INV · Inventory
Economic Order Quantity (EOQ): Formula and Application
The classic model for balancing ordering cost and holding cost to find the optimal order size.
Key Takeaways
- 01EOQ minimizes the sum of ordering cost and holding cost.
- 02EOQ = sqrt(2DS/H), where D is annual demand, S order cost, H holding cost.
- 03The total cost curve is flat near the optimum, so EOQ is forgiving.
The trade-off EOQ solves
Order too often and you rack up ordering costs. Order too much at once and you pay to hold inventory. Economic Order Quantity finds the order size that minimizes the total of these two opposing costs.
The formula
EOQ = √(2DS / H) where D = annual demand, S = fixed cost per order, and H = annual holding cost per unit. The square root means order size grows with the square root of demand — doubling demand increases the order by about 41%, not 100%.
A worked example
If D = 10,000 units/year, S = $50 per order, and H = $4 per unit per year, then EOQ = √(2 × 10,000 × 50 / 4) = √250,000 ≈ 500 units per order, placing 20 orders a year.
Practical caveats
EOQ assumes steady demand and constant costs — rarely perfectly true. Its real value is as a starting point and because the total-cost curve is flat near the optimum, so small deviations barely matter. Pair EOQ with safety stock to handle the variability the model ignores.
The Formula, Visualized
Formula
EOQ = √(2DS / H) D = annual demand · S = cost per order · H = annual holding cost per unitTry the calculators