Develop a solution for the following line balancing problem, allowing a cycle time of 5 minutes

a. Draw the precedence diagram for the set of tasks.
b. Calculate the theoretical minimum number of workstations.
c. Balance this line using the longest task time heuristic.
d. What tasks are assigned to which stations?
e. Does the solution have the minimum number of stations? Explain.
f. How much idle time is there, summed over all workstations?
g. What is the efficiency of this line?

Work Task Task Time (seconds) Task Predecessor(s)
A 70 -
B 60 A
C 120 B
D 60 -
E 240 C, D
F 100 A
G 190 E, F

The theoretical minimum number of workstations is 3. Balance places ABDF in station 1, C in station 2, E in station 3, and G in station 4. The solution uses four stations, not three. The POM for Windows solution is shown below. Idle time is distributed 10, 180, 60, and 110 per station. There are 360 seconds of idle time in the system. Efficiency is 70.0%.

Station Task Time (seconds) Time left (seconds) Ready tasks
A,D
1 A 70. 230. D,B,F
F 100. 130. D,B
D 60. 70. B
B 60. 10. C
2 C 120. 180. E
3 E 240. 60. G
4 G 190. 110.
Summary Statistics
Cycle time 300 seconds
Time allocated (cycle time * #) 1200 seconds/cycle
Time needed (sum of task times) 840 seconds/unit
Idle time (allocated-needed) 360 seconds/cycle
Efficiency (needed/allocated) 70%
Balance Delay (1-efficiency) 30%
Min (theoretical) # of stations 3