Q&A Hero

Question

Station Task Time (minutes) Time left (minutes) Ready tasks
A
1 A 69 0.735 B
B 0.55 0.185 C,D,E,F
2 F 1.1 0.325 C,D,E
3 C 0.92 0.505 D,E
4 E 0.7 0.725 D
D 0.59 0.135 G
5 G 0.75 0.675 H
H 0.43 0.245 I
6 I 0.29 1.135
Summary Statistics
Cycle time 1.425 minutes
Time allocated (cycle time * #) 8.549999 minutes/cycle
Time needed (sum of task times) 6.02 minutes/unit
Idle time (allocated-needed) 2.529999 minutes/cycle
Efficiency (needed/allocated) 70.40936%
Balance Delay (1-efficiency) 29.59064%
Min (theoretical) # of stations 5

Key Term: Assembly-line balancing

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?

Answer: (a) Minimum cycle time is 2.4 minutes. Maximum cycle time is 18 minutes. (b) Maximum output is 600/2.4 = 250; minimum output is 600/18 = 33.3. (c) For maximum output, 18/2.4 = 7.5 or 8 stations will be needed. (d) To produce 200 units per day requires a 3-minute cycle time.

Key Term: Assembly-line balancing

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 Time to perform (sec.)
A -- 20
B -- 30
C -- 25
D -- 10
E A 55
F D, B, C 30
G E 25
H F, G 40

(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)?

Answer: (a) The precedence diagram appears below. (b) Required cycle time is 480(2)/600 = 1.6 minutes or 96 seconds. (c) 235/96 = 2.45 or 3 workstations are needed. (d) The computer output places tasks A-B-C-D in station 1, E-F in station 2, and G-H in station 3. (e) Efficiency is about 82 percent.

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