Model
Wilson EOQ: the classic model
By Oliver Wakefield-Smith, Founder, Digital Signet
Direct answer
The Wilson EOQ model returns Q* = sqrt(2DS/H) under five assumptions: constant demand, instantaneous resupply, single product, no quantity discounts, and no shortages. The first one (constant demand) is the one that breaks first in real operations. The U-curve flatness near Q* makes the model surprisingly robust to small input errors[1].
optimal order quantity
Q* = sqrt( 2 * D * S / H ) H = i * C
The five assumptions
- Constant demand: D is steady across the cycle. Breaks first under seasonality, fashion, and short-lifecycle items.
- Instantaneous resupply: the lot arrives all at once. EPQ relaxes this for in-house production.
- Single product: no interaction with other SKUs on the same PO. Multi-item joint replenishment relaxes this.
- No quantity discounts: unit cost is constant across order sizes. The quantity-discount model relaxes this.
- No shortages: demand is always met from stock. The backorder model relaxes this.
The robustness property
The Wilson total-cost function is flat near Q*. A 30 percent error on Q raises total cost by about 4 percent. This makes the model unusually forgiving of input uncertainty: you can be 20 to 30 percent wrong on i and still land within 5 to 7 percent of the true optimum. The implication: do not over-engineer your H estimate. Defend a range, pick the midpoint, ship the answer.
When to extend
- Supplier offers price breaks: use the quantity-discount calculator.
- You make the part in-house: use EPQ.
- Backorders are acceptable and cheaper than carrying: use the planned-shortage model.
- Demand is deterministic but lumpy: use Wagner-Whitin or Silver-Meal.
- Demand is intermittent: use Croston (not EOQ).