Develop a solution for the following line balancing problem, allowing a cycle ti
ID: 362214 • Letter: D
Question
Develop a solution for the following line balancing problem, allowing a cycle time of 5 minutes.
Draw the precedence diagram for the set of tasks.
Calculate the theoretical minimum number of workstations.
Balance this line by assigning tasks to stations.
Does the solution have the minimum number of stations? Explain.
How much idle time is there, summed over all workstations?
What is the efficiency of this line?
Work Task
Task Time (seconds)
Task Predecessor(s)
A
70
-
B
60
A
C
120
B
D
60
-
E
240
C, D
F
100
A
G
190
E, F
Work Task
Task Time (seconds)
Task Predecessor(s)
A
70
-
B
60
A
C
120
B
D
60
-
E
240
C, D
F
100
A
G
190
E, F
Explanation / Answer
The Precedence Diagram as follows :
A
D
F
B
C
E
G
Total duration of all tasks together ( A to G )
= 70 + 60 + 120 + 60 + 240 + 100 + 190
= 840 seconds
Required cycle time = 5 minutes = 300 seconds
Therefore ,
Theoretical minimum number of workstations
= Total duration of all tasks / Cycle time
= 840/300
= 2.8 ( 3 rounded to nearest whole number )
THEORETICAL MINIMUM NUMBER OF WORKSTATIONS = 3
The line is being balanced as per following in such a way so that total duration of tasks in any workstation shall not exceed required cycle time of 300 seconds :
WORKSTATION
TASKS
DURATION (SECS)
IDLE TIME = 300 SECS - DURATION
1
A,B,C
70 + 60+ 120 + 250
300 – 250 = 50
2
D,E
60 + 240 = 300
0
3
F, G
100 + 190 = 290
300 – 290 = 10
As per above arrangement , the solution achieves minimum number of stations of 3
Total idle time for 3 workstations together = 50 + 0 + 10 seconds = 60 seconds
Efficiency of this line
= ( Total duration of tasks ) / ( 3 x Cycle time ) x 100
= 840/ ( 3 x 300) x 100
= 93.33 %
TOTAL IDLE TIME = 60 SECONDS
EFFICIENCY OF THE LINE = 93.33 %
A
D
F
B
C
E
G
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