Problem 8-9 An assembly line is to be designed to operate 7 1 / 2 hours per day
ID: 469072 • Letter: P
Question
Problem 8-9
An assembly line is to be designed to operate 71/2 hours per day and supply a steady demand of 300 units per day. Here are the tasks and their performance times:
What is the theoretical minimum number of workstations? (Round up your answer to the next whole number.)
Assign tasks to workstations using the longest operating time. (Leave no cells blank - be certain to enter "0" wherever required.)
Suppose demand increases by 10 percent. How would you react to this? Assume that you can operate only 71/2 hours per day. (Round your answers to the nearest whole number.)
An assembly line is to be designed to operate 71/2 hours per day and supply a steady demand of 300 units per day. Here are the tasks and their performance times:
Explanation / Answer
Activity
Predecessor
Duration (week)
a
None
70
b
None
40
c
None
45
d
a
10
e
b
30
f
C
20
g
d
60
h
e
50
i
f
15
j
g
25
k
h, i
20
l
j, k
25
Total Work Time
410
Demand = D =300 units per day
Available hours = 7.5 hours per day
Available time (seconds) = 7.5 x 60 x 60 = 27,000 seconds
Total Work time = 410 seconds
a.
Determine Cycle Time
Cycle time of the Line = Available time (seconds)/Demand
Ct = 27000/300 = 90 seconds
So assembly must be capable of processing units once every 90 seconds.
Cycle time gives idea of how frequently the products are processed by assembly line.
b.
Determine number of workstation required:
Number of workstation required in assembly line depends on the cycle time and total work content that is total amount of time required to produce the product.
So for assembly line number of workstation required is as follows:
Number of workstation = (total work content)/(required cycle time)
Number of workstation required = 410/90 = 4.56
Actual numbers of workstations required are 5 workstations.
Arrange the tasks according to longest tasks first as shown below:
Activity
Predecessor
Duration (week)
a
None
70
g
d
60
h
e
50
c
None
45
b
None
40
e
b
30
j
g
25
l
j, k
25
f
c
20
k
h, i
20
i
f
15
d
a
10
Applying largest candidate rule to balance the line:
Work Elements Assigned to Stations According to the Largest Candidate Rule. For a workstation select tasks with largest duration task such that:
For example workstation #1 consists of task a with duration 70 and task d which required task a to complete with duration 10. Thus the WS #1 cycle time is 80 seconds
Workstation #
Tasks
workstation, Work Time (CW)
Cycle Time (Ct)
Idle = Ct + CW
1
a, d
70+10 = 80
90
10
2
g, j
60+25 = 85
90
5
3
c, b
45+40 = 85
90
5
4
e, h
30+50 = 80
90
10
5
f, i, k, l
20+15+20+25 = 80
90
10
C.
Efficiency of assembly line = Total work time/(no. of workstation x Cycle time)
Efficiency = 410/(5 x 90)
Efficiency = 91.11%
D
Revised Demand = 300 * 1.10 = 330 units
Revised Cycle Time = 27000/330 = 81.82 seconds
As there is no idle time for Workstations #2 and #3, do not reduce the cycle time, instead work overtime.
Overtime production units = Revised demand - Production per day as per CT = 20 sec
Overtime production units = 30 – 300 = 30 units
Overtime (seconds) = 30 units x CT = 30 x 90 = 2700 seconds
Overtime in minutes = 2700/60 = 45 minutes.
Thus, work 45 minutes of overtime
Activity
Predecessor
Duration (week)
a
None
70
b
None
40
c
None
45
d
a
10
e
b
30
f
C
20
g
d
60
h
e
50
i
f
15
j
g
25
k
h, i
20
l
j, k
25
Total Work Time
410