What is the Ranked Positional Weight (RPW) method?

A line-balancing heuristic by Helgeson and Birnie (1961). Each task's positional weight is its time plus the times of all tasks that follow it in the precedence diagram. Tasks are assigned in order of decreasing weight to the first station where they fit and their predecessors are already placed, so tasks that hold up a lot of downstream work go first.

What is the Largest Candidate Rule?

A simpler heuristic: among the tasks whose predecessors are done and that fit in the station's remaining time, assign the one with the longest task time. It is quick by hand but ignores how much work depends on each task, so RPW often needs fewer stations.

How do you calculate line efficiency and balance delay?

Efficiency = total task time ÷ (number of stations × cycle time). Balance delay = 1 − efficiency, the share of paid station time that is idle. Example: 152 s of work on 3 stations at a 60 s cycle gives 152 ÷ 180 = 84.44% efficiency and 15.56% balance delay.

What is the smoothness index?

SI = √Σ(S_max − Sᵢ)², where Sᵢ is each station's time and S_max the largest one. It measures how evenly work is spread; 0 means every station has the same load. Some texts use the cycle time instead of S_max — the ranking of alternatives is usually the same.

How is the theoretical minimum number of workstations found?

Divide the total task time by the cycle time and round up: N_min = ⌈Σt ÷ C⌉. It is a lower bound; precedence and indivisible tasks often force one or more extra stations.

How do I enter predecessors?

Give each task a short ID (A, B, C …) and list the IDs of the tasks that must be finished immediately before it, separated by commas, for example "B, C". Leave it blank for tasks that can start first. The calculator rejects unknown IDs and loops.

Why does my line need more stations than the theoretical minimum?

Precedence constraints and task times that do not pack neatly into the cycle time leave idle gaps. Try the other rule, a slightly longer cycle time, or splitting a long task.

Line Balancing Calculator

List tasks with their times and predecessors, set demand and available time, and get a workstation-by-workstation assignment using RPW or the Largest Candidate Rule, with efficiency, balance delay and smoothness index.

Line balancing assigns tasks to workstations so no station exceeds the cycle time and every task follows its predecessors.

Assigns tasks with precedence to stations. For a quick cycle-time or takt check without a task list, use the Cycle Time Calculator.

Production Parameters

Demand (units/day)

Available time/day (s)

8 hours = 28,800 s | 7.5 hours = 27,000 s

Cycle time (optional)

Assignment rule

Tasks

IDTime (s)Predecessors

Actual Workstations (optional)

Line Balancing Results

Cycle Time

—

s / unit

Total Task Time

—

s (Σt)

Theoretical Min

—

stations

Stations Used

—

workstations

Smoothness Index

—

√Σ(S_max − Sᵢ)²

Total Idle

—

s per cycle

Line Efficiency —%

Balance Delay (Idle Time) —%

Workstation Assignment

WS	Tasks	Time (s)	Idle (s)	Load

Positional Weights

Rank	Task	Time	Predecessors	Followers	Weight

Line Balancing Formulas

Worked with the example on this page: 8 tasks, Σt = 152 s, 480 units in 28,800 s.

Measure	Formula	Example
Cycle time	C = available time ÷ demand	28,800 s ÷ 480 = 60 s
Theoretical minimum stations	N_min = ⌈Σt ÷ C⌉	⌈152 ÷ 60⌉ = 3
Line efficiency	E = Σt ÷ (N × C) × 100%	152 ÷ (3 × 60) = 84.44%
Balance delay	BD = 100% − E	100% − 84.44% = 15.56%
Smoothness index	SI = √Σ(S_max − Sᵢ)²	√(0² + 0² + 28²) = 28
Positional weight	PW = tᵢ + Σ t of all followers	A: 20 + 132 = 152

Quick answer

Line balancing assigns tasks to workstations so no station exceeds the cycle time and every task follows its predecessors. Cycle time C = available time ÷ demand; the theoretical minimum number of stations is ⌈Σt ÷ C⌉; line efficiency = Σt ÷ (N × C); balance delay = 1 − efficiency; smoothness index SI = √Σ(S_max − Sᵢ)². The Ranked Positional Weight method fills each station with the available task that has the largest positional weight (its own time plus all tasks that follow it); the Largest Candidate Rule picks the longest available task.

Examples

Example (8 tasks, Σt = 152 s, demand 480/day, 8 h)	Result
Cycle time	28,800 s ÷ 480 = 60 s
Theoretical minimum stations	⌈152 ÷ 60⌉ = 3
RPW assignment	WS1: A, C, B (60 s) · WS2: D, E, F (60 s) · WS3: G, H (32 s)
Efficiency / balance delay / SI	84.44% / 15.56% / 28

Edit the example tasks (ID, time, predecessors) or add your own, then choose RPW or Largest Candidate Rule.

Summary

This line balancing calculator does the full textbook procedure. Enter each task's time and its immediate predecessors, plus the daily demand and available time (or a cycle time). It builds the precedence network, ranks tasks by positional weight, and assigns them to workstations with either the Ranked Positional Weight (Helgeson–Birnie) heuristic or the Largest Candidate Rule, never exceeding the cycle time or breaking precedence. You get the station-by-station assignment, idle time, theoretical minimum number of stations, line efficiency, balance delay, smoothness index and the bottleneck station that sets the real output. For a quick cycle-time or takt check without precedence, use the Cycle Time Calculator.

How it works

Cycle time C = available production time per day ÷ daily demand (or type a cycle time directly).
Each task's positional weight = its own time + the times of every task that must come after it (all followers, counted once).
Stations are filled one at a time. A task is a candidate when all its predecessors are already assigned and its time fits in the station's remaining time. RPW picks the candidate with the largest positional weight; the Largest Candidate Rule picks the longest task. Ties go to the task listed first.
When no candidate fits, the station is closed and a new one opened, until every task is assigned.
Efficiency = Σt ÷ (N × C) × 100, balance delay = 100% − efficiency, smoothness index SI = √Σ(S_max − Sᵢ)² where S_max is the largest station time.

Use cases

Solve operations-management homework on RPW and Largest Candidate Rule line balancing.
Design a new assembly line to meet a daily output target with the fewest stations.
Compare two assignment rules and see which gives higher efficiency and a lower smoothness index.
Find the bottleneck station that limits actual throughput.
Check how many operators a line needs when demand changes.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu