To calculate the process utilization, we need to determine how much of the available time the process is being used to meet demand. Here are the steps:

Step 1: Determine total production time for one batch

The process requires a 14-minute setup time for each batch and can produce one unit every 16 minutes. With a batch size of 12 units, the total production time for a batch is:

$\text{Production time for a batch} = 12 \times 16 = 192 \text{ minutes}$

So, the total time to complete one batch, including setup, is:

$\text{Total time per batch} = \text{Setup time} + \text{Production time} = 14 + 192 = 206 \text{ minutes}$

Step 2: Determine how many batches are required to meet demand

The demand is 3 units per hour, which equals:

$3 \times 24 = 72 \text{ units per day (assuming a 24-hour operation)}$

Now, divide the total demand by the batch size to determine how many batches are required:

$\text{Number of batches required} = \frac{72}{12} = 6 \text{ batches per day}$

Step 3: Calculate total time spent producing batches

Each batch takes 206 minutes to complete. For 6 batches, the total time spent producing during the day is:

$\text{Total production time per day} = 6 \times 206 = 1236 \text{ minutes}$

Step 4: Determine available time

There are 24 hours in a day, or:

$24 \times 60 = 1440 \text{ minutes per day}$

Step 5: Calculate utilization

The process utilization is the ratio of the time spent producing to the total available time:

$\text{Utilization} = \frac{\text{Total production time per day}}{\text{Available time}} = \frac{1236}{1440} = 0.8583 \text{ or } 85.83\%$

Final Answer:

The process utilization is 85.83%.

Would you like further details or have any questions?

Related Questions:

1. How does changing the batch size affect process utilization?
2. What happens to utilization if the demand increases to 4 units per hour?
3. How would reducing the setup time to 10 minutes impact utilization?
4. What is the impact on utilization if the production time per unit drops to 12 minutes?
5. How does the utilization change if the process runs only for 16 hours per day?

Tip:

Batch size directly affects the balance between setup time and production time, so optimizing batch sizes can improve overall process efficiency.