Line Balancing & Stations
Assign tasks with times and precedence to workstations for a cycle time or demand: ranked positional weight heuristic, minimum stations, efficiency, idle time.
A station-by-station layout that respects precedence and the cycle time, the theoretical minimum, line efficiency, balance delay, smoothness index and the bottleneck station.
Example: Six tasks totalling 21 at a cycle time of 7: A alone, then C + B, then E, then D + F — four stations against a minimum of three, 75 % efficiency, 25 % balance delay.
Tasks into stations,
precedence respected.
How the cycle time is set, how tasks are assigned, and how to read the efficiency.
Cycle time and the minimum
The cycle time is the time each station may take per unit — entered directly or as available time ÷ demand. Since a station cannot exceed it, the theoretical minimum number of stations is ⌈Σ task time ÷ cycle time⌉; precedence usually pushes the real count higher.
Assignment
Each task gets a positional weight: its own time plus that of every task that must follow it. Tasks are then placed in weight order into the first station where they fit and where all their predecessors are already placed — the ranked positional weight (Helgeson–Birnie) heuristic. A task longer than the cycle time cannot be placed and is reported.
Efficiency and limits
Efficiency = Σ task time ÷ (stations × cycle time); balance delay is its complement; smoothness = √Σ(idle²) rewards even loading. The result is a good precedence-feasible layout, not a proven optimum — deterministic times, one operator per station, no parallel stations or zoning rules. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Cycle time = available time ÷ demand; n_min = ⌈Σt ÷ CT⌉; ranked positional weight (Helgeson–Birnie) assignment; efficiency = Σt ÷ (n·CT); smoothness = √Σ(CT − station)² — a heuristic
Last reviewed 21 September 2026. How results are checked: How we verify.