Classic Wilson EOQ formula
The classic Wilson EOQ formula is Q* = sqrt(2DS/H), where D is annual demand in units, S is the fixed cost per order, and H is the annual holding cost per unit (often expressed as i * C, where i is carrying-cost percent and C is unit cost)[1]. The formula appears in Wilson’s 1934 HBR article but the derivation is Harris 1913[2].
The five assumptions
- Demand D is known and constant across the year.
- Order cost S is fixed per order (independent of Q).
- Holding cost H is constant per unit per year.
- Lead time is zero, or known and fixed (no demand-variability risk during lead time).
- No quantity discounts, no shortages allowed, no shelf-life constraint.
When it breaks
Break assumption 1 with seasonal apparel and you need a newsvendor model. Break assumption 4 with stochastic lead time and you need safety stock plus ROP. Break assumption 5 with all-units discounts and you need the price-break extension. Each of those variant pages walks the corresponding rework.
The flat-curve robustness property
Q* depends on the square root of D and on 1/sqrt(H). That makes the total cost function notoriously flat near its minimum: a 25 percent over- or under-estimate of H typically moves Q* by 11 to 13 percent and total cost by under 2 percent. This is the "robustness property" cited in Silver, Pyke and Peterson[3]: the model is forgiving of mis-estimated inputs, which is why it ranks so well as a default lot-sizing rule even when assumptions don’t cleanly hold.
Sensitivity in plain numbers
At D = 12,000, S = 85, C = 40, i = 25 percent, Q* = 715. Move i to 22 percent and Q* becomes 762. Move i to 28 percent and Q* becomes 676. The annual total variable cost at Q = 715 with the wrong i is within 0.5 percent of the cost at the true Q*. That is the practical answer to "how precise does H need to be?" The answer: less precise than the spreadsheet jockey thinks.