Understanding your EOQ result
The EOQ balances two opposing costs. The table evaluates the worked example (D = 12,000, S = $50, H = $2) at different order sizes to show why 774.6 units is optimal — and how flat the curve is near it.
| Order size | Annual ordering cost | Annual holding cost | Total |
|---|---|---|---|
| 400 units | $1,500 | $400 | $1,900 |
| 774.6 units (EOQ) | $774.60 | $774.60 | $1,549.19 |
| 1,500 units | $400 | $1,500 | $1,900 |
- At the EOQ, ordering and holding costs are equal — that equality is the optimality condition, and it is a useful check on any EOQ computation.
- The total-cost curve is shallow near the optimum: ordering 20% more or less than the EOQ raises total cost by only about 2%, so rounding to practical pack sizes costs little.
- The classic model assumes constant demand, no quantity discounts, and instant replenishment; quantity-discount and safety-stock extensions modify the answer when those assumptions bind.
- EOQ minimizes ordering plus holding costs only — it does not consider stockout risk, which safety stock and reorder-point policies handle separately.
What is the economic order quantity?
The economic order quantity is the classical answer to a core inventory question: order in large batches (few orders, but lots of stock sitting in the warehouse) or small batches (little stock, but frequent ordering costs)? The EOQ model, formulated by Ford W. Harris in 1913 and popularized by R.H. Wilson — hence the 'Wilson formula' — finds the batch size where annual ordering cost and annual holding cost are exactly balanced, which is where their sum is minimized.
The model's inputs are annual demand in units (D), the fixed cost of placing one order (S) — administrative work, setup, shipping charges independent of quantity — and the cost of holding one unit in inventory for a year (H), covering capital cost, storage, insurance, and obsolescence. At the optimum, average inventory is Q*/2 and the two cost lines cross: ordering cost D·S/Q equals holding cost H·Q/2.
EOQ rests on simplifying assumptions — constant known demand, a fixed cost per order, instant replenishment, and no quantity discounts — yet it remains the foundation of inventory theory taught in every operations management text, because the total-cost curve is flat near the optimum: even rough inputs get close to minimum cost, and the formula gives a principled starting point that extensions (safety stock, discounts, backorders) build on.
How to use this EOQ calculator
- Enter annual demand — the number of units sold or consumed per year.
- Enter the fixed cost of placing one order: administration, setup, and any delivery charges that do not depend on quantity.
- Enter the holding cost per unit per year — often estimated as 15–30% of the unit's value, covering capital, storage, insurance, and obsolescence.
- Read the economic order quantity, how many orders per year it implies, and the minimized annual ordering-plus-holding cost.
- Worked example: with 12,000 units of annual demand, a $50 cost per order, and a $2 holding cost per unit per year, EOQ = √(2 × 12,000 × 50 ÷ 2) = 774.6 units, about 15.5 orders per year, with a minimum combined cost of $1,549.19.
The Wilson EOQ formula
Total annual cost as a function of order quantity Q is ordering cost (D/Q orders times S each) plus holding cost (average inventory Q/2 times H). Setting the derivative to zero — equivalently, setting ordering cost equal to holding cost — yields the square-root formula. The minimized total cost has its own closed form, √(2DSH), and the order frequency is demand divided by the EOQ.
Common mistakes
- Using the purchase price of the units as the holding cost — H is the cost of holding one unit for a year (often 15–30% of unit value), not the unit's price.
- Mixing time bases, such as monthly demand with annual holding cost; all inputs must be on the same (annual) basis.
- Including per-unit costs in the order cost S — only costs that are fixed per order (admin, setup, flat shipping) belong there.
- Ignoring quantity discounts, which can justify ordering above the EOQ; the discount-adjusted model compares total costs at each price break.
- Treating the EOQ as a stockout policy — it says how much to order, not when; the reorder point and safety stock govern timing and buffer.
अक्सर पूछे जाने वाले सवाल
How is the economic order quantity calculated?
With the Wilson formula: EOQ = √(2DS ÷ H), where D is annual demand in units, S the fixed cost per order, and H the holding cost per unit per year. For 12,000 units of demand, $50 per order, and $2 holding cost: √(2 × 12,000 × 50 ÷ 2) = √600,000 ≈ 774.6 units per order, placed about 15.5 times a year.
What counts as ordering cost and holding cost?
Ordering cost (S) is everything incurred per order regardless of size: purchasing administration, machine setup for production runs, and flat delivery fees. Holding cost (H) is the annual cost of keeping one unit in stock: the capital tied up (opportunity cost), warehouse space, insurance, shrinkage, and obsolescence — commonly estimated at 15–30% of the unit's value per year in operations management practice.
Where does the EOQ formula come from?
From minimizing total annual cost T(Q) = (D/Q)·S + (Q/2)·H — ordering cost falls with larger batches while holding cost rises. Setting the derivative to zero gives Q* = √(2DS/H), the point where the two costs are exactly equal. The model was published by Ford W. Harris in 1913 and later associated with R.H. Wilson, which is why it is called the Wilson formula.
Does EOQ still apply if I get quantity discounts?
The basic formula assumes one price for all quantities. With price breaks, the standard extension computes the EOQ at each price tier, adjusts infeasible quantities to the nearest break, and compares total annual cost — including the purchase cost itself — across the candidates. A discount can rationally justify ordering more than the plain EOQ when the price saving exceeds the extra holding cost.
How accurate does my cost data need to be?
Less than you might expect. The EOQ total-cost curve is flat near its minimum: errors in S or H pass through as the square root, so a 25% error in an input moves the optimal quantity by only about 12% and total cost by roughly 1%. This robustness is a celebrated property of the model and is why rough estimates of ordering and holding costs still produce near-optimal policies.
What does EOQ not tell me?
When to order and how much buffer to hold. EOQ sets the batch size under smooth, certain demand; the reorder point (demand during lead time) decides timing, and safety stock covers demand and lead-time variability. Real inventory policies combine all three, and modern systems layer forecasting on top — EOQ remains the batch-size backbone of that stack.
संदर्भ
- Harris FW. How Many Parts to Make at Once. Factory, The Magazine of Management, 1913 (reprinted in Operations Research 38(6), 1990).
- Wilson RH. A Scientific Routine for Stock Control. Harvard Business Review 13, 1934.
- Chopra S, Meindl P. Supply Chain Management: Strategy, Planning, and Operation. 7th ed. Pearson, 2019 — cycle inventory and EOQ.
- Nahmias S, Olsen TL. Production and Operations Analysis. 7th ed. Waveland Press, 2015 — inventory control subject to known demand.