Kanban Sizing When Demand Variability Exceeds the Formula
A lean conversion sets up a two-bin kanban for a purchased component. Daily demand averages 400 units with a standard deviation of 120. Lead time is 3 days, supplier lead-time standard deviation 1 day. Container size is 50 units. The team computed kanban quantity with the simple formula: (average demand × lead time)/container size = (400×3)/50 = 24 kanbans, and added 2 for safety, total 26. Within a month, the line ran out of the component four times, each time stopping the line for ~40 minutes. The supplier ships weekly, and a quality hold on one lot removed 600 units from stock.
1. Recompute the kanban quantity with a safety-stock approach that accounts for demand and lead-time variability, and compare with 26.
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Safety stock for variable demand and lead time: SS = z × sqrt(LT × σ_d² + d² × σ_LT²) = z × sqrt(3 × 120² + 400² × 1²) = z × sqrt(43,200 + 160,000) = z × sqrt(203,200) ≈ z × 450.8.
At z = 1.65 (95% service): SS ≈ 744 units. At z = 2.33 (99%): SS ≈ 1,050 units.
Total kanban quantity = demand during LT (1,200) + SS. At 95%: 1,944 units → 1,944/50 ≈ 39 kanbans. At 99%: 2,250/50 = 45 kanbans.
So 26 is far too low - it ignores variability entirely. The four stockouts confirm it. The 600-unit quality hold alone exceeds the safety stock at 95%.
2. The team wants to 'just add kanbans' until stockouts stop. Evaluate this and propose a better approach.
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Adding kanbans blindly trades stockouts for inventory and hides the real causes. The stockouts have distinct causes: (1) demand/lead-time variability (addressed by calculated safety stock), (2) a quality hold removing 600 units (addressed by supplier quality and incoming inspection, not more stock), and (3) weekly shipping (a long, lumpy replenishment cycle that inflates effective lead time).
Better approach: calculate the SS as above, then attack the drivers - move the supplier to twice-weekly or daily delivery to cut lead time and its variance, qualify the supplier to eliminate holds, and monitor demand. As σ_LT and σ_d fall, the kanban count falls with them. Set the count from data, then reduce it deliberately as the process improves.
3. What does the 40-minute line stop per stockout cost, and how should that inform the service-level choice?
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If the line's throughput value is, say, $X/hour, four stops × 40 min = 2.67 h/month of lost output. The cost of a stockout should be compared with the holding cost of extra safety stock. Going from 95% to 99% service adds 300 units ($ value) of inventory; if each stockout costs more than the annual holding cost of that increment, the higher service level is justified. The decision should be made explicitly: estimate stockout cost per event, compare with holding cost, and choose z accordingly - not by trial and error on the floor.