a)
To determine: The theoretical minimum number of workstations.
a)
Answer to Problem 23P
The theoretical minimum number of workstations is 5 workstations.
Explanation of Solution
Given information:
Task | Time (seconds) | Immediate predecessors |
A | 40 | - |
B | 30 | A |
C | 50 | A |
D | 40 | B |
E | 6 | B |
F | 25 | C |
G | 15 | C |
H | 20 | D, E |
I | 18 | F, G |
J | 30 | H, I |
Total | 274 |
- Output is 60 iStars / hour
Calculation of cycle time:
The requirement is to produce 60 iStars / hour. Hence, the cycle time for one iStar will be:
Formula to calculate theoretical minimum number of workstations:
Calculation of theoretical minimum number of workstations:
The theoretical minimum number of workstations is 5 workstations.
b)
To balance: The assembly line.
b)
Explanation of Solution
Precedence diagram:
List of most following tasks:
Tasks | Following tasks |
A | 9 |
B | 4 |
C | 4 |
D | 2 |
E | 2 |
F | 2 |
G | 2 |
H | 1 |
I | 1 |
J | 0 |
Assignment of different tasks to different workstations:
Workstation | Elligible tasks | Selected tasks | Task time (seconds) | Available cycle time (seconds) | Remarks |
1 | 60 | ||||
A | A | 40 | 20 | ||
B,C | 20 (Idle time) | Cycle time is less than task time | |||
2 | 60 | ||||
B, C | C | 7 | 50 | Tie broken randomnly | |
B, F, G | 10 (Idle time) | Cycle time is less than task time | |||
3 | 60 | ||||
B, F, G | B | 30 | 30 | Task B has most following tasks. | |
D, E, F, G | F | 25 | 24 | Tie broken randomnly | |
D, E, G | 1 (Idle time) | Cycle time is less than task time | |||
4 | 60 | ||||
D, E, G | D | 40 | 20 | Tie broken randomnly | |
E, G | G | 15 | 5 | Tie broken randomnly | |
E,I | 5 (Idle time) | Cycle time is less than task time | |||
5 | 60 | ||||
E, I | E | 6 | 54 | Task E has most following tasks. | |
I, H | H | 20 | 34 | Tie broken randomnly | |
I | I | 18 | 2 | Task I is only elligible task | |
2 (Idle time) | |||||
6 | 60 | ||||
J | J | 30 | 30 | Task J is the remaining task | |
30 (Idle time) |
Workstation | Task assigned | Idle time |
1 | A | 20 |
2 | C | 10 |
3 | B, F | 1 |
4 | D, G | 5 |
5 | E, H, I | 2 |
6 | J | 30 |
Total | 68 |
c)
To determine: The actual number of workstations.
c)
Answer to Problem 23P
The actual number of workstations is 6.
Explanation of Solution
Workstation | Task assigned | Idle time |
1 | A | 20 |
2 | C | 10 |
3 | B, F | 1 |
4 | D, G | 5 |
5 | E, H, I | 2 |
6 | J | 30 |
Total | 68 |
The actual number of workstations is 6.
d)
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.
d)
Answer to Problem 23P
The efficiency is 76.11%.
Explanation of Solution
Formula to calculate efficiency:
Calculation of efficiency:
The efficiency is 76.11%.
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Chapter 9 Solutions
Principles Of Operations Management
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