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 are: $$\begin{array} { l l l }
\text { Task } & \text { Time (secs) } & \text { Immediate Predecessor } \
\hline \mathrm { u } & 30 & \text { none } \
\mathrm { v } & 30 & \mathrm { u } \
\mathrm { w } & 6 & \mathrm { u } \
\mathrm { x } & 12 & \mathrm { w } \
\mathrm { y } & 54 & \mathrm { x } \
\mathrm { z } & 30 & \mathrm { v } , \mathrm { y }
\end{array}$$ If the company wants the output rate to be equal to demand, what is the last task performed at the second workstation in the balance which uses the minimum number of workstations?
A) u
B) v
C) w
D) x
E) y

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 are: $$\begin{array} { l l l } 
\text { Task } & \text { Time (secs) } & \text { Immediate Predecessor } \
\hline \mathrm { u } & 30 & \text { none } \
\mathrm { v } & 30 & \mathrm { u } \
\mathrm { w } & 6 & \mathrm { u } \
\mathrm { x } & 12 & \mathrm { w } \
\mathrm { y } & 54 & \mathrm { x } \
\mathrm { z } & 30 & \mathrm { v } , \mathrm { y }
\end{array}$$ If the company wants the output rate to be equal to demand, what is the last task performed at the second workstation in the balance which uses the minimum number of workstations?
A) u
B) v
C) w
D) x
E) y

Quizplus · Accepted Answer

In order to determine the last task performed at the second workstation, we need to first determine the cycle time necessary to meet the demand of 480 units per day.

Cycle time = 8 hours/day * 3600 seconds/hour / 480 units/day = 60 seconds/unit

Next, we can draw a precedence diagram to help us determine the minimum number of workstations needed and the tasks assigned to each workstation.

u      v
 \    /
  w  x  y
    |
    z

Using the longest task first heuristic, we can assign tasks to workstations starting with the longest task (y) and working backwards, assigning tasks to the first workstation until the cycle time is met.

Workstation 1: Tasks y and z (total time = 84 seconds) 
Workstation 2: Tasks x and v (total time = 42 seconds) 
Workstation 3: Tasks u and w (total time = 36 seconds)

Therefore, the last task performed at the second workstation is task x.

The answer is D.

A Company Is Designing a Product Layout for a New