Use this scenario for the following question(s).
The process design team at a manufacturer has broken an assembly process into eight basic steps, each with a required time, and predecessor as shown in the table. There are 7.5 productive hours available in a day and the manufacturer wishes to produce 400 units. Balance the line by assigning tasks to workstations to fill up as much takt time as possible. Break ties by assigning the longest task first.
$$\begin{array} { | c | c | c | }
\hline \text { Task } & \text { Time } ( \mathrm { sec } ) & \text { Predecessor } \
\hline \text { A } & 45 & \cdots \
\hline \text { B } & 50 & \text { A } \
\hline \text { C } & 20 & \text { A } \
\hline \text { D } & 55 & \text { A } \
\hline \text { E } & 15 & \text { D } \
\hline \text { F } & 65 & \text { D } \
\hline \text { G } & 25 & \text { E } \
\hline \text { H } & 35 & \text { B, C, F, G } \
\hline
\end{array}$$
-Refer to the scenario above. What is the theoretical minimum number of stations that will be used if the line is balanced using the appropriate takt time?
A)3
B)4
C)5
D)6

Question

Use this scenario for the following question(s).
The process design team at a manufacturer has broken an assembly process into eight basic steps, each with a required time, and predecessor as shown in the table. There are 7.5 productive hours available in a day and the manufacturer wishes to produce 400 units. Balance the line by assigning tasks to workstations to fill up as much takt time as possible. Break ties by assigning the longest task first.
 $$\begin{array} { | c | c | c | } 
\hline \text { Task } & \text { Time } ( \mathrm { sec } ) & \text { Predecessor } \
\hline \text { A } & 45 & \cdots \
\hline \text { B } & 50 & \text { A } \
\hline \text { C } & 20 & \text { A } \
\hline \text { D } & 55 & \text { A } \
\hline \text { E } & 15 & \text { D } \
\hline \text { F } & 65 & \text { D } \
\hline \text { G } & 25 & \text { E } \
\hline \text { H } & 35 & \text { B, C, F, G } \
\hline
\end{array}$$
-Refer to the scenario above. What is the theoretical minimum number of stations that will be used if the line is balanced using the appropriate takt time?
A)3
B)4
C)5
D)6

Quizplus · Accepted Answer

To determine the minimum number of stations required, we need to calculate the theoretical minimum number of stations (balance delay). The takt time is the total available time divided by the required output rate. The required output rate is 400 units divided by the available time of 7.5 hours or 27 seconds per unit.

We then calculate the minimum cycle time by adding up the longest task time for each step. Starting with Task A, the longest task time is 45 seconds. For Task B and Task C, we choose Task B as it has a longer duration of 50 seconds. For Task D, the longest task time is 55 seconds. For Task E and Task F, we choose Task F as it has a longer duration of 65 seconds. For Task G, the task time is 25 seconds. Finally, for Task H, the task time is 35 seconds.

The minimum cycle time is therefore 45 + 50 + 55 + 65 + 35 = 250 seconds.

To determine the minimum number of stations required, we divide the sum of the task times by the cycle time and round up to the nearest integer.

Sum of task times = 45 + 50 + 20 + 55 + 15 + 65 + 25 + 35 = 310 seconds.

Minimum number of stations required = ceil (310/250) = 2.

Therefore, the theoretical minimum number of stations required is 2. However, we need to round up to the next odd number to avoid creating unbalanced stations. Therefore, the minimum number of stations required is 3. We can assign tasks to workstations to fill up as much takt time as possible, starting with the longest task time and breaking ties by assigning the longest task first.

Station 1: Tasks F (65 sec) + B (50 sec) + A (45 sec) = 160 seconds 
Station 2: Tasks D (55 sec) + C (20 sec) + E (15 sec) = 90 seconds 
Station 3: Task H (35 sec) + G (25 sec) + A (45 sec) = 105 seconds

Each station has a total duration less than or equal to the cycle time of 250 seconds, and the line is balanced. Therefore, the best choice is C, 5 stations.

Use This Scenario for the Following Question(s) -Refer to the Scenario Above