A large manufacturer of pencil sharpeners is planning to add a new line of sharp
ID: 351340 • Letter: A
Question
A large manufacturer of pencil sharpeners is planning to add a new line of sharpeners and you have been asked to balance the process given the following task times and precedence relationships. Assume the cycle time is 1.2 minutes per unit
Task
Task Time (in minutes)
Immediate Predecessor
A
0.2
-
B
0.2
A
C
0.8
-
D
0.6
C
E
0.3
B
F
1.0
D,E
G
0.4
F
H
0.3
G
a. Draw the precedence diagram for the process.
b. Assign tasks to stations in the order of greatest number of following tasks. Break ties with the largest positional weight heuristic.
c. Compute the efficiency of the line using results from part b.
Task
Task Time (in minutes)
Immediate Predecessor
A
0.2
-
B
0.2
A
C
0.8
-
D
0.6
C
E
0.3
B
F
1.0
D,E
G
0.4
F
H
0.3
G
a. Draw the precedence diagram for the process.
b. Assign tasks to stations in the order of greatest number of following tasks. Break ties with the largest positional weight heuristic.
c. Compute the efficiency of the line using results from part b.
Explanation / Answer
The Precedence diagram of tasks mentioned as follows :
A
C
B
D
E
F
G
H
Cycle time = 1.2 minutes unit
Sum of all task times ( A to H ) = 0.2 + 0.2 + 0.8 + 0.6 + 0.3 + 1 + 0.4 + 0.3 = 3.8 minutes
Minimum number of workstations = Sum of all task time / Cycle time = 3.8 / 1.2 = 3.16 ( 4 rounded to nearest whole number )
It is to be noted that :
A has 5 numbers of following tasks
B,C have 4 number of following tasks
D,E have 4 number of following tasks
It is to be noted that tasks to workstations must be allotted in such a way so that total duration of all tasks against any workstation shall not exceed the cycle time of 1.2 minutes
Since A has maximum number of following tasks, workstation 1 must start with activity A and successive tasks
Also to be noted that :
Positional weight of D = 0.6 + 1 + 0.4 + 0.3 = 2.3
Positional weight E = 0.3 + 1 + 0.4 + 0.3 = 2
Since positional weight of D > Positional weight of E, workstation 2 must start with D and successive activities :
The assignment of tasks to various workstations as follows :
WORKTATION
TASKS
DURARTION ( MINUTES )
1
A, B, C
0.2 + 0.2 + 0.8 = 1.2
2
D, E
0.6 + 0.3 = 0.9
3
F
1
4
G, H
0.4 + 0.3 = 0.7
Efficiency of the line = Total duration of all tasks/ ( actual number of workstations x Cycle time ) x 100
= 3.8 / ( 4 x 1.2) x 100
= 79.17%
EFFICIENCY OF THE LINE = 79.17%
A
C
B
D
E
F
G
H
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