Consider the following assembly line information for manufacturing the latest cell phone in Table 2. The firm wants to produce 80 cell phones per hour.
Table 2
$\begin{array}{ccc}\text { Task } & \text { Time (n minutes) } & \text { Predecessor(s) } \
\text { A } & 0.5 & \text { none } \
\text { B } & 0.4 & \text { A } \
\text { C } & 0.6 & \text { A } \
\text { D } & 0.2 & \text { B, C } \
\text { E } & 0.3 & \text { B } \
\text { F } & 0.7 & \text { E, D } \
\text { G } & 0.4 & \text { F C }
\end{array}$
-Using the longest-task-time rule, the efficiency of an assembly-line balance is _____.
A) Less than 65%
B) more than 65% but less than 75%
C) more than 75% but less than 85%
D) more than 85% but less than 95%

Question

Consider the following assembly line information for manufacturing the latest cell phone in Table 2. The firm wants to produce 80 cell phones per hour.
Table 2
 $\begin{array}{ccc}\text { Task } & \text { Time (n minutes) } & \text { Predecessor(s) } \
\text { A } & 0.5 & \text { none } \
\text { B } & 0.4 & \text { A } \
\text { C } & 0.6 & \text { A } \
\text { D } & 0.2 & \text { B, C } \
\text { E } & 0.3 & \text { B } \
\text { F } & 0.7 & \text { E, D } \
\text { G } & 0.4 & \text { F C }
\end{array}$
-Using the longest-task-time rule, the efficiency of an assembly-line balance is _____.
A) Less than 65%
B) more than 65% but less than 75%
C) more than 75% but less than 85%
D) more than 85% but less than 95%

Quizplus · Accepted Answer

The longest-task-time rule focuses on arranging tasks in a sequence that prioritizes the longest tasks first, aiming to minimize the total idle time across the assembly line and improve efficiency. To calculate the efficiency of an assembly-line balance, we first need to determine the cycle time and the theoretical minimum number of workstations.Given that the firm wants to produce 80 cell phones per hour, the cycle time can be calculated as follows:$$ \text{Cycle Time} = \frac{60 \text{ minutes per hour}}{80 \text{ cell phones per hour}} = 0.75 \text{ minutes per cell phone} $$Next, we sum up the times for all tasks to find the total work content:$$ \text{Total Work Content} = 0.5 + 0.4 + 0.6 + 0.2 + 0.3 + 0.7 + 0.4 = 3.1 \text{ minutes} $$The theoretical minimum number of workstations (N) can be calculated as:$$ N = \frac{\text{Total Work Content}}{\text{Cycle Time}} = \frac{3.1}{0.75} \approx 4.13 $$Since we cannot have a fraction of a workstation, we round up to the nearest whole number, which is 5 workstations.Finally, the efficiency of the assembly line can be calculated as:$$ \text{Efficiency} = \frac{\text{Total Work Content}}{\text{(Number of Workstations} \times \text{Cycle Time)}} = \frac{3.1}{(5 \times 0.75)} = \frac{3.1}{3.75} \approx 82.67\% $$Therefore, the efficiency of the assembly-line balance, using the longest-task-time rule, is more than 75% but less than 85%.

Consider the Following Assembly Line Information for Manufacturing the Latest