homework 2
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School
University of Houston, Downtown *
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Course
6206
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
docx
Pages
5
Uploaded by MasterWaterBuffaloMaster925
1.
An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all
tasks is 18 minutes. The line will operate for 450 minutes per day.
1.
What are the minimum and maximum cycle times?
Minimum cycle time – 2.4 minutes
maximum cycle time
= 18 minutes
2.
What range of output is theoretically possible for the line?
Minimum cycle time 450/2.4 = 187.5 units
max cycle time 450/18 = 25 units
Range is from 25 to 187.5 units
3.
What is the minimum number of workstations needed if the maximum output rate is to be
sought?
18 min/2.4 min = 7.5
8 workstations are needed if the maximum output rate is to be sought
4.
What cycle time will provide an output rate of 125 units per day?
CT= OT/125
= 450/125
= 3.6 minutes
5.
What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes?
When cycle time is 9 minutes 450/9 = 50 Units
When cycle time is 15 minutes 450/15 = 30 Units
3.
2. A manager wants to assign tasks to workstations as efficiently as possible and achieve an hourly output
of four units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the
accompanying precedence diagram (times are in minutes) to workstations using the following rules:
Cycle time = 56/4
= 14 minutes
1.
In order of most following tasks. Tiebreaker: greatest positional weight.
Workstation 1 – A, F, G total time 14 minutes
Workstation 2 – B, C, D total times 13 minutes
Workstation 3 – E, H total time 13 minutes
Workstation 4 – I total time 5 minutes
2.
In order of greatest positional weight. Tiebreaker: most following tasks.
Workstation 1 – F, D
Workstation 2 – G, A, B
Workstation 3 – C, E
Workstation 4 -
H, I
3.
What is the efficiency?
Efficiency = total task times / (workstation x cycle time ) x 100
(45/56) x 100 = 80.36% rounded up
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 Task (minutes)
1.
a 0.2
-
2.
b 0.4
A
3.
c 0.3
-
4.
d 1.3
B, C
5.
e 0.1
-
6.
f 0.8
E
7.
g 0.3
D, F
8.
h 1.2
G
a. Do each of the following:
(1) Draw the precedence diagram.
(2) Assign tasks to stations in order of the following tasks—tiebreaker: greatest positional weight.
Task
Number of Following Tasks
A
4
B
3
C
3
D
2
E
3
F
2
G
1
H
0
(3) Determine the percentage of idle time.
I = (I/NxC) x 100
.6/4x1.3) = 11.5% is the 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.
420/1.3 = 323.08
323 Units
b. Answer these questions:
1.
(1) What is the shortest cycle time that will permit use of only two workstations? Is this cycle
time feasible? Identify the tasks you would assign to each station.
Sum of total task time / cycle time
4.6/2 = 2.3
2.
(2) Determine the percentage of idle time that would result if two stations were used.
Workstation
Task Assigned
Sum of task times.
Idle time
1
A,B,C,D,E
2.3
0
2
F,G,H
2.3
0
Total idle time = 0
3.
(3) What is the daily output under this arrangement?
Output rate
= operating time per day/ cycle time
420/ 2.3
= 183 units
4.
(4) Determine the output rate that would be associated with the maximum cycle time.
Output rate = operating time per day/ cycle time 420/4.6
= 91 Units
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