Q2. (PowerToys) PowerToys Inc. produces small remote-controlled toy truck on a w
ID: 442393 • Letter: Q
Question
Q2. (PowerToys) PowerToys Inc. produces small remote-controlled toy truck on a worker-paced line with nine stations. Each station has, under the current process layout, one worker assigned to it. Stations and processing times are summarized in the following table.
Station
Task
Processing time (seconds)
1
Mount battery units
70
2
Insert remote control receiver
80
3
Insert chip
90
4
Mount front axle
30
5
Mount rear axle
70
6
Install electric motor
60
7
Connect motor to battery unit
45
8
Connect motor to rear axle
80
9
Mount plastic body
75
a. What is the bottleneck in this process?
b. What is the capacity, in toy trucks per hour, of the assembly line?
c. What is the utilization of the worker in Station 7?
d. What is the direct labor cost for the toy truck with the current process if each worker receives $20 per hour, expressed in dollars per toy truck?
e. How long does it take the process to produce 100 units starting with an empty system?
Suppose work is now organized in a work cell, that is, one worker performs all tasks.
f. What is the capacity now (in toy trucks per hour)?
g. What is the corresponding direct labor cost?
Because of a drastically reduced forecast, the plant management has decided to cut staffing from nine to just two workers per shift. Assume that (i) the nine tasks in the preceding table cannot be further subdivided; (ii) the nine tasks are assigned to the two workers in the most efficient way possible; and (iii) if one worker is in charge of two tasks, the tasks have to be adjacent (e.g. one worker cannot work on tasks 4 and 8 if he is not also assigned tasks 5, 6, and 7).
h. How would you assign the nine tasks to the two workers?
i. What is the new capacity (in toy trucks per hour)?
j. What would be the new direct labor cost?
Station
Task
Processing time (seconds)
1
Mount battery units
70
2
Insert remote control receiver
80
3
Insert chip
90
4
Mount front axle
30
5
Mount rear axle
70
6
Install electric motor
60
7
Connect motor to battery unit
45
8
Connect motor to rear axle
80
9
Mount plastic body
75
Explanation / Answer
The following would be the solution of the defined problem
Station
Task
Processing time (seconds)
Theoretical Capacity (per Hour)
(3600/Processing time)
1
Mount battery units
70
51.4
2
Insert remote control receiver
80
45.0
3
Insert chip
90
40.0
4
Mount front axle
30
120.0
5
Mount rear axle
70
51.4
6
Install electric motor
60
60.0
7
Connect motor to battery unit
45
80.0
8
Connect motor to rear axle
80
45.0
9
Mount plastic body
75
48.0
a. The bottleneck of the process is the one which has minimum capacity. Therefore, in our assembly line Station 3 for Inserting chips is the bottleneck because it has the minimum capacity of only 40 toy trucks per hour.
b. Capacity for an assembly line is equal to the capacity of the bottleneck in a running process. In our problem, the capacity of the bottleneck is 40 toy trucks per hour and that would also be the process capacity.
c. Resource Utilization = Process Capacity / Resource Capacity. The resource at Station 7 has the capacity to produce 80 units in one hour but is able to produce only 40 owing to the bottleneck. Therefore, the resource utilization = 50% (40/80)
d. Direct Cost
Station
Theoretical Capacity (per Hour)
(3600/Processing time)
Resource Utilization
(40/Resource Capacity)
Direct Labour Cost ($12/hour)
(Resource Utilization X 12
1
51.4
77.8%
9.34
2
45.0
88.9%
10.67
3
40.0
100%
12.00
4
120.0
33.3%
4.00
5
51.4
77.8%
9.34
6
60.0
66.7%
8.00
7
80.0
50%
6.00
8
45.0
88.9%
10.67
9
48.0
83.3%
10.00
Total Direct Labor cost for 1 Hour
80.02
Therefore, the direct cost of labor to produce 40 units of toy trucks is equal to $80. Hence Direct cost of labor of producing 1 toy truck is $2 ($80/40units)
e. If one worker is performing all the tasks and we start with an empty system, then the total time taken to produce one unit of toy truck shall be 600 seconds ~ 10 minutes (70 + 80 + 90 + 30 + 70 + 60 + 45 + 80 + 75). With 9 workers being there 9 units will be produced in 10 minutes. Hence 99 units will be completed in 110 minutes. And one additional unit will take 10 more minutes as the work is in the work cell and will be done by one person and remaining 8 being idle.
Therefore to produce 100 units we shall need 110 + 10 minutes = 120 minutes = 2 hours
f. With no capacity / resource reduction we shall be able to produce 9 units in 10 minutes. Therefore, we shall be able to produce 54 units in 60 minutes. So in the new scheme of things the capacity of the unit reduces to 54 units per hour.
g. With the capacity of 54 units per hour and all workers performing all tasks we obtain 100% resource utilization. Therefore, the total direct labor cost per hour is $180. So the per unit labor cost now increases to $3.33/toy truck.
h. If the management reduces the staff from 9 to 2 then the work should be distributed between the 2 workers so that the difference between their lead times should be minimum. This shall reduce the idle time and shall prevent the WIP building up. Therefore the tasks at Station 1, 2, 3, and 4 should be clubbed with one. And tasks at Station 5, 6, 7, 8 and 9 should be clubbed with other worker. For the former clubbing the total lead time will be 270 (70+80+90+30) seconds and the lead time for the other worker will be 330 (70+60+45+80+75) seconds.
i. In the new scheme of things, the task group containing 5,6,7,8, and 9 which has more time utilization becomes the bottleneck. In the running process we shall be able to produce 1 truck in 330 seconds. So in one hour we shall be able to produce 10.9 toy trucks. Therefore the new capacity now will be 10.9 toy trucks / hour.
j. The new direct labor cost computation shall be as follows.
Work Group
Theoretical Capacity (per Hour)
(3600/Processing time)
Resource Utilization
(10.9/Resource Capacity)
Direct Labour Cost ($12/hour)
(Resource Utilization X 12
1 (1-4)
13.33
81.8%
9.81
2 (5-9)
10.91
100.0%
10.91
Total Direct Labor cost for 1 Hour
20.72
Therefore, the direct cost of labor to produce 10.9 units of toy trucks is equal to $20.72. Hence Direct cost of labor of producing 1 toy truck is $1.9 ($20.72/10.9units)
Station
Task
Processing time (seconds)
Theoretical Capacity (per Hour)
(3600/Processing time)
1
Mount battery units
70
51.4
2
Insert remote control receiver
80
45.0
3
Insert chip
90
40.0
4
Mount front axle
30
120.0
5
Mount rear axle
70
51.4
6
Install electric motor
60
60.0
7
Connect motor to battery unit
45
80.0
8
Connect motor to rear axle
80
45.0
9
Mount plastic body
75
48.0
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