Basic Inventory Formula Example: EOQ & Min-Max

The basic inventory formula calculates the Economic Order Quantity (EOQ), which tells you the optimal number of units to order at one time to minimize total inventory costs. You enter your annual demand, ordering cost per order, and holding cost per unit per year, and the formula returns the order quantity that balances these two opposing costs. For example, if annual demand is 1,000 units, ordering cost is $50 per order, and holding cost is $2 per unit per year, the EOQ is 224 units.

Formula

The Economic Order Quantity formula is written as:

EOQ = √(2DS / H)

Where:

• D = Annual demand in units (how many units you sell or use in a year)
• S = Ordering cost per order in dollars (fixed cost to place one order, including shipping, handling, and administrative time)
• H = Holding cost per unit per year in dollars (cost to store one unit for one year, including warehousing, insurance, spoilage, and capital tied up)

The formula assumes that demand is constant and known, lead time is zero or fixed, and that orders arrive all at once. It works best for items with steady, predictable usage rather than seasonal or erratic demand.

Worked Example

Using the default values from the calculator above:

• D = 1,000 units per year
• S = $50 per order
• H = $2 per unit per year

Step 1: Multiply 2 × D × S = 2 × 1,000 × 50 = 100,000

Step 2: Divide by H = 100,000 / 2 = 50,000

Step 3: Take the square root = √50,000 ≈ 223.61, which rounds to 224 units.

So you should order 224 units each time you place an order. That means you’ll place about 1,000 / 224 ≈ 4.46 orders per year, or roughly every 82 days if you operate 365 days a year.

The total annual inventory cost is (1,000 / 224) × $50 + (224 / 2) × $2 = $223.21 + $224.00 = $447.21.

Why the EOQ Formula Matters

Every time you order inventory, you pay a fixed cost—shipping, receiving, paperwork, and setup. If you order too frequently, those costs add up. But if you order in huge batches, you pay more to store the extra units: rent, insurance, spoilage, and the opportunity cost of cash tied up in stock. The EOQ formula finds the sweet spot where the sum of ordering and holding costs is lowest.

For example, ordering 100 units at a time would give you 10 orders per year, costing 10 × $50 = $500 in ordering costs, and average inventory of 50 units costing 50 × $2 = $100 in holding costs, for a total of $600. Ordering 500 units at a time gives you 2 orders per year ($100) and average inventory of 250 units ($500), also totaling $600. The EOQ of 224 units gives the lowest total of $447.

This formula is most useful for:

• Retailers managing thousands of SKUs
• Manufacturers planning raw material purchases
• Warehouses setting reorder points
• Any business that wants to reduce working capital tied up in stock

How to Choose the Right Inputs

The accuracy of your EOQ depends entirely on the quality of your inputs. Here’s what to use for each:

• Annual demand (D): Use historical sales data from the past 12 months, adjusted for expected growth or decline. If you’re launching a new product, use a forecast based on comparable items.
• Ordering cost (S): Include all costs that occur only when you place an order: supplier shipping, receiving labor, inspection, purchase order processing, and payment processing. Do not include the cost of the goods themselves—that’s a variable cost that doesn’t affect the order quantity decision.
• Holding cost (H): Include warehouse rent or depreciation, utilities, insurance, taxes, spoilage, shrinkage, and the cost of capital (interest you could have earned on the money tied up in inventory). Many businesses use 20-30% of the unit cost as a rough estimate, but you can calculate it more precisely.

If you don’t have exact numbers, start with reasonable estimates. The EOQ is relatively flat around the minimum, so a 20% error in inputs might only change the optimal order quantity by a small amount.

