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 260 units per 8-hour day. Task times and precedence relationships are as follows: Task Duration (minutes) Immediate Predecessor
a 0.5 -
b 0.6 a
c 0.2 b
d 0.3 -
e 1.7 d
f 1.8 c
g 1.9 e, f

Do each of the following:

a. Draw the precedence diagram.
b. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time.
c. Determine the minimum number of stations needed.
d. Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.
e. Compute the percentage of idle time for the assignment in part d.

a. Attached in the attachment

b.

1.Minimum Cycle Time = 1.9 minutes

2.Maximum Cycle Time = 7 minutes  

3.Calculated Cycle Time = 1.84 minutes    

c. Number of minimum Stations = 4

d. Attached in the attachment

e. Idle % = 5.70 %    

Explanation:

This problem is very interesting and really simple to solve. Just to have some basic definitions to remember.

We are told to calculate all the questions while keeping in mind the operation time = 8 hours = 8x60 minutes = 480 minutes. And required output units = 260 units/day.

First of all, we are asked to calculate the precedence graph for the data given.

a. NOTE:

Solution of a, which is the precedence graph is attached below in the attachment.

Secondly, we are asked to calculate:

1. Minimum Cycle Time

2. Maximum Cycle Time

3. Calculated Cycle Time

So,

b.

1. In order to calculate the minimum cycle time, we need to see the maximum task duration in the data given.

Minimum Cycle Time = Maximum task duration

Minimum Cycle Time = 1.9 minutes

2. In order to calculate the maximum cycle time, we need to see all the task times and add all of them together.

Maximum Cycle Time = ∑ (Task Times)

Maximum Cycle Time =  0.5+ 0.6+ 0.2+ 0.3+ 1.7+ 1.8+ 1.9

Maximum Cycle Time = 7 minutes        

3. In order to calculate the calculated cycle time, we need to plug in the values into the following formula:

Calculated Cycle Time =   Operational Time / Output (No. of required units per day)

Calculated Cycle Time = 480/260

Calculated Cycle Time = 1.84 minutes      

Thirdly, we are asked to calculate the minimum number of stations needed.

c. In order to calculated the minimum number of stations, we need to apply the following formula:

Number of minimum Stations = Sum of all task times / Minimum Cycle Time

Number of minimum Stations = 7 minutes / 1.9 minutes

Number of minimum Stations = 3.68 ≈ 4 Stations

Number of minimum Stations = 4

Fourthly, we are asked to assign tasks to workstations on the basis of greatest number of following tasks.

d. NOTE: Assigning task has been tabulated and attached in the attachment to this answer. Please refer to the attachment for this.      

Finally, we are asked to calculated the idle percentage.

e. In order to calculated the idle percentage, we need to apply the following formula:

idle percentage = Total Idle time/ (Calculated Cycle Time x No. of stations)

Total Idle time = 0.42

Idle % =   0.42/(1.84x4)

Idle % = 5.70 %    

answer; is usually (less than) the socially optimal level of consumption;

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%