---
title: "Assembly line balancing with cycle time"
subject: "Industrial Engineering and Management"
chapter: 2
key: "semester_6/industrial_engineering_and_management:assembly-line-balancing-problem"
source: https://www.bctengineer.com/q/semester_6/industrial_engineering_and_management/assembly-line-balancing-problem
site: BCT Engineering
---

# Assembly line balancing with cycle time

Industrial Engineering and Management · Chapter 2: Design of Production Systems

- Asked in: year not given, 8 marks
- Video: [Assembly Line Balancing | Precedence Diagram, Cycle Time, Number of Workstations, and Efficiency](https://www.youtube.com/watch?v=4osFVQ1YsjA) — Industrial Engineering IE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/industrial_engineering_and_management/assembly-line-balancing-problem
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_engineering_and_management/chapter-2

## Question

An assembly line must make 60 units in an 8-hour day (480 minutes). The tasks, their times and immediate predecessors are:

| Task | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Time (min) | 4 | 3 | 5 | 4 | 3 | 6 | 2 | 3 |
| Predecessor | - | A | A | B | C | D, E | F | G |

Find (a) the cycle time, (b) the theoretical minimum number of stations, (c) a balanced assignment of tasks to stations using the ranked positional weight method, and (d) the efficiency of the line and balance delay.

## Short answer

Cycle time = 480/60 = 8 min. Total task time = 30 min, theoretical minimum stations = 4. Using ranked positional weight, 5 stations assigned; efficiency = 30/(5×8) = 75%, balance delay = 25%.

## Answer

#### (a) Cycle time

$$
C = \frac{\text{available time}}{\text{required output}} = \frac{480}{60} = 8\ \text{min}
$$

#### (b) Minimum number of stations
Total task time $= 4+3+5+4+3+6+2+3 = 30$ min.

$$
N_{min} = \frac{\sum t}{C} = \frac{30}{8} = 3.75 \Rightarrow 4\ \text{stations}
$$

#### (c) Ranked positional weight (RPW)
RPW of a task = its own time plus the times of all tasks that follow it.

| Task | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| RPW | 30 | 18 | 19 | 15 | 14 | 11 | 5 | 3 |

Order of rank: A, C, B, D, E, F, G, H. Assign to each station the highest-ranked available task that fits in the remaining cycle time.

| Station | Tasks | Time (min) | Idle (min) |
|---|---|---|---|
| 1 | A (4), B (3) | 7 | 1 |
| 2 | C (5), E (3) | 8 | 0 |
| 3 | D (4) | 4 | 4 |
| 4 | F (6), G (2) | 8 | 0 |
| 5 | H (3) | 3 | 5 |

Explanation: after A (4 min) only 4 min remain in the station. C (RPW 19) needs 5 min, which does not fit, so B (3 min) is taken. Task D cannot join station 2 because C+E already use 8 min, and F cannot start until D is finished, so D takes a station alone. F (6) and G (2) fill station 4 exactly.

#### (d) Efficiency and balance delay

$$
\text{Efficiency} = \frac{\sum t}{N\,C} \times 100 = \frac{30}{5 \times 8} \times 100 = 75\%
$$

$$
\text{Balance delay} = 100 - 75 = 25\%
$$

The four-station minimum is not reachable because of the precedence limits, so five stations are needed.

**Answer: Cycle time 8 min; minimum stations 4 (theoretical); 5 stations used; efficiency 75%; balance delay 25%.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the cycle time for 60 units in 480 minutes?
   A. 8 min
   B. 4 min
   C. 30 min
   D. 60 min
   Answer: A. C = available time / required output = 480/60 = 8 min. (Key point: Cycle time)

2. What is the theoretical minimum number of stations?
   A. 3
   B. 5
   C. 4
   D. 8
   Answer: C. Total task time is 30 min; 30/8 = 3.75, rounded up to 4. (Key point: Minimum stations)

3. What is the ranked positional weight of a task?
   A. Its own time only
   B. The times of its predecessors only
   C. The cycle time minus its time
   D. Its own time plus the times of all tasks that follow it
   Answer: D. RPW = task time plus all following tasks; tasks are assigned in descending order of RPW if they fit. (Key point: RPW rule)

4. With 5 stations and cycle time 8 min, what are the efficiency and balance delay?
   A. 75% and 25%
   B. 94% and 6%
   C. 60% and 40%
   D. 80% and 20%
   Answer: A. Efficiency = 30/(5 x 8) = 75%, so balance delay = 25%. (Key point: Efficiency)

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