Concept

Just-in-time (JIT)

Direct answer

JIT under Ohno’s Toyota Production System treats setup cost S as endogenous and drives it toward zero via SMED (single-minute exchange of die)^[1]. As S approaches zero, Wilson Q* approaches 1: single-piece flow. JIT does not abandon EOQ math; it re-engineers the input.

Concept

JIT (Just-In-Time)

Pull-based replenishment system that drives batch size toward 1 by attacking setup cost.

When it matters: Where setup cost can be engineered down (manufacturing changeovers, SMED) and lead times are short and reliable, JIT dominates EOQ. Where lead times are long (international ocean), JIT cannot run pure and a hybrid is required.

The math behind SMED

Wilson Q* = sqrt(2DS/H). Halving S reduces Q* by sqrt(2). A 16x reduction in S (from 4-hour changeover to 15-minute changeover) reduces Q* by 4x. Compounding return on setup-reduction investment is the entire economic case for SMED^[2].

When JIT is impossible

Pure JIT requires lead times of hours or single-digit days. International ocean transit of 30 to 60 days breaks JIT for the offshore leg. The practical hybrid: kanban (single-piece-flow) downstream of a strategic buffer; the buffer sized by EOQ logic against offshore lead time.

Kanban as continuous EOQ at Q = 1

A kanban card = one container of inventory. Each consumed kanban triggers a replenishment order of size 1 container. The setup cost has been driven so low (because replenishment is one ship-truck-pallet motion) that Q = 1 is optimal. Wilson hasn’t been replaced; it has been driven to its degenerate optimum.

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