An assembly line produces 800 products per hour, with a standard deviation of demand during the lead time of 100. The lead time from the inventory location to the assembly line is 2 hours. The boxes, the product is transported, carry 200 items, and the company uses an Alfa factor of 0.1. what service level does the safety stock represent? 

To determine the service level represented by the safety stock, we can use the following formula related to safety stock and service level:

\[
\text{Safety Stock} = Z \times \sigma_d \times \sqrt{L}
\]

Where:
- \( Z \) is the Z-score corresponding to the desired service level (which we'll find).
- \( \sigma_d \) is the standard deviation of demand during the lead time.
- \( L \) is the lead time.

Given:
- \( \sigma_d = 100 \) (standard deviation of demand during the lead time)
- \( L = 2 \) hours (lead time)
- \( \alpha \) (Alpha factor) = 0.1

### Step 1: Calculate the Safety Stock

First, calculate the safety stock using the given formula. However, the service level is typically derived from the safety stock, so we first need to understand what the Safety Stock should be.

Since the demand rate per hour is not directly linked to the calculation (only the variability, which is \( \sigma_d \)), we can directly calculate the safety stock as follows:

\[
\text{Safety Stock} = Z \times 100 \times \sqrt{2}
\]

We do not have the exact value of the safety stock but have been provided the Alpha factor, which is typically used to calculate the Reorder Point:

\[
\text{Reorder Point} = \text{Average Demand} \times L + \text{Safety Stock}
\]

Given the Reorder Point is not directly provided, we are supposed to deduce the service level.

### Step 2: Use the Alfa factor to find the Z-score

The alpha factor \( \alpha \) corresponds to the probability of stockout (1 - service level). The relationship between the Alfa factor and Z-score (for a normal distribution) is:

\[
\alpha = 1 - \text{Service Level}
\]

So,

\[
\text{Service Level} = 1 - \alpha = 1 - 0.1 = 0.9
\]

### Step 3: Find the Z-score corresponding to a 0.9 Service Level

From standard normal distribution tables, the Z-score that corresponds to a service level of 0.9 is approximately:

\[
Z = 1.28
\]

Thus, the service level corresponding to the given Alfa factor of 0.1 is 0.9, or **90%**.

### Final Answer:
The service level represented by the safety stock is **90%**.

---

Would you like more details on this, or have any other questions?

Here are 8 questions that extend from this problem:
1. How would the service level change if the lead time were increased to 3 hours?
2. What would happen to the service level if the standard deviation of demand increased to 150?
3. How is the reorder point calculated in this scenario?
4. What is the impact of reducing the Alfa factor to 0.05?
5. How would the safety stock change if the Z-score corresponding to the service level increased?
6. What assumptions are made in using the standard deviation in this context?
7. How does the lead time variability affect the safety stock calculation?
8. How would you adjust the safety stock if demand variability increased?

**Tip:** The Z-score is crucial in determining service levels; understanding its relation to the normal distribution is vital in inventory management.

Understand how to calculate the service level represented by safety stock in inventory management scenarios. Learn the application of statistical concepts such as the safety stock formula, Z-score, and the relationship to lead time and demand variability. Example calculations provided for clarity.

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