Annual demand for a product is 16,120 units; weekly demand is 310 units with a standard deviation of 65 units. The cost of placing an order is $155, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.65 per unit.

 

a. To provide a 90 percent service probability, what must the reorder point be? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

 



b. Suppose the production manager is told to reduce the safety stock of this item by 75 units. If this is done, what will the new service probability be? (Use Excel's NORMSDIST() function to find the correct probability for your computed Z-value. Round your answer to the nearest whole number.)

 



Let’s break the problem into two parts: part (a) is about finding the reorder point, and part (b) involves calculating the new service probability after reducing the safety stock.

### **Part (a) – Reorder Point Calculation**

The reorder point (ROP) is the point at which a new order should be placed to avoid running out of stock. It is calculated using the formula:

\[
\text{ROP} = d \cdot L + Z \cdot \sigma_L
\]

Where:
- $ d $ = average weekly demand = 310 units
- $ L $ = lead time in weeks = 4 weeks
- $ Z $ = z-value corresponding to the desired service probability (90%)
- $ \sigma_L $ = standard deviation of demand during lead time = $ \sigma \cdot \sqrt{L} $

Steps:
1. **Calculate the standard deviation of demand during lead time** ($ \sigma_L $):
   \[
   \sigma_L = 65 \cdot \sqrt{4} = 65 \cdot 2 = 130
   \]

2. **Find the Z-value** for a 90% service level using Excel's `NORMSINV(0.90)`. 
   From tables or using Excel:
   \[
   Z = 1.28
   \]

3. **Calculate the reorder point (ROP)**:
   \[
   \text{ROP} = (310 \cdot 4) + (1.28 \cdot 130)
   \]
   \[
   \text{ROP} = 1240 + 166.4 = 1406.4
   \]
   Rounded to the nearest whole number:
   \[
   \text{ROP} = 1406
   \]

### **Part (b) – New Service Probability**

The safety stock is calculated as:

\[
\text{Safety Stock} = Z \cdot \sigma_L
\]
From part (a), the initial safety stock was:

\[
\text{Safety Stock} = 1.28 \cdot 130 = 166.4
\]

If the safety stock is reduced by 75 units, the new safety stock will be:

\[
\text{New Safety Stock} = 166.4 - 75 = 91.4
\]

Now, calculate the new $ Z $-value corresponding to this new safety stock:

\[
Z_{\text{new}} = \frac{91.4}{130} = 0.703
\]

Use Excel's `NORMSDIST(0.703)` to find the new service probability. This gives:

\[
\text{New Service Probability} = 0.758
\]

So, the new service probability is approximately **75.8%**, or rounded to the nearest whole number:

\[
\text{New Service Probability} = 76\%
\]

### **Summary of Results**:
- **(a)** The reorder point for a 90% service probability is **1406 units**.
- **(b)** After reducing the safety stock by 75 units, the new service probability is approximately **76%**.

---

Would you like a detailed breakdown of any part of the solution?

Here are 5 related questions you might be interested in:
1. How does changing the lead time affect the reorder point?
2. What happens to the reorder point if the demand variability increases?
3. How is safety stock calculated for different service levels?
4. What role does carrying cost play in inventory management decisions?
5. How do changes in ordering costs impact the economic order quantity (EOQ)?

**Tip**: Always adjust safety stock based on both demand variability and desired service levels to balance inventory costs effectively.

Annual demand for a product is 16,120 units; weekly demand is 310 units with a standard deviation of 65 units. The cost of placing an order is $155, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.65 per unit. To provide a 90 percent service probability, what must the reorder point be? Suppose the production manager is told to reduce the safety stock of this item by 75 units. If this is done, what will the new service probability be?

Solve for the reorder point to maintain a 90% service level with a weekly demand of 310 units and a standard deviation of 65. Learn how reducing safety stock impacts service probability using key inventory formulas.

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