38
39) An assembly line has been designed to make battery-powered beverage mixers. Task details are
shown in the table below:
Station
Task Assigned
Task Time
(minutes)
1
1
3.0
2
3; 4
1.5; 2.0
3
2; 5; 6
1.5; 1.5; 1.0
4
7
3.0
5
8
2.5
6
9; 10; 11
2.0; 1.0; 1.0
a. What is the assigned cycle time (in minutes)?
b. What is the maximum output rate of this line in mixers per hour?
c. What is the total idle time per cycle?
d. What is the assembly line’s efficiency?
40
40) Cyclone Appliances has developed a new European-style convection oven that will be made on an
assembly line. The schedule requires 80 ovens in an 8-hour day. The assembly includes seven tasks. The
table below indicates the performance time and the sequence requirements for each task.
Task
Performance Time
(minutes)
A
1
B
2
C
3
D
2
E
4
F
1
G
2
(a) What is the cycle time for this assembly operation?
(b) What is the theoretical minimum number of workstations?
(c) Draw the precedence diagram.
41
41) An electronics manufacturer makes remote control devices for interactive-cable-TV systems. The
following assembly tasks must be performed on each device.
Task
Description
Predecessor(s)
Time (min.)
A
Place circuit into circuit frame
—
0.50
B
Solder circuit connections to central circuit
control
A
0.70
C
Place circuit assembly in device frame
B
0.40
D
Attach circuit assembly to device frame
C
0.30
E
Place and attach display to frame
—
0.30
F
Place and attach keypad to frame
—
0.20
G
Place and attach top body of device to frame
E, F
0.35
H
Place and attach battery holder to frame
D
0.40
I
Place and attach bottom body of device to frame
G, H
0.60
J
Test device
I
0.30
a. Draw the precedence diagram for this problem.
b. What is the sum of the task times?
c. What cycle time will allow the production of 200 units over a ten-hour day?
d. What is the theoretical number of workstations needed?
e. Balance this assembly line using the heuristic most following tasks and the heuristic longest operation
time.
f. How do these two solutions differ? Which do you prefer; why?
42
42) A company is designing a product layout for a new product. It plans to use this production line eight
hours a day in order to meet a schedule of 400 units per day. The tasks necessary to produce this product
are detailed in the table below.
Task
Predecessor
Time (seconds)
A
–
50
B
A
36
C
–
26
D
–
22
E
B, D
70
F
C, E
30
a. Draw the network described in the table.
b. Without regard to a production schedule, what is the minimum possible cycle time (in seconds) for
this situation; what is the maximum?
c. What is the required cycle time (in seconds) in order to meet the schedule?
d. What is the theoretical minimum number of workstations needed to meet the schedule?
e. Balance this line using longest processing time.
f. What is the efficiency of the balance obtained in part e?
43
43) You have been asked to balance a flow shop assembly operation to achieve an output rate of 80 units
per eight-hour day. Task times and precedence relationships are shown in the table below.
Task
Predecessor(s)
Duration
(minutes)
A
—
1.4
B
—
0.8
C
A, B
0.4
D
—
1.8
E
—
0.4
F
C
2.1
G
E, F
2.0
H
D, G
1.2
a. Draw the precedence diagram.
b. Determine the desired cycle time.
c. Determine the theoretical minimum number of stations needed.
d. Balance this line using the most following tasks heuristic.
e. What is the efficiency of the line obtained in part d?
45
44) A firm operates a flow shop building kitchen cabinetry for recreational vehicles. The major activities
of this process are listed below.
Task
Duration
(hours)
Predecessor 1
Predecessor 2
Predecessor 4
A
4
—
B
6
—
C
2
A
D
6
A
E
3
B
C
F
3
B
C
G
5
D
E
F
H
1
G
a. Draw the appropriate network for this project.
b. What would the cycle time be if the goal is to produce 20 units per month (the plant operates
160 hours per month)?
c. What is the theoretical minimum number of workstations needed?
d. Balance with the most following tasks heuristic. What tasks are assigned to which stations?
e. What is the efficiency of the line obtained in part d?
47
45) Hemo-tech, Inc., a biomedical technology and research laboratory, produces a standard blood filtering
device on an assembly-line basis. Six basic tasks are performed along the assembly line. The time to
perform each task and the tasks that must immediately precede each task are in the table below. Twenty
pumps per 450-minute day must be produced by the assembly line.
Task
Preceding Task
A
—
B
A
C
—
D
B, C
E
D
F
E
(a) Draw the network diagram of the precedence relationships.
(b) Identify the absolute minimum and maximum cycle times.
(c) What is the cycle time required to meet demand?
(d) What is the minimum number of workstations required to meet the schedule?
(e) Balance this line using the most following tasks heuristic.
(f) What is the efficiency of the line obtained in part (e)?
(g) Can the efficiency of this solution be improved? Explain.
49
46) A firm is planning to set up an assembly line to assemble 40 units per hour, and 57 minutes per hour
are productive. The time to perform each task and the tasks that precede each task are contained in the
following table.
Task
Preceding Task
Time to
perform (min.)
A
—
.69
B
A
.55
C
B
.92
D
B
.59
E
B
.70
F
B
1.10
G
C, D, E
.75
H
G, F
.43
I
H
.29
(a) Draw a network diagram of precedence relationships.
(b) Compute the required cycle time per unit in minutes.
(c) Compute the theoretical minimum number of workstations required to produce 40 units per hour.
(d) Balance this line using the longest processing time heuristic.
(e) What is the efficiency of the line obtained in part d?
47) An assembly line with 11 tasks is to be balanced. The longest task is 2.4 minutes, the shortest task is
0.4 minutes, and the sum of the task times is 18 minutes. The line will operate for 600 minutes per day.
(a) Determine the minimum and maximum cycle times.
(b) What range of output is theoretically possible for the line?
(c) What is the minimum number of stations needed if the maximum output rate is to be sought?
(d) What cycle time will provide an output rate of 200 units per day?
52
48) A facility is trying to set up an assembly line, and has identified the various tasks, and their
relationship to each other, as shown in the following table. Managers wish to produce 600 units per day,
working two 8-hour shifts.
Task
Preceding Task
A
—
B
—
C
—
D
—
E
A
F
D, B, C
G
E
H
F, G
(a) Draw a network diagram of precedence relationships.
(b) Compute the required cycle time per unit in seconds.
(c) Compute the minimum number of workstations required to produce 600 units per day.
(d) Balance this line using the longest processing time heuristic.
(e) What is the efficiency of the line obtained in part (d)?
53
54
49) A company is trying to balance production between 3 workstations on an assembly line. Currently
there are 5 tasks that need to be performed. These tasks, ABCDE, have required times of 2 minutes, 4
minutes, 1 minutes, 3 minutes, and 10 minutes, respectively. The assembly line needs to produce 40 units
per day to meet demand and can work for up to 8 hours each day.
(a) What is the required cycle time?
(b) What is the theoretical minimum # of workstations?
(c) Assign the tasks according to the shortest task time heuristic.
50) An assembly line is assigned as follows. Station 1– task A, B, and C. Station 2- task D. Station 3- task E
and F. The task times are 7, 3, 2, 9, 4, and 5 minutes respective to A, B, C, D, E, and F. (Assume that there
is no precedence relationship between the tasks, i.e., they can be performed in any order)
(a) Calculate the efficiency.
(b) What would the assignment of tasks to stations be using the shortest processing time heuristic
(assuming the current maximum station time remains the cycle time)?