EOQ vs JIT: where the formula breaks
EOQ assumes setup / order cost S is exogenous and works the carrying-cost trade-off within it. JIT under Ohno’s Toyota Production System treats S as endogenous and engineers it downward via SMED (single-minute exchange of die)[1]. As S approaches zero, Wilson Q* approaches 1: the algebra of a single-piece-flow kanban replenishment.
The trade-off Toyota reframed
Wilson takes S as given and minimises total cost holding S fixed. Toyota observed that Q* shrinks with sqrt(S), so cutting S by a factor of 16 cuts Q* by a factor of 4 - a compounding return on setup-reduction investment. SMED programs cut die-change times from hours to minutes, allowing manufacturing batches a fraction of the Wilson Q*[2].
When JIT is impossible
JIT requires reliable, short, predictable lead times. International sourcing with 4 to 8 week ocean transit fundamentally cannot run JIT for the offshore leg. The practical compromise: JIT (kanban, single-piece-flow) downstream of a strategic buffer, with the buffer sized by EOQ logic against the offshore lead time. This is the "hybrid" most small-mid manufacturers actually run.
Kanban as continuous EOQ at Q = 1
A kanban card represents one container of inventory. Each consumed kanban triggers a replenishment order of size 1 container. The setup cost has been driven so low that the Wilson optimisation is degenerate: Q = 1 (or 1 container) is optimal. The math hasn’t been abandoned; it has been re-engineered by changing the inputs.
The pragmatic hybrid
For SMBs neither lean enough for pure JIT nor unsophisticated enough for naive EOQ, the practical hybrid is a kanban trigger sized by an EOQ-based replenishment quantity. Set the kanban size = Wilson Q* at the supplier’s realistic S; trigger when on-hand falls to the ROP; reorder Q. This pattern reads as "EOQ inside a kanban skin."