An assembly line produces 800 products per hour, with a standard deviation of demand during the lead time of 100. For every product they make, they use a Kanban system. 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. 
How many units will be there if they use a ROP system?


To determine the number of units required in a Reorder Point (ROP) system, we'll use the following formula:

\[
\text{ROP} = D \times L + \text{Safety Stock}
\]

Where:
- \(D\) = Demand rate per hour
- \(L\) = Lead time (in hours)
- \(\text{Safety Stock}\) is calculated as \(Z \times \sigma_{LT}\)

### Step 1: Calculate the Demand During Lead Time

\[
\text{Demand during lead time} = D \times L = 800 \, \text{products/hour} \times 2 \, \text{hours} = 1600 \, \text{products}
\]

### Step 2: Calculate the Safety Stock

\[
\text{Safety Stock} = Z \times \sigma_{LT}
\]

Where:
- \(\sigma_{LT} = 100 \, \text{(given standard deviation)}\)
- \(Z\) is the Z-score corresponding to the desired service level.

Given the Alfa factor (\(\alpha\)) of 0.1, we previously calculated the safety stock as:

\[
\text{Safety Stock} = \alpha \times D \times L = 0.1 \times 1600 = 160 \, \text{products}
\]

### Step 3: Calculate the Reorder Point (ROP)

\[
\text{ROP} = 1600 + 160 = 1760 \, \text{products}
\]

### Conclusion:
If the company uses a Reorder Point (ROP) system, they will need **1,760 units** to meet demand during the lead time, including safety stock.

Would you like to go over any details or calculations in this process?

### Relative Questions
1. What factors could affect the accuracy of the Reorder Point calculation?
2. How does increasing the Alfa factor impact the safety stock and ROP?
3. What service level does a Z-score of 1.28 represent in inventory management?
4. How would reducing the lead time to 1 hour change the ROP?
5. What happens if demand variability increases significantly?
6. How can a company determine the optimal Alfa factor?
7. What is the difference between a Kanban system and an ROP system in practice?
8. How does the size of the container affect the number of units in an ROP system?

### Tip:
Regularly reviewing and adjusting your safety stock based on actual demand patterns can help maintain optimal inventory levels and avoid stockouts.

Learn how to calculate the number of units required in a Reorder Point (ROP) system based on demand rate, lead time, and safety stock. Includes step-by-step calculation and considerations for inventory management.

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