Problem 6-4 A producer of inkjet printers is planning to add a new line of print
ID: 357584 • Letter: P
Question
Problem 6-4 A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible Length Immediate Task (minutes) Predecessor 0.2 0.4 0.3 0.1 0.8 0.3 a. Do each of the following (1) Enter the number of following tasks for each of the tasks shown in the table below Number of Following Tasks (2) Assign tasks to stations in order of greatest number of following tasks. Use greatest positional weight as a tiebreaker rule Work Station Task Assigned Click to select)v (Click to select) (Click to select) (Click to select)V (3) Determine the percentage of idle time. (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Percentage of idle time (4) Compute the rate of output in printers per day that could be expected for this line assuming a 420- minute working day. (Round your answer to the nearest whole number.) Rate of output units per day b. Answer these questions (1) What is the shortest cycle time that will permit use of only two workstations? (Round your answer to 1 decimal place.) Shortest cycle time minutes (2) Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b(1). (Leave no cells blank be certain to enter "O wherever required. Omit the '%" sign in your response.) Percentage of idle time (3) What is the daily output under this arrangement a using the cycle time from Partb(1)? (Round your answer to 1 decimal place.) units per day (4) Determine the output rate that would be associated with using the maximum cycle time. (Round your answer to 2 decimal places.) Rate of output units per dayExplanation / Answer
1)
Start with extreme right task of the line. Positional weight for task is sum of the task’s time and the time of all following tasks.
Task
# of following tasks
Positional weight
a
4
3.4 =0.2+0.4+1.3+0.3+1.2
b
3
3.2 =0.4+1.3+0.3+1.2
c
3
3.1 =0.3+1.3+0.3+1.2
d
2
2.8 =1.3+0.3+1.2
e
3
2.4 =0.1+0.8+0.3+1.2
f
2
2.3 =0.8+0.3+1.2
g
1
1.5 =0.3+1.2
h
0
1.2
2)
Minimum cycle time for the line = longest duration among the tasks = 1.3 for task D
Cycle time = 1.3 minutes
Number of workstation required = Total work content/Cycle time = 4.6/1.3 = 3.53
# of workstation required = 4
For the first workstation, select the task with greatest number of following task, in case of tie select task with highest positional weight, prerequisite that preceding task of the selected task is completed and the duration is less than the desired cycle time (C).
Obtain remaining time on the workstation by subtracting the cumulative assigned time from cycle time.
If remaining time becomes less than cycle time, move for next workstation. Repeat the procedure till all the tasks are assigned.
Workstation #
Cycle Time Remaining
Eligible Tasks
Assign Task
Idle time
I
1.3
A
A
1.3-0.2 = 1.1
B, C, E
B (highest positional weight)
1.1-0.4 = 0.7
C, E
C (highest positional weight)
0.7-0.3 = 0.4
D, E
E (Most following)
0.4-0.1 = 0.3
None
0.3
2
1.3
D, F
D (highest positional weight)
1.3-1.3 = 0
0
3
1.3
F
F
1.3-0.8 = 0.5
G
G
0.5-0.3 = 0.2
None
0.2
4
1.3
H
H
1.3-1.2 = 0.1
0.1
Total Idle Time
0.6
WS #1 – A, B, C, E
Ws #2 - D
WS #3 – F, G
WS #4 - H
Total Idle time = 0.6
3)
% of idle time = Idle time/(cycle time x # of Workstations) x 100 = 0.1154 x 100
% of idle time = 11.54%
4)
Output rate = Available time/Cycle time = 420 minutes/1.3 = 323 units per day
Output Rate = 323 units per day
Task
# of following tasks
Positional weight
a
4
3.4 =0.2+0.4+1.3+0.3+1.2
b
3
3.2 =0.4+1.3+0.3+1.2
c
3
3.1 =0.3+1.3+0.3+1.2
d
2
2.8 =1.3+0.3+1.2
e
3
2.4 =0.1+0.8+0.3+1.2
f
2
2.3 =0.8+0.3+1.2
g
1
1.5 =0.3+1.2
h
0
1.2