Cost | Operational Trade-off |
|---|---|---|---|---|---|---|
| Under-ordering | 200 Units | 50.0 | ₹25,000 | ₹2,500 | ₹27,500 | Excessive purchase order paperwork and inbound inspection overhead. |
| Optimal (EOQ) | 632 Units | 15.8 | ₹7,906 | ₹7,906 | ₹15,811 | Perfect balance point; total inventory overhead minimized. |
| Moderate Bulk | 2,000 Units | 5.0 | ₹2,500 | ₹25,000 | ₹27,500 | Warehousing congestion and bloated working capital debt carrying costs. |
| Extreme Bulk | 5,000 Units | 2.0 | ₹1,000 | ₹62,500 | ₹63,500 | Severe cash lockup; 4× higher carrying expense than optimal EOQ. |
Anatomy of Holding vs. Ordering Costs
- Holding Costs (H): Warehouse lease per sq ft, climate control, insurance policies, security personnel, product shrinkage/theft, damage, obsolescence, and the opportunity cost of working capital (typically 15%–25% of unit purchase value).
- Ordering Costs (S): Procurement staff salary time to generate POs, vendor negotiation, shipping freight handling charges per delivery, pallet unloading, and quality assurance inspection fees.
When Suppliers Offer Volume Discounts
If a vendor offers a price break at a higher order threshold (e.g., 5% discount for orders ≥ 1,000 units), you should evaluate:
Net Savings = Annual Price Discount − Increase in Total Carrying & Ordering Costs
If annual purchase discount exceeds the added inventory holding cost, ordering above the standard EOQ is financially advantageous.
Assumptions & Supply Chain Limitations
- Uniform Steady Demand: Assumes consumption is flat and predictable throughout 365 days. Highly seasonal items (apparel, holiday goods) require dynamic safety stock models.
- Instantaneous Replenishment: Assumes delivery lead time is zero. In practice, procurement managers establish a Reorder Point (ROP = Lead Time Demand + Safety Stock) to avoid stockouts.
- Unlimited Storage & Working Capital: Assumes the business has unrestricted warehouse footprint and available liquidity to finance any batch size calculated.
Frequently asked questions
What assumptions does the EOQ model make?
What is typically included in holding cost per unit?
What is included in ordering or setup cost?
How do quantity discounts affect the standard EOQ calculation?
What happens if actual demand differs from estimated demand?
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Optimal Order Batch Size
632 Units