Question

A company is designing a product layout for a new product. It plans to use this production line eight hours a day in order to meet projected demand of 480 units per day. The tasks necessary to produce this product:

Task Time (sec) Immediate Predecessor
u 30 none
v 30 u
w 6 u
x 12 w
y 54 x
z 30 v, y

1. Without regard to demand, what is the minimum possible cycle time (in seconds) for this situation?
A. 162
B. 72
C. 54
D. 12
E. 60

Answer 1

The minimum possible cycle time for the product layout is calculated based on the longest sequence of dependent tasks, which in this case totals 114 seconds, not matching any of the provided options.

Step-by-step explanation:

The minimum possible cycle time for the described product layout, without regard to demand, is determined by the task or series of tasks that take the longest time to complete, known as the 'critical path'. We need to sum the times for the longest sequence of tasks where each task directly depends on the one before it. When we look at the provided task sequence:

• Task u: 30 seconds
• Task v: 30 seconds (follows u)
• Task w: 6 seconds (follows u)
• Task x: 12 seconds (follows w)
• Task y: 54 seconds (follows x)
• Task z: 30 seconds (follows v and y)

The longest sequence of tasks is u (30 s) to v (30 s) to y (54 s) to z (30 s), which totals to 144 seconds. However, because tasks v and y can be performed simultaneously after task u is completed, we must add the longest of these two paths to the time for task u. Therefore the longest path is u (30 s) + max[v (30 s), y (54 s)] + z (30 s). Since y is the longest of the tasks v and y, we add y to u and z, which gives us 30 + 54 + 30 = 114 seconds.

Thus, the minimum possible cycle time is 114 seconds, and none of the provided options (A. 162 B. 72 C. 54 D. 12 E. 60) are correct.