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. 
Kanban card is 9 cards 
ROP is 1760
What service level does the safety stock represent?


To determine the service level that the safety stock represents, we can approach this problem using the information provided about the assembly line, Kanban cards, Reorder Point (ROP), and other given data. The process involves calculating the safety stock and then determining the service level using the Z-score that matches the Alfa factor.

### Step 1: Calculate the Safety Stock

The Reorder Point (ROP) is given as 1760 units. We can use the relationship between the Reorder Point, average demand, lead time, and safety stock:

\[
\text{ROP} = \text{Average Demand} \times \text{Lead Time} + \text{Safety Stock}
\]

Given:
- ROP = 1760 units
- Average Demand = 800 products/hour
- Lead Time = 2 hours

First, calculate the average demand during the lead time:

\[
\text{Average Demand during Lead Time} = 800 \times 2 = 1600 \text{ units}
\]

Now, solve for Safety Stock:

\[
\text{Safety Stock} = \text{ROP} - \text{Average Demand during Lead Time} = 1760 - 1600 = 160 \text{ units}
\]

### Step 2: Calculate the Z-score

We have the Safety Stock and know that:

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

Where:
- \( \sigma_d = 100 \) (standard deviation of demand during the lead time)
- \( L = 2 \) hours (lead time)

Substituting the known values:

\[
160 = Z \times 100 \times \sqrt{2}
\]

\[
160 = Z \times 100 \times 1.414
\]

\[
160 = Z \times 141.4
\]

\[
Z = \frac{160}{141.4} \approx 1.13
\]

### Step 3: Determine the Service Level

Using a Z-score table or a standard normal distribution, we can find the service level corresponding to a Z-score of 1.13.

For a Z-score of 1.13, the corresponding service level is approximately 0.8708, or **87.08%**.

### Final Answer:
The service level that the safety stock represents is approximately **87.08%**.

---

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 Reorder Point (ROP) were set at 1800 units?
2. What would be the effect of increasing the standard deviation of demand to 150 units?
3. How does the number of Kanban cards affect the overall inventory levels?
4. What is the significance of the Alfa factor in inventory management?
5. How would a lead time reduction to 1 hour affect the service level?
6. How can the company improve its service level without increasing safety stock?
7. What role does the Z-score play in determining the safety stock?
8. How would the safety stock change if the hourly production rate increased to 900 units?

**Tip:** Always ensure to verify the accuracy of your calculations by cross-referencing with the Z-score table when determining service levels.

Learn how to calculate the service level represented by safety stock in inventory management. This problem involves determining safety stock using the ROP formula and calculating the Z-score to find the corresponding service level. Suitable for advanced learners and professionals in supply chain and inventory management.

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