Lean Manufacturing, Toyota Production System & Industrial Eng
Yamazumi Operator Balance, Takt & Line Efficiency Formula
Calculate Toyota Production System Customer Takt Time, Theoretical Minimum Operator Headcount ROUNDUP(Total_Work_Sec / Takt_Sec, 0), Yamazumi Line-Balance Efficiency Total_Work / (N_ops * Bottleneck_Sec), and Takt Compliance.
Balance Yamazumi operator work stacks against Takt Time AND bottleneck cycle pace!
In Toyota Production System (TPS) assembly cells, a Yamazumi (stacked-bar) operator balance chart stacks standardized work elements for each station against the horizontal red Customer Takt Time line: Takt_Sec = Net_Available_Shift_Seconds / Shift_Customer_Demand! Industrial engineers audit three numbers together: (1) Theoretical Minimum Operators = ROUNDUP(Total_Work_Content_Sec / Takt_Sec, 0); (2) Takt Compliance—the tallest Yamazumi bar (Bottleneck_Cycle_Sec) must NEVER exceed Takt_Sec (and typically targets ~90%–95% of Takt to absorb micro-variability); and (3) Line-Balance Efficiency = Total_Work_Content_Sec / (Staffed_Operators * Bottleneck_Cycle_Sec), where 1 - Efficiency measures idle "balance delay" waiting on the pace-setting bottleneck station!
Verify on a 4-Station Medical Device Assembly Cell—Net_Shift_Time = 27,000 sec (450 working minutes, B2), Shift_Demand = 450 units (B3 -> Takt Time = 27,000 / 450 = 60.00 sec/unit in E2), Total_Work_Content = 189 sec (stations stacked at 54s + 48s + 45s + 42s, B4), Tallest_Bottleneck_Bar = 54 sec (B5), and Staffed_Operators = 4 (B6): Theoretical Min Headcount is ROUNDUP(189 / 60, 0) = 4 operators (E3); Line-Balance Efficiency is 189 / (4 * 54) = 189 / 216 = 0.8750 (87.50%, i.e., 12.50% balance loss in E4); and Bottleneck 54s <= 60s confirms "Takt Compliant: Meets Demand" (E5)!
| Yamazumi Assembly Metric (27,000s / 450 u, Work=189s, Bottleneck=54s, 4 Ops) | Formula | Verified Output |
|---|---|---|
| Customer Takt Time (sec/unit) | Net_Available_Sec / Customer_Demand | 60.00 sec/unit |
| Theoretical Min Headcount | ROUNDUP(Total_Work_Sec / Takt_Sec, 0) | 4 Operators |
| Yamazumi Line-Balance Eff | Total_Work_Sec / (N_Ops * Bottleneck_Sec) | 0.8750 (87.50% Line Balance) |
| Tallest-Bar Takt Gate | Bottleneck_Sec <= Takt_Sec | Takt Compliant: Meets Demand |
Yamazumi Line-Balance Efficiency Formula
Validate positive shift seconds, customer demand, work content, bottleneck cycle, staffed operators >= 1, and physical consistency Total_Work <= Staffed_Operators * Bottleneck_Sec!
=LET(av_s, B2, dm_u, B3, wk_t, B4, bn_c, B5, op_n, B6, IF(OR(av_s <= 0, dm_u <= 0, wk_t <= 0, bn_c <= 0, op_n < 1, wk_t > op_n * bn_c), "Invalid Yamazumi Study", ROUND(wk_t / (op_n * bn_c), 4)))Bottleneck Takt Breach Simulation (Set Tallest Station = 65 sec)
If Station 1 creeps up to B5 = 65 sec (> 60 sec Takt): E5 immediately alerts "Takt Breach: Bottleneck Exceeds Takt", prompting kaizen element splitting across under-loaded Station 4!
=IF(ISTEXT(E4), E4, IF(B5 > E2, "Takt Breach: Bottleneck Exceeds Takt", "Takt Compliant: Meets Demand"))Try the example
Use the original values or change them to test your understanding.