Economic Order Quantity (EOQ)

The EOQ Formula

EOQ = √(2 × D × S / H)

• D = Annual Demand: Total units needed per year. Based on historical sales or forecasts.

• S = Ordering Cost: Cost to place and receive one order. Includes admin, shipping, inspection.

• H = Holding Cost: Cost to hold one unit for a year. Storage, insurance, obsolescence, capital.

Example Calculation

Let's calculate EOQ for a product with the following data:

• D: 1,000 units — Annual demand

• S: $50 — Cost per order

• H: $5 — Holding cost per unit per year

EOQ = √(2 × 1,000 × 50 / 5) EOQ = √(100,000 / 5) EOQ = √20,000 EOQ ≈ 141 units

The optimal order quantity is about 141 units. With annual demand of 1,000 units, you would place about 7 orders per year (1,000 / 141 ≈ 7), or roughly every 7-8 weeks.

When to Use EOQ

Good fit for EOQ:

• Stable, predictable demand

• Known, consistent ordering costs

• Known, consistent holding costs

• No significant quantity discounts

• Replenishment is relatively quick

EOQ may not fit:

• Highly seasonal or variable demand

• New products with no demand history

• Significant bulk discounts available

• Perishable items with short shelf life

• Long, variable lead times

Related Calculations

• Orders Per Year — D / EOQ: Annual demand divided by EOQ gives you how many orders to place per year.

• Reorder Interval — 365 / (D / EOQ): Days between orders. Helps you plan ordering schedules.

• Total Annual Cost — (D/Q × S) + (Q/2 × H): Sum of ordering costs and holding costs. EOQ minimizes this value.

• Reorder Point — Lead Time × Daily Demand + Safety Stock: When to place the order. Combine with EOQ for complete ordering strategy.

Why you can round EOQ to a convenient number

The most useful and least-known property of EOQ is that the total-cost curve is flat near the bottom. Move the order quantity a fair way in either direction and total cost barely rises, because ordering cost and holding cost trade off gently around the optimum rather than spiking.

That matters in practice because the EOQ answer is almost never a round number. Take the earlier example: EOQ came out to about 141 units. Ordering exactly 141 is awkward — suppliers sell in cases, layers, or pallets. Rounding up to 144 (a full 12-case pack) or even 150 changes total annual cost by well under 1%, so you get the convenience of a whole case quantity at effectively no penalty.

The practical takeaway: treat EOQ as a target zone, not a precise integer. Calculate it, then round to the nearest supplier pack size or minimum order quantity. If your supplier sets a minimum order quantity above your EOQ, order the minimum — EOQ is telling you the extra holding cost is small relative to being able to buy at all.

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Frequently asked questions

What is Economic Order Quantity (EOQ)?

EOQ is the optimal order quantity that minimizes total inventory costs, balancing ordering costs (placing and receiving orders) with holding costs (storing inventory). It tells you how much to order to spend the least on inventory overall.

What is the EOQ formula?

EOQ = square root of (2 x D x S) / H, where D is annual demand, S is ordering cost per order, and H is holding cost per unit per year. The formula finds the point where ordering costs equal holding costs.

When should I use EOQ?

EOQ works best for items with stable, predictable demand, known ordering and holding costs, and no significant quantity discounts. It is less useful for seasonal items, new products, or items with highly variable demand.

What are the limitations of EOQ?

EOQ assumes constant demand, fixed ordering and holding costs, instant replenishment, and no quantity discounts. In reality, demand fluctuates, costs change, and suppliers offer bulk discounts. Treat EOQ as a starting point, not a strict rule.

How do I calculate holding cost for EOQ?

Holding cost includes storage, insurance, obsolescence, and capital cost. A common estimate is 20-30% of the item value per year. For a $10 item, holding cost might be $2-3 per unit per year.

How often should I order using EOQ?

Divide annual demand by EOQ to get the number of orders per year. If demand is 1,000 units and EOQ is 200, you would order 5 times per year (about every 10-11 weeks).

When should I NOT use EOQ?

Avoid using EOQ for: products with highly seasonal demand, new products without demand history, perishable items with short shelf life, items with significant quantity discounts from suppliers, or products with long and variable lead times.

What is ordering cost in EOQ?

Ordering cost (S) includes all expenses to place and receive an order: purchase order processing, communication with suppliers, receiving and inspection, invoice processing, and shipping fees. Calculate by dividing total annual ordering expenses by number of orders placed.