Answer:
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 %
