Economic Order Quantity (EOQ) is the order quantity at which the total annual ordering cost and inventory holding cost are minimised under the assumptions of the classical EOQ model.
Ordering smaller quantities reduces average inventory but increases the frequency of purchase orders. Ordering larger quantities reduces the number of orders but increases storage costs and the capital tied up in stock.
EOQ identifies the order size that balances these two costs. The model is also known as the Wilson formula, after R. H. Wilson, who popularised its application.
Why EOQ Matters in Supply Chain
Order quantity is often decided by habit, by supplier minimum order quantity, or by whatever fills a truck. EOQ gives a costed basis for the decision instead.
It matters because:
- It exposes the real trade-off. Buying in bulk looks cheaper per unit but can cost more once holding cost, interest, storage, and obsolescence are counted.
- It reduces total cost, not just one line item. Procurement optimising for unit price and warehousing optimising for space usually pull in opposite directions. EOQ gives both a shared number.
- It sets a baseline for negotiation. Knowing the economic quantity tells a buyer whether a supplier’s minimum order quantity or slab discount is actually worth taking.
- It feeds replenishment settings. EOQ answers how much to order. The reorder point answers when. Together they form a basic replenishment policy.
EOQ Formula and How It Works
Formula:
EOQ = √( 2DS / H )
Where:
- D = annual demand in units
- S = ordering cost per order (administration, transport, inspection, and other cost incurred per order placed, regardless of size)
- H = holding cost per unit per year (storage, insurance, interest on capital, shrinkage, obsolescence)
Total annual cost:
Total Cost = (D / Q × S) + (Q / 2 × H)
Where Q is the order quantity. The first term is annual ordering cost, the second is annual holding cost on average inventory. At the EOQ, these two terms are equal.
Related outputs:
- Number of orders per year = D / EOQ
- Average inventory = EOQ / 2
- Time between orders = 365 / (D / EOQ) days
Assumptions in the classical model:
- Demand is known and steady through the year
- Lead time is constant
- Unit price is fixed, with no quantity discounts
- The full order arrives at once
- Stockouts do not occur
- Only ordering and holding costs are considered
Components of the EOQ Formula
Ordering cost (S): Incurred per order placed, not per unit. Includes purchase processing, freight where charged per consignment, inward inspection, and goods receipt work.
Holding cost (H): Usually expressed as a percentage of unit value per year, commonly between 15 and 30 percent depending on warehousing cost, interest rates, and obsolescence risk.
Annual demand (D): Forecast or historical consumption, which must be reasonably stable for EOQ to hold.
Order quantity (Q): The decision variable the model optimises.
Limitations to be aware of:
- It does not handle quantity discounts without extending the model
- It assumes steady demand, so it fits poorly for seasonal or highly erratic items
- It ignores perishability and shelf life
- It treats each item in isolation, so it misses the savings from combining items into one consignment
- It takes no account of supplier minimum order quantities or pallet and truck capacity constraints
Because the formula uses a square root, it is forgiving. Doubling demand raises EOQ by only about 41 percent, and ordering moderately above or below the EOQ adds little total cost. The output should be treated as a guide quantity to be rounded to a practical pack, pallet, or vehicle size.
How to Calculate EOQ: Example
A distributor of industrial fasteners has the following figures for one SKU:
Annual demand (D): 36,000 units
Ordering cost (S): ₹1,200 per order
Holding cost (H): ₹30 per unit per year
EOQ calculation: EOQ = √( 2 × 36,000 × 1,200 / 30 ) = √2,880,000 = approximately 1,697 units
At this order size:
Measure | Value |
|---|---|
Orders per year | About 21 |
Average inventory | About 849 units |
Annual ordering cost | About ₹25,450 |
Annual holding cost | About ₹25,450 |
Total annual ordering and holding cost | About ₹50,900 |
The distributor currently orders 6,000 units at a time, six times a year. At that quantity, annual ordering cost is ₹7,200 and annual holding cost is ₹90,000, giving a total annual ordering and holding cost of ₹97,200.
Moving closer to the EOQ reduces these costs by approximately 48% for this item, assuming the stated demand and costs remain unchanged.
In practice, the distributor would round 1,697 units to a suitable carton or pallet quantity and check it against the supplier’s minimum order quantity before finalising the policy.
Related Terms
- Reorder Point
- Safety Stock
- Inventory Turnover
- Total Cost of Ownership (TCO)
- Carrying Cost
- Purchase Order (PO)
- Demand Forecasting
- ABC Inventory Analysis
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FAQs
Q1. What is the difference between EOQ and reorder point?
EOQ tells you how much to order. The reorder point tells you when to place that order. Most replenishment policies use both.
Q2. Does EOQ work with quantity discounts?
Not in its basic form. When a supplier offers slab pricing, the total cost including purchase price is calculated at each discount break and at the EOQ, and the lowest total is chosen.
Q3. Which items is EOQ least suited to?
Items with highly seasonal or erratic demand, perishable goods, items with short product life cycles, and items where supplier constraints such as minimum order quantity leave no real choice of order size.
Q4. How is holding cost worked out?
It is normally estimated as a percentage of the item’s unit value per year, covering warehouse space, handling, insurance, interest on the capital tied up, shrinkage, and obsolescence risk.