387. Kanban Sizing
The classical Toyota Production System formula for sizing kanban (replenishment-authorization cards) between two production stages:
where:
- : number of kanban cards needed
- : demand rate (units per period)
- : processing lead time (production time for one container)
- : waiting lead time (queue, transport)
- : safety factor (typically 0.05–0.30)
- : container size (units per card)
387.1. Logic
Each kanban authorizes one container of parts. Total inventory in the loop = units.
Required inventory must cover:
- Demand during the (processing + waiting) lead time:
- Plus safety: multiplier
Round up so is an integer.
387.2. Example
Assembly line uses gear-boxes at /hour. Supplier has hr processing, hr waiting. Container holds gear-boxes. Safety factor .
Total inventory loop: gear-boxes.
387.3. Two-card kanban (Toyota)
Toyota’s classic system uses two card types:
- Production kanban (P-kanban): authorizes the producer to make a container
- Withdrawal kanban (W-kanban): authorizes downstream to pull from producer’s output buffer
P-kanban + W-kanban coordinate the pull. Modern simplified versions use just one card type.
387.4. Compared to CONWIP
| Kanban | CONWIP | |
|---|---|---|
| Granularity | Per-part-type, per-stage | Global cap on all WIP |
| Setup | More cards to manage | Simpler |
| Mix flexibility | Lower (each card is specific) | Higher (any part can fill cap) |
| Best for | Repetitive, stable mix | Variable mix, fewer-part-types |
387.5. When kanban sizing breaks down
The formula assumes:
- Stationary demand — varying demand requires resizing periodically
- Reliable supplier — if upstream stations break down, fixed won’t compensate
- Small mix — separate kanbans per part-type only practical for moderate part counts
- Short lead times — long lead times require many cards, defeating leanness
In practice, is recalibrated regularly (monthly / quarterly) based on observed performance.
387.6. Lean reduction strategies
The formula highlights levers:
- Reduce (faster production, less queueing) → fewer cards needed
- Smaller → more cards needed but smaller batches, more flexibility
- Lower (reduce variability, more reliability) → fewer cards needed
Each improvement reduces inventory while maintaining service.
387.7. See also
- CONWIP — alternative discipline
- Takt Time
- Heijunka
- Factory Physics