a)
To draw: The precedence diagram.
a)
Answer to Problem 20P
Explanation of Solution
Given information:
Task | Time (minutes) | Immediate predecessors |
A | 3 | - |
B | 6 | - |
C | 7 | A |
D | 5 | A, B |
E | 2 | B |
F | 4 | C |
G | 5 | F |
H | 7 | D, E |
I | 1 | H |
J | 6 | E |
K | 4 | G, I, J |
Total | 50 |
- Number of hours / day is 24
- Output is 96 instruments / day.
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.
b)
Answer to Problem 20P
The cycle time is 15 minutes / unit.
Explanation of Solution
Formula to calculate cycle time:
Calculation of cycle time:
The cycle time is 15 minutes / unit.
c)
To determine: The production rate.
c)
Answer to Problem 20P
The production rate is 144 units / day.
Explanation of Solution
Given information:
Cycle time = 10 minutes
Formula to calculate production rate:
Calculation of cycle time:
The production rate is 144 units / day.
d)
To determine: The theoretical minimum number of workstations.
d)
Answer to Problem 20P
The theoretical minimum number of workstations is 5 workstations.
Explanation of Solution
Given information:
Cycle time = 10 minutes
Formula to calculate theoretical minimum number of workstations:
Calculation of theoretical minimum number of workstations:
The theoretical minimum number of workstations is 5 workstations.
e)
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.
e)
Answer to Problem 20P
The efficiency is 83.3%.
Explanation of Solution
Given information:
Cycle time = 10 minutes
Number of workstations = 6
Formula to calculate efficiency:
Calculation of efficiency:
The efficiency is 83.3%.
f)
To determine: The total idle time per cycle.
f)
Answer to Problem 20P
The idle time is 10 minutes / cycle.
Explanation of Solution
Given information:
Number of workstations = 6
Cycle time = 10
Calculation of total idle time per cycle:
The total idle time is 10 minutes / cycle.
g)
To assign: The different tasks to different workstations and identify the efficiency.
g)
Explanation of Solution
Assignment of different tasks to different workstations:
Workstation | Elligible tasks | Selected tasks | Task time (minutes) | Available cycle time (minutes) |
1 | 10 | |||
A, B | A | 3 | 7 | |
B | B | 6 | 1 | |
1 (Idle time) | ||||
2 | 10 | |||
C, D, E | C | 7 | 3 | |
3 (Idle time) | ||||
3 | 10 | |||
D, E, F | D | 5 | 5 | |
E, F | E | 2 | 3 | |
3 (Idle time) | ||||
4 | 10 | |||
F, G, H, I | F | 4 | 6 | |
G, H, I | G | 5 | 1 | |
1 (Idle time) | ||||
5 | 10 | |||
J, H, I, K | H | 7 | 3 | |
H, I, K | I | 1 | 2 | |
2 (Idle time) | ||||
6 | 10 | |||
K, J | J | 6 | 4 | |
K | K | 4 | 0 |
Workstation | Task assigned | Idle time |
1 | A, B | 1 |
2 | C, D | 3 |
3 | D, E | 3 |
4 | F, G | 1 |
5 | H, I | 2 |
6 | J, K | 0 |
Total | 10 |
Efficiency:
Formula to calculate efficiency:
Calculation of efficiency:
The efficiency is 83.3%.
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Chapter 9 Solutions
Principles Of Operations Management
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