Common Mistakes and Misconceptions

Several errors regularly trip up people using the EOQ formula:

• Unit mismatch: Make sure D is annual demand, not monthly or weekly. If you only have monthly demand, multiply by 12. Similarly, H must be per unit per year, not per month.
• Confusing ordering cost with unit cost: The cost of the product itself is not part of S. S is only the fixed cost per order, independent of quantity.
• Ignoring quantity discounts: If your supplier offers a lower price for larger orders, the EOQ may not be optimal. You need to compare total costs at the EOQ versus at each discount threshold.
• Assuming constant demand: The formula assumes steady, known demand. If your demand is seasonal or highly variable, you’ll need safety stock and a reorder point, not just an EOQ.
• Using EOQ for perishable or trendy items: For items with short shelf life or rapid obsolescence (like food or fashion), the EOQ will likely recommend ordering more than you can sell before expiry.

Beyond EOQ: The Min-Max Method

Another basic inventory formula is the min-max system, which sets a minimum stock level (reorder point) and a maximum stock level. When inventory drops to the minimum, you order enough to bring it back up to the maximum.

The reorder point formula is:

Reorder Point = (Daily Usage × Lead Time) + Safety Stock

For example, if you sell 10 units per day, your supplier takes 5 days to deliver, and you want 20 units of safety stock, your reorder point is (10 × 5) + 20 = 70 units. When your stock hits 70, you place an order.

The maximum level is typically set as the reorder point plus the EOQ, or based on storage capacity. This method is easier to implement than pure EOQ because it doesn’t require recalculating every time demand changes—you just monitor stock levels.

Safety Stock and Service Level

The EOQ formula doesn’t account for uncertainty in demand or supply. To protect against stockouts, you add safety stock. The basic safety stock formula for normally distributed demand is:

Safety Stock = Z × σ_d × √L

Where Z is the z-score for your desired service level (1.28 for 90%, 1.65 for 95%, 2.33 for 99%), σ_d is the standard deviation of daily demand, and L is the lead time in days.

For example, if daily demand has a standard deviation of 5 units, lead time is 4 days, and you want a 95% service level, safety stock = 1.65 × 5 × √4 = 1.65 × 5 × 2 = 16.5 units, so round up to 17 units.

This is separate from the EOQ, which only tells you how much to order, not when to order. The reorder point combines lead time demand and safety stock to trigger the order.

Limitations of the Basic Formula

The basic EOQ formula makes several simplifying assumptions that may not hold in real business:

• Demand is constant and known: Most businesses face variability, which is why safety stock is needed.
• No quantity discounts: The formula assumes the unit price is fixed regardless of order size.
• No stockouts: It assumes you never run out, which is rarely true.
• Instantaneous replenishment: It assumes the entire order arrives at once, not gradually over time.
• No constraints: It ignores storage capacity, budget limits, or minimum order quantities.

For more complex scenarios, you might need the production order quantity model (for goods produced gradually), the quantity discount model, or periodic review systems. However, the basic EOQ remains a valuable starting point for understanding the trade-off between ordering and holding costs.

Frequently Asked Questions

What is the basic inventory formula in simple terms?

The most common basic inventory formula is the Economic Order Quantity (EOQ): EOQ = √(2DS/H). It tells you the ideal number of units to order each time to minimize total inventory costs. You multiply 2 by annual demand (D) and ordering cost (S), divide by holding cost (H), then take the square root.

How do I calculate reorder point?

Reorder point = (Average daily usage × Lead time in days) + Safety stock. For example, if you use 20 units per day, lead time is 7 days, and you keep 30 units of safety stock, your reorder point is (20 × 7) + 30 = 170 units. When stock drops to 170, place a new order.

What is the difference between EOQ and reorder point?

EOQ answers

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in d | Annual demand (units) | units | 1000 | 1 | 1000000
in s | Ordering cost per order | $ | 50 | 0 | 10000
in h | Holding cost per unit per year | $ | 2 | 0 | 10000
out eoq | Economic Order Quantity | units | sqrt((2 * d * s) / h) | 0
out n | Orders per year | orders | d / eoq | 1
out tic | Total annual inventory cost | $ | (d / eoq) * s + (eoq / 2) * h | 2