Economic Order Quantity (EOQ)

What EOQ Is

Economic Order Quantity (EOQ) is a formula used to find the optimal order size that minimizes the total inventory cost: ordering costs plus holding (carrying) costs. It helps businesses balance how often they place orders against how much stock they keep on hand, reducing cash tied up in inventory while avoiding frequent stockouts.

The EOQ Formula

EOQ (Q) is calculated as:

Q = sqrt(2DS / H)

where:
* Q = optimal order quantity (units)
* D = annual demand (units per year)
* S = fixed cost per order (ordering/setup cost)
* H = annual holding cost per unit

Key consequences of the formula:
* Q increases with the square root of demand (D) and order cost (S).
* Q decreases with the square root of holding cost (H).

How to Use EOQ (Step-by-step)

1. Estimate annual demand (D).
2. Determine the fixed cost to place an order (S).
3. Determine annual holding cost per unit (H), including storage, insurance, and capital cost.
4. Compute Q = sqrt(2DS / H).
5. Use Q to plan order frequency: orders per year = D / Q.
6. Compute average inventory = Q / 2 (useful for estimating holding costs).
7. Set a reorder point based on lead time and demand during lead time (add safety stock if necessary).

Practical Example

A retail shop sells 1,000 pairs of jeans per year (D = 1,000). Ordering cost is $2 per order (S = $2). Annual holding cost is $5 per pair (H = $5).

Q = sqrt(2 × 1,000 × 2 / 5) = sqrt(800) ≈ 28.3 → order about 28 pairs per order.

Additional results:
* Orders per year ≈ 1,000 / 28.3 ≈ 35 orders.
* Average inventory ≈ Q / 2 ≈ 14.15 pairs.
* Annual ordering cost ≈ S × (D / Q) ≈ $2 × 35 ≈ $70.
* Annual holding cost ≈ H × (Q / 2) ≈ $5 × 14.15 ≈ $70.
Total ≈ $140 per year (ordering + holding), with costs balanced.

Reorder Point and Safety Stock

EOQ gives order size but not when to reorder. Reorder point (R) is typically:

R = demand during lead time + safety stock

Safety stock accounts for demand or lead-time variability and aims to reduce stockout risk.

Limitations and When EOQ May Not Apply

EOQ relies on simplifying assumptions:
* Constant, known demand and lead time.
* Fixed ordering and holding costs.
* No quantity discounts or capacity constraints.
* Instantaneous replenishment (or deterministic production rate in production EOQ variations).

Real-world situations that reduce EOQ accuracy:
* Seasonal or highly variable demand.
* Quantity discounts (vendor price breaks) that alter optimal trade-offs.
* Uncertain lead times or frequent stockouts.
* Multiple product interactions (space, budget, or supplier constraints).

Practical Adjustments

• Add safety stock to cover variability in demand or lead time.
• Use the EOQ as a baseline and test quantity discounts—sometimes larger orders lower total cost despite higher holding costs.
• For production environments, use the production EOQ variant that accounts for gradual replenishment.
• Many businesses implement EOQ within inventory-management software that can incorporate dynamic parameters.

When EOQ Is High or Low

• EOQ increases when demand (D) or order/setup costs (S) rise.
• EOQ decreases when holding costs (H) rise.

Conclusion

EOQ is a simple, practical tool for minimizing combined ordering and holding costs and for sizing regular replenishment orders. It works best in stable environments; when demand, costs, or lead times vary, use EOQ as a starting point and adjust for discounts, safety stock, and other real-world constraints.

Key Takeaways

• EOQ balances ordering and holding costs to find an economical order size.
• Use Q = sqrt(2DS / H) and then compute order frequency and average inventory.
• Add safety stock and consider discounts or variable demand before finalizing ordering policy.