How to calculate the number of kanban cards
The loop needs enough cards to cover what the line uses while an empty container travels, gets refilled and comes back. This is the formula from the Toyota Production System:
N = D × L × (1 + α) ÷ C, rounded up
| Term | Meaning |
|---|---|
| N | number of kanban cards (one per container) |
| D | average daily demand of the customer process |
| L | replenishment lead time in days: from the card being pulled to the full container returning |
| α | safety factor, for swings in demand and replenishment |
| C | parts per container |
The most inventory the loop can hold is N × C. Divided by daily demand, it becomes days of coverage.
Production kanban and supplier kanban
The same formula works for both. What changes is what you add up in the lead time:
- Production kanban: the time the card waits on the board before it is scheduled, queue time, changeover, the time to run the lot and the move to the supermarket.
- Supplier or withdrawal kanban: the pickup or ordering interval (if the truck comes every 2 days, a card can wait up to 2 days), the supplier lead time and transit.
If you have the time in hours, turn it into working days: 4 hours in an 8 hour day is 0.5 day.
Worked example
The values already in the calculator are for a part used on an assembly line:
- Demand: 480 parts per day
- Replenishment lead time: 2 days
- Safety factor: 10%
- Container: 50 parts per bin
The math:
- Usage during replenishment = 480 × 2 = 960 parts
- With safety = 960 × 1.10 = 1,056 parts
- Cards = 1,056 ÷ 50 = 21.12, rounded up: 22 cards
- Most inventory in the loop = 22 × 50 = 1,100 parts, or 1,100 ÷ 480 = 2.3 days of demand
Without the safety factor it would be 20 cards. Rounding up alone adds 44 parts to the loop, almost a full container.
Two bins: the simplest case
When the math gives 2 cards or fewer, the loop becomes a two-bin system: one bin in use at the station and a full one in reserve. When the first empties, it goes back for refilling and the operator switches to the second. The calculator never shows fewer than 2 cards, because with one there is nothing to use while the container is being refilled.
How to read the result
- Too many cards means too much inventory in the loop. The levers are a shorter lead time (faster changeovers, more frequent pickups) and smaller containers. The safety factor is the last thing to touch.
- Days of coverage tell you how long the line can run if replenishment stops. Compare it with how long a supply problem really takes to fix.
- Daily demand is the same figure that sets the pace of the line. When demand changes, recalculate the kanban and the takt time together.
- Inventory and lead time move together: by Little’s law, more parts in the loop at the same throughput means longer flow time.
For bought parts run on an order quantity and a reorder point instead of cards, use the safety stock and reorder point calculator and the EOQ calculator.
Common mistakes
- Using only the run time as the lead time. The card also waits on the board, in the queue and in transit. Leaving those waits out starves the loop.
- Rounding down. 21.12 cards is 22. With 21 the loop has no margin beyond the safety factor.
- Never revisiting the card count. Demand, changeovers and pickup frequency change. Review the cards whenever demand shifts, or at least monthly.
- Using the safety factor to hide problems. If replenishment is always late, raising α only hides the cause. Kanban is there to show where flow gets stuck.
Sources
- Monden, Yasuhiro. Toyota Production System: An Integrated Approach to Just-In-Time. 4th ed. CRC Press, 2011. Chapter on determining the number of kanbans.
- Ohno, Taiichi. Toyota Production System: Beyond Large-Scale Production. Productivity Press, 1988.