To solve the problem of determining the combined idle time for this production line, we need to break down the details provided:

Problem Breakdown:

• Tasks: A to I, with their respective required times and predecessors.
• Production Details:
  • Daily demand: 82 units.
  • Shifts: 3 shifts per day, each shift is 8 hours (480 minutes per shift).

Steps to Calculate:

1. Cycle Time: This represents how much time can be allocated per unit produced to meet the daily demand. It is given by:

   $\text{Cycle Time} = \frac{\text{Total Available Time per Day}}{\text{Units Required per Day}}$

   The available time per day is $3 \times 480 \, \text{minutes} = 1440 \, \text{minutes}$.

   So,

   $\text{Cycle Time} = \frac{1440}{82} \, \text{minutes/unit}$

2. Total Task Time: This is the sum of the times required for each task. Based on the table provided:

   $\text{Total Task Time} = 16 + 15 + 6 + 5 + 16 + 3 + 9 + 14 + 4 = 88 \, \text{minutes}$

3. Number of Workstations: To calculate the minimum number of workstations, we divide the total task time by the cycle time calculated above.

4. Idle Time per Station: Once we have the number of workstations, we calculate the idle time by comparing the allocated cycle time to the actual task time for each workstation.

Let me compute the cycle time and use that to calculate idle time next.The calculated cycle time is approximately $17.56$ minutes per unit, and the total task time is 88 minutes.

Next, I will calculate the minimum number of workstations and the combined idle time.

To determine the number of workstations:

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

After this, we calculate the idle time per workstation based on task assignments that fit into the cycle time. Let's compute the number of workstations and their corresponding idle times.The production line will require 6 workstations. The idle times for each workstation are as follows:

1. Workstation 1: $1.56$ minutes
2. Workstation 2: $2.56$ minutes
3. Workstation 3: $6.56$ minutes
4. Workstation 4: $1.56$ minutes
5. Workstation 5: $5.56$ minutes
6. Workstation 6: No idle time (slightly over-scheduled by $0.44$ minutes)

The combined idle time across all workstations is approximately 17.37 minutes.

Would you like further details or have any additional questions?

Here are 5 related questions to explore:

1. How can we minimize the number of workstations?
2. What is the effect of increasing daily demand on idle time?
3. How would we adjust the schedule if one task takes longer than expected?
4. How does precedence impact task allocation across workstations?
5. Can we automate task distribution to optimize for minimal idle time?

Tip: Balancing task times across workstations is crucial for minimizing idle time and increasing production efficiency.