389. Line Balancing
The task of allocating work to stations on a production line so each station’s work time is below the takt time, minimizing idle time and station count.
389.1. Setup
- A product is assembled via tasks with processing times
- Tasks have precedence constraints: task must finish before task starts
- Tasks are grouped into stations; each station’s total time
Goals (often trade-offs):
- Minimize number of stations (capital cost)
- Minimize cycle time (= maximum station time)
- Smooth station loads (workforce equity)
389.2. Theoretical bounds
Minimum stations:
(Total work ÷ takt time, rounded up.)
Minimum cycle time: (longest indivisible task sets a floor).
389.3. Balance efficiency
100% means every station fully loaded — no idle time. Lower efficiency means wasted capacity.
389.4. Heuristics
The problem (Assembly Line Balancing Problem, ALBP) is NP-hard. Common heuristics:
Longest Task Time (LTT): pick assignable tasks (precedences satisfied, fits in remaining station time) in decreasing order of .
Ranked Positional Weight (RPW, Helgeson-Birnie 1961):
- Compute each task’s positional weight = + sum of for all successors
- Assign tasks in decreasing positional weight, respecting precedences
COMSOAL (Arcus 1966): Random assignment with backtracking. Multi-start.
389.5. Worked example
10 tasks with times , total minutes. Takt time minutes.
Minimum stations: .
LTT heuristic with simple precedence chain: place tasks into stations one at a time, picking the longest available task that fits.
Result might give 6 or 7 stations, balance efficiency 89%–100%.
389.6. Mixed-model line balancing
Real lines produce multiple products with different task sets. Mixed-model balancing:
- Define product mix (proportion of each)
- Compute expected task times weighted by mix
- Balance using weighted times
- Sequence products through stations to avoid bottleneck overload
389.7. Single-product vs U-shaped lines
| Layout | Pros | Cons |
|---|---|---|
| Straight line | simple, fast | workers can’t help each other |
| U-shaped | workers reach multiple stations, can help bottleneck | more complex, requires multi-skilled workers |
| Cell | flexible, small batches | coordinating multiple cells |
U-shaped (cellular) layout is the lean ideal — natural for CONWIP / kanban control.
389.8. Variability and balance
Even a perfectly balanced deterministic line behaves much worse than the formula suggests when variability is added (per VUT). Real balancing requires both:
- Mean balance: station load averages match
- Variance balance: station variability matches
Otherwise the high-variance station becomes a “virtual bottleneck” that drives queueing throughout.
389.9. See also
- Takt Time — the constraint
- Best/Worst/PWC
- Factory Physics
- CONWIP