Monthly Economic Order Quantity Formula
Learn how monthly Economic Order Quantity is calculated from demand, order cost and inventory holding cost.
Monthly Economic Order Quantity (EOQ) estimates an order size that balances the cost of placing orders against the cost of carrying stock. It can help with inventory planning by also estimating order frequency, time between orders, relevant inventory cost and a basic reorder point.
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Economic Order Quantity
Where:
Multiply monthly demand by twice the cost of placing an order, divide by the monthly holding cost for one unit, then take the square root.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| EOQ - Economic order quantity | The estimated cost-efficient number of units to order at one time. | units |
| D - Monthly demand | Expected number of units used or sold in an average month. | units |
| S - Cost per order | Cost incurred each time a replenishment order is placed. | currency |
| H - Monthly holding cost per unit | Monthly cost of carrying one unit in inventory. | currency |
| C - Unit purchase cost | Purchase or production cost of one inventory unit. | currency |
| i - Annual holding cost rate | Annual inventory carrying cost expressed as a percentage of unit cost. | percent |
| L - Supplier lead time | Average operating days between placing an order and receiving it. | days |
| M - Operating days per month | Number of operating days used to spread monthly demand. | days |
Step-by-Step Calculation
Convert the annual holding rate to a monthly cost
The annual holding percentage is applied to the unit cost and divided by 12 to estimate the cost of holding one unit for a month.
monthlyHoldingCostPerUnit = unitCost * (annualHoldingRate / 100) / 12
Calculate the economic order quantity
EOQ finds the order size where ordering and holding costs are balanced under the model assumptions.
economicOrderQuantity = sqrt((2 * monthlyDemand * orderCost) / monthlyHoldingCostPerUnit)
Estimate order frequency
Monthly demand divided by the recommended order quantity estimates the number of orders needed each month.
ordersPerMonth = monthlyDemand / economicOrderQuantity
Estimate the order interval
Operating days per month divided by estimated orders gives the average time between orders.
daysBetweenOrders = daysPerMonth / ordersPerMonth
Calculate relevant monthly inventory cost
This combines ordering cost and average-inventory holding cost, excluding the purchase cost of goods.
monthlyRelevantInventoryCost = (ordersPerMonth * orderCost) + ((economicOrderQuantity / 2) * monthlyHoldingCostPerUnit)
Calculate the basic reorder point
The reorder point covers expected demand during lead time and does not include safety stock.
reorderPoint = (monthlyDemand / daysPerMonth) * leadTimeDays
Worked example: 1,000 units of monthly demand
Monthly holding cost per unit
£20 × (24 ÷ 100) ÷ 12
£0.40 per unit per month
Economic order quantity
sqrt((2 × 1,000 × £50) ÷ £0.40)
500 units
Orders per month
1,000 ÷ 500
2 orders
Days between orders
30 ÷ 2
15 days
Monthly ordering and holding cost
(2 × £50) + ((500 ÷ 2) × £0.40)
£200.00
Reorder point
(1,000 ÷ 30) × 5
166.67 units
Final Result
The estimated EOQ is 500 units, with about 2 orders per month, a 15-day order interval and a basic reorder point of about 167 units.
Assumptions
- ✓Monthly demand is steady and reasonably predictable.
- ✓The cost per order remains constant for each replenishment.
- ✓The annual holding rate and unit cost remain constant during the period.
- ✓Inventory is received in full after a consistent lead time.
- ✓Average inventory is assumed to be half of the order quantity.
- ✓The reorder point excludes safety stock.
Limitations
- !Actual demand may fluctuate from day to day or month to month.
- !Supplier lead times can vary, making a basic reorder point insufficient.
- !Quantity discounts, minimum order quantities and capacity limits are not included.
- !The model does not price stockouts, expired inventory or lost sales.
- !Results are planning estimates rather than accounting, financial or operational advice.
Common Mistakes to Avoid
Entering an annual holding rate as a decimal when the input expects a percentage, such as entering 0.24 instead of 24%.
Using the purchase price as the cost per order rather than including order-specific administration, delivery and receiving costs.
Using calendar days when demand is based on operating days only.
Treating EOQ as the reorder point; EOQ says how much to order, while the reorder point says when to order.
Forgetting to add a separately determined safety-stock allowance where demand or lead time is uncertain.
Related Formulas
Frequently Asked Questions
What is the monthly EOQ formula?
The monthly EOQ formula is √((2 × monthly demand × cost per order) ÷ monthly holding cost per unit).
How is monthly holding cost per unit calculated?
Multiply unit cost by the annual holding rate as a decimal, then divide by 12.
Why is unit cost included in an EOQ calculation?
It converts a percentage-based annual holding rate into a currency holding cost per unit. Purchase cost is otherwise not part of the relevant EOQ cost total.
Why are ordering and holding costs equal at EOQ?
Under the standard EOQ model, the cost-minimising order size occurs where estimated monthly ordering cost equals estimated monthly holding cost.
How is the EOQ reorder point calculated?
Divide monthly demand by operating days per month, then multiply by lead time in days. This gives expected lead-time demand without safety stock.
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