Wilson EOQ vs Just-in-Time: the crossover
JIT beats Wilson when the ordering cost S falls toward zero and the supplier is reliable enough that planned shortages stay rare. Wilson collapses to lot-for-lot as S to 0, which is the same as JIT. The crossover is not philosophical; it is arithmetic on S and on carrying-cost percent i[1].
The crossover, in one line of algebra
Wilson Q* = sqrt(2DS/H). As S to 0, Q* to 0 and orders/year to infinity. That is JIT in disguise: each order is a kanban pull. The economic question is whether you can drive S low enough (EDI, supplier portal, vendor-managed inventory) that the holding-cost saving from a small Q outweighs the per-order overhead.
When JIT wins, when Wilson wins
- JIT wins: S can be driven low (under five dollars per order via EDI), supplier reliability is 99 percent plus, demand is level, holding cost i is high (perishable, fashion, electronics), and stockout cost is bounded (a missed cycle is recoverable).
- Wilson wins: S is sticky (manual PO, customs clearance, freight consolidation), supplier lead time is long or variable, demand is bursty, holding cost i is moderate (15 to 25 percent), and quantity-break discounts are meaningful.
- Hybrid wins: EOQ with a frequent-delivery schedule. Compute Q* but split each order across two or three deliveries. Used at apparel and grocery DCs where the buyer wants Wilson math with JIT cadence.
The Toyota and Dell context
Toyota’s JIT works because the kanban system drove S toward zero at the assembly line and suppliers were geographically co-located in Aichi prefecture[2]. Dell’s build-to-order JIT in PCs worked because the unit economics of obsolescence (carrying a Pentium chip for 30 days was a write-down event) made any holding catastrophic. Neither case generalises to a $5M D2C brand on Shopify with a Chinese factory and a six-week ocean freight cycle. Wilson with a quantity-discount overlay is usually the right tool there.
The U-curve flatness defence
Even if you suspect JIT is theoretically better, the Wilson U-curve is flat near Q*. A 30 percent error on Q costs about 4 percent on total cost. The cost of mis-implementing JIT (a stockout that shuts the line) is rarely flat. The asymmetry tilts the call toward Wilson plus a safety stock buffer in most mid-market settings.