Consider a four-step serial process with processing times given in the following list. There is one machine at each step of the process, and this is a machine-paced process.

Step 1: 25 minutes per unit

Step 2: 15 minutes per unit

Step 3: 30 minutes per unit

Step 4: 20 minutes per unit

Round your answer to 3 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

The resource capacity of step 2 is 
 units per hour.

The resource capacity of step 4 is 
 units per hour.

The process capacity is 
 units per hour.

Assume unlimited demand, the cycle time is 
 hours.

Assume that the process starts out empty. It will take 
 hours for the first flow unit to go through an empty system, and it will take a total of 
 hours to complete a batch of 105 units.

Let's break this problem down step by step:

### 1. **Resource Capacity of Step 2**:
Resource capacity is calculated as the number of units a resource (machine) can process in one hour. The processing time for Step 2 is given as **15 minutes per unit**.

To convert this to units per hour:

\[
\text{Capacity of Step 2} = \frac{60}{15} = 4 \text{ units per hour}
\]

### 2. **Resource Capacity of Step 4**:
Similarly, the processing time for Step 4 is **20 minutes per unit**.

\[
\text{Capacity of Step 4} = \frac{60}{20} = 3 \text{ units per hour}
\]

### 3. **Process Capacity**:
The process capacity is determined by the slowest (bottleneck) step, which has the highest processing time. Here are the processing times for each step:

- Step 1: 25 minutes per unit
- Step 2: 15 minutes per unit
- Step 3: 30 minutes per unit
- Step 4: 20 minutes per unit

The bottleneck is **Step 3** with **30 minutes per unit**. The capacity of Step 3 is:

\[
\text{Capacity of Process} = \frac{60}{30} = 2 \text{ units per hour}
\]

### 4. **Cycle Time**:
The cycle time is the time it takes to complete one unit in a machine-paced process, which is governed by the bottleneck. Since Step 3 is the bottleneck:

\[
\text{Cycle Time} = \frac{1}{\text{Process Capacity}} = \frac{1}{2} = 0.5 \text{ hours per unit}
\]

### 5. **Time for First Flow Unit Through an Empty System**:
For the first unit to go through an empty system, it must pass through all four steps. The time is the sum of the processing times at each step:

\[
\text{Time for First Unit} = 25 + 15 + 30 + 20 = 90 \text{ minutes} = \frac{90}{60} = 1.5 \text{ hours}
\]

### 6. **Total Time to Complete 105 Units**:
Once the system is full, units are completed at the rate of the bottleneck. The first unit takes 1.5 hours, and each subsequent unit takes the cycle time of 0.5 hours. So, to complete 105 units:

- Time for the first unit: 1.5 hours
- Time for the remaining 104 units: \(104 \times 0.5 = 52\) hours

Thus, the total time to complete 105 units is:

\[
1.5 + 52 = 53.5 \text{ hours}
\]

### Final Answers:
- **Resource capacity of Step 2**: 4 units per hour
- **Resource capacity of Step 4**: 3 units per hour
- **Process capacity**: 2 units per hour
- **Cycle time**: 0.5 hours
- **Time for the first unit to go through the system**: 1.5 hours
- **Total time to complete 105 units**: 53.5 hours

Would you like more details on any step? Here are five related questions to consider:

1. How would adding an additional machine to Step 3 affect the process capacity?
2. If Step 1’s processing time increased to 35 minutes per unit, what would the new bottleneck be?
3. What would happen if Step 2 could process in 10 minutes per unit?
4. How do you calculate throughput time in systems with multiple machines?
5. How would a downtime of 30 minutes affect the total time for 105 units?

**Tip**: Identifying the bottleneck is crucial in optimizing a machine-paced process. Focusing on improving the bottleneck step can significantly increase overall process capacity.

Consider a four-step serial process with processing times given in the following list. There is one machine at each step of the process, and this is a machine-paced process. Step 1: 25 minutes per unit. Step 2: 15 minutes per unit. Step 3: 30 minutes per unit. Step 4: 20 minutes per unit. Round your answer to 3 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers. The resource capacity of step 2 is units per hour. The resource capacity of step 4 is units per hour. The process capacity is units per hour. Assume unlimited demand, the cycle time is hours. Assume that the process starts out empty. It will take hours for the first flow unit to go through an empty system, and it will take a total of hours to complete a batch of 105 units.

Learn how to calculate process capacity and cycle time for a four-step machine-paced serial process with varying step times. This detailed solution covers key concepts like bottleneck analysis, unit conversion, and resource capacity, ideal for industrial engineering students.

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