As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day.
Task times and precedence relationships are as follows:

Task Duration (minutes) Immediate Predecessor
a 0.2 -
b 0.4 a
c 0.2 b
d 0.4 -
e 1.2 d
f 1.2 c
g 1.0 e, f

Do each of the following:
(a) Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.)
(b) Determine the minimum number of stations needed. (Round your answer to the next whole number.)
(c) Assign tasks to workstations on the basis of the greatest number of following tasks. Use the longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.
(d) Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

A)Minimum = 0.2 minutes

Maximum = 4.6 minutes

Cycle time = = 2 minutes per unit

B) Number of Stations = 3

D) the percentage of idle time for the assignment in decimal = 0.43

Explanation:

A) Operating output = 240 units per 8hours.

Converting to per hour, we get; 240/8 = 30 units per hour.

Minimum cycle time = longest task time

Maximum cycle time = sum of task times

Minimum = 0.2 minutes

Maximum = 0.2 + 0.4 + 0.2 + 0.4 + 1.2 + 1.2 + 1.0 = 4.6 minutes

Now, operational time(OT) is 8 hours a day. Converting that to minutes, we have =60x8 = 480 minutes

Cycle time(CT) = OT (per day) /desired output

Therefore, calculated cycle time = 480/240

= 2 minutes per unit

B) Number of stations = Maximum time / CT

= 4.6/2 = 2.3 which is approximately 3 stations

C) The task diagram is drawn in image 1 attached. Therefore, we can assign tasks based in the greatest number of following tasks as follows;

Task Number of following tasks

a 4

b 3

c 2

d 2

e 1

f 1

g 0

D) for the idle time from the assigned tasks in "c" above, from the "image 2" attached; the percentage of the idle time will be=

Total remaining time of tasks without remaining feasibility tasks/ {(number of these tasks) x(CT)}

Which gives percentage of idle time = (0.8 + 0.8 + 0.8 + 1.0)/{(4)x(2)}

= 3.4/8 = 42.5%

Since we are to convert to decimal,

= 0.425 approximately 0.43

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