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%.

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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.