Concept explainers
The Action Toy Company has decided to manufacture a new train set the production of which is broken into six steps. The demand for the train is 4,800 units per 40-hour workweek:
a) Draw a precedence diagram of this operation.
b) Given the demand, what is the cycle time for this operation?
c) What is the theoretical minimum number of workstations?
d) Assign tasks to workstations.
e) How much total idle time a present each cycle?
f) What is the efficiency of the assembly line with five stations? With six stations?
a)
To draw: The precedence diagram.
Answer to Problem 15P
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 20 | - |
B | 30 | A |
C | 15 | A |
D | 15 | A |
E | 10 | B, C |
F | 30 | D, E |
Total | 120 |
- Weekly demand is 4,800 units / 40 hours workweek.
Precedence diagram:
b)
To determine: The cycle time.
Introduction:
Cycle time:
Cycle time is the total time taken to complete an unit of work from the beginning of the process to the end of the process.
Answer to Problem 15P
The cycle time is 30 seconds / unit.
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 20 | - |
B | 30 | A |
C | 15 | A |
D | 15 | A |
E | 10 | B, C |
F | 30 | D, E |
Total | 120 |
- Weekly demand is 4,800 units / 40 hours workweek.
Formula to calculate cycle time:
Calculation of cycle time:
The cycle time is 30 seconds / unit.
c)
To determine: The theoretical minimum number of workstations.
Answer to Problem 15P
The theoretical minimum number of workstations is 4 workstations.
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 20 | - |
B | 30 | A |
C | 15 | A |
D | 15 | A |
E | 10 | B, C |
F | 30 | D, E |
Total | 120 |
- Weekly demand is 4,800 units / 40 hours workweek.
- Average daily demand is 50 chairs.
Formula to calculate theoretical minimum number of workstations:
Calculation of theoretical minimum number of workstations:
The theoretical minimum number of workstations is 4 workstations.
d)
To assign: The different tasks to different workstations.
Explanation of Solution
Assignment of different tasks to different workstations:
Workstation | Elligible tasks | Selected tasks | Task time (seconds) | Available cycle time (seconds) | Remarks |
1 | 30 | ||||
A | A | 20 | 10 | Task A is the only elligible ask | |
10 (Idle Time) | No other elligible task is available | ||||
2 | 30 | ||||
B, C, D | B | 30 | 0 | Task B has the highest task time | |
3 | 30 | ||||
C, D | C | 15 | 15 | Task C is assigned | |
D | D | 15 | 0 | Task D is assigned | |
4 | 30 | ||||
E | E | 10 | 20 | Task E is the only elligible task available | |
20 (Idle time) | The available cycle time is less than the task time | ||||
5 | F | F | 30 | 0 | Task F is assigned |
Workstation | Task assigned | Idle time |
1 | A | 10 |
2 | B | 0 |
3 | C, D | 0 |
4 | E | 20 |
5 | F | 0 |
Total | 30 |
e)
To determine: The idle time per cycle.
Answer to Problem 15P
The idle time is 30 seconds / cycle.
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 20 | - |
B | 30 | A |
C | 15 | A |
D | 15 | A |
E | 10 | B, C |
F | 30 | D, E |
Total | 120 |
- Weekly demand is 4,800 units / 40 hours workweek.
- Average daily demand is 50 chairs.
Calculation of idle time per cycle:
The idle time is 30 seconds / cycle.
f)
To determine: The efficiency.
Introduction:
Efficiency:
Efficiency is the measure of what is actually produced as opposed to what can be theoretically produced with the same amount of resources.
Answer to Problem 15P
The efficiency with five and six workstations is 80% and 66.6% respectively.
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 20 | - |
B | 30 | A |
C | 15 | A |
D | 15 | A |
E | 10 | B, C |
F | 30 | D, E |
Total | 120 |
- Weekly demand is 4,800 units / 40 hours workweek.
- Average daily demand is 50 chairs.
Formula to calculate efficiency:
Calculation of efficiency for five workstations:
Calculation of efficiency for six workstations:
The efficiency with five and six workstations is 80% and 66.6% respectively.
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Chapter 9 Solutions
Principles Of Operations Management
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