EOQ Calculator
From annual demand, ordering cost and holding cost, compute the economic order quantity that minimises total inventory cost.
Input Data
Results
At a glance:Economic Order Quantity (EOQ) is the order size that minimises the sum of ordering cost and holding cost. EOQ = √(2 × annual demand × ordering cost ÷ unit annual holding cost). The trade-off: order a lot → fewer orders, low ordering cost, but high average inventory and holding cost; order little → the reverse. EOQ is the balance point minimising the sum — a classic procurement and supply-chain model.
Formula
EOQ = √(2 × D × S ÷ H), where D = annual demand, S = ordering cost, H = unit holding cost.
Orders per year = D ÷ EOQ.
$$EOQ = \\sqrt{\\dfrac{2 \\times D \\times S}{H}}$$How to Use
- Enter the annual demand for the item.
- Enter the fixed cost per order and the unit annual holding cost.
- View the EOQ that minimises total cost.
EOQ examples by annual demand D, ordering cost S and holding cost H (base: D=10,000, S=HK$50, H=HK$2)
| Annual demand D | Ordering S | Holding H | EOQ (units) | Orders/yr |
|---|---|---|---|---|
| 10,000 | HK$50 | HK$2 | 707 | ~14.1 |
| 10,000 | HK$50 | HK$4 | 500 | ~20 |
| 10,000 | HK$100 | HK$2 | 1,000 | ~10 |
| 20,000 | HK$50 | HK$2 | 1,000 | ~20 |
| 10,000 | HK$50 | HK$1 | 1,000 | ~10 |
Case Studies
Case 1: Base-scenario EOQ
Item: annual demand D = 10,000, ordering cost S = HK$50, holding cost H = HK$2. EOQ = √(2 × 10,000 × 50 ÷ 2) = √500,000 ≈ 707 units.
Orders per year = 10,000 ÷ 707 ≈ 14.1, i.e. about every 26 days. At this point ordering and holding costs are about equal and their sum is lowest.
EOQ quantifies 'how much to order to save most', as a starting point for batch and reorder planning.
Case 2: How rising holding cost changes the decision
Same as above, but unit holding cost rises from HK$2 to HK$4 due to storage and capital cost; rest unchanged. EOQ = √(2 × 10,000 × 50 ÷ 4) = √250,000 = 500 units.
EOQ drops from 707 to 500; orders per year rise from ~14 to ~20 — the more expensive stock is, the more you order little and often to cut average inventory.
Conclusion: EOQ falls as holding cost rises. When capital or storage cost climbs, shrink batch size and raise order frequency.
FAQ
Why is there an optimal order quantity?
Because ordering and holding costs move in opposite directions: order a lot → fewer orders, low ordering cost, but high average inventory and high holding cost; order little → the reverse. The two cost curves cross, and their sum hits a minimum at one quantity — that is the EOQ, the most economical order size overall.
Do EOQ's assumptions hold in reality?
The basic model assumes stable known demand, fixed price/cost, instant delivery, no quantity discount. Reality often breaks these — seasonal demand, supplier volume discounts, lead-time variance. In practice use EOQ as a starting point, then adjust with extensions (discounts, shortage cost, safety stock) or pair with a reorder point and safety stock.
What if the computed quantity is not an integer?
EOQ is a continuous formula and often yields decimals (e.g. 707.11). In practice round to an integer, or match the supplier's minimum order quantity and packaging (cartons, pallets). Because the total-cost curve is fairly flat near the optimum, small deviations barely affect total cost, so rounding is harmless.
How do parameter changes affect EOQ?
From EOQ = √(2DS/H): rising annual demand D or ordering cost S raises EOQ (order more, less often); rising holding cost H lowers EOQ (stock is expensive, order little and often). Because all are under a square root, EOQ responds gently — e.g. doubling demand raises EOQ by only ~41% (√2), not double. That is why EOQ is robust to small parameter swings and useful as a starting point.
Can I still use EOQ with quantity discounts?
The basic EOQ assumes fixed unit price, but suppliers often give volume (step) discounts. Then you need the 'EOQ with quantity discount' model: compute EOQ for each discount price bracket; if the EOQ falls below that bracket's minimum order quantity, raise the order to just meet it; then compute total cost = purchase + ordering + holding for each option and pick the lowest. The key is weighing the purchase-cost saving from the discount against the higher holding cost of a larger batch — sometimes stocking up for the discount backfires, sometimes a deep discount makes it worth it. So with discounts, EOQ is only the analysis start; compare each bracket's total cost to decide.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.