To solve this problem, we will develop two alternative layouts using the following guidelines:

1. Longest task time rule: This rule suggests that we assign tasks to workstations in the order of the longest task time first.
2. Largest number of following tasks: After the longest task, tasks with the largest number of following tasks should be assigned to subsequent workstations.

Given Information:

• Cycle time: 25 minutes
• Tasks and times:

Step 1: Calculate the Total Task Time

The total task time is the sum of all task durations:

$\text{Total Task Time} = 8 + 8 + 9 + 8 + 10 + 8 + 8 + 9 + 8 = 76 \text{ minutes}$

Step 2: Calculate the Required Number of Workstations

The number of workstations required is the total task time divided by the cycle time:

$\text{Number of Workstations} = \frac{\text{Total Task Time}}{\text{Cycle Time}} = \frac{76}{25} = 3.04$

Since we can't have a fraction of a workstation, we need 4 workstations.

Step 3: Apply the Longest Task Time Rule and Largest Number of Following Tasks as a Secondary Criterion

Let's start by assigning tasks to workstations following the two rules:

1. Workstation 1: The longest task is E (10 min).
2. Workstation 2: The next longest task is C (9 min).
3. Workstation 3: The next longest task is H (9 min).
4. Workstation 4: The remaining tasks can be assigned, starting with A (8 min), followed by B (8 min), D (8 min), F (8 min), G (8 min), and I (8 min).

Step 4: Calculate the Efficiency

Efficiency can be calculated using the formula:

$\text{Efficiency} = \frac{\text{Total Task Time}}{\text{Number of Workstations} \times \text{Cycle Time}} \times 100$

Substitute the known values:

$\text{Efficiency} = \frac{76}{4 \times 25} \times 100 = \frac{76}{100} \times 100 = 76\%$

Conclusion

The highest efficiency of the layout, assuming the 25-minute cycle time, is 76.00%.

Would you like further details on how this was computed or have additional questions on other layouts? Here are some follow-up questions:

1. How do different task distribution methods (like the shortest task rule) affect layout efficiency?
2. What would happen to the efficiency if the cycle time were changed to 30 minutes?
3. How can we improve the layout to reduce the number of workstations?
4. What are some real-world applications of these assembly line techniques?
5. How can bottlenecks in task assignments be identified and resolved in such layouts?

Tip: Always review the dependencies between tasks carefully. Incorrectly assigning tasks can result in bottlenecks that will reduce overall efficiency.