To determine the optimal reorder point, we use the formula for reorder point that incorporates both lead time demand and safety stock:

Formula:

$R = D_L + Z \cdot \sigma_{DL}$

Where:

• $R$ = Reorder point
• $D_L$ = Average demand during lead time
• $Z$ = Service level factor (given as 1.04 here)
• $\sigma_{DL}$ = Standard deviation of demand during lead time (capturing demand variability and lead time variability)

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Step 1: Calculate $D_L$:

$D_L = \text{Average demand per week} \times \text{Lead time in weeks}$ Average weekly demand: $\text{Weekly demand} = \frac{\text{Annual demand}}{52} = \frac{1000}{52} \approx 19.23 \, \text{units/week}$ So, $D_L$ becomes: $D_L = 19.23 \times 5 = 96.15$

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Step 2: Calculate $\sigma_{DL}$:

The standard deviation of lead time demand is calculated as: $\sigma_{DL} = \sqrt{ (\text{Lead time} \cdot \sigma_d^2) + ( \bar{D}^2 \cdot \sigma_{\text{Lead Time}}^2 ) }$ Where:

• $\sigma_d$ = Standard deviation of weekly demand = 200
• $\bar{D}$ = Average weekly demand = 19.23
• $\sigma_{\text{Lead Time}}$ = Standard deviation of lead time = 1

Now compute step-by-step:

1. Variability due to demand: $\text{Demand term} = \text{Lead time} \cdot \sigma_d^2 = 5 \cdot (200)^2 = 5 \cdot 40,000 = 200,000$
2. Variability due to lead time: $\text{Lead time term} = \bar{D}^2 \cdot \sigma_{\text{Lead Time}}^2 = (19.23)^2 \cdot 1 = 369.12$
3. Total variability: $\sigma_{DL}^2 = 200,000 + 369.12 \implies \sigma_{DL} = \sqrt{200,369.12} \approx 447.63$

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Step 3: Calculate reorder point $R$:

$R = D_L + Z \cdot \sigma_{DL}$ Substitute: $R = 96.15 + 1.04 \cdot 447.63$ $R = 96.15 + 465.53 = 561.68 \, \text{units}$

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Your answer of 1139.27 or 1157.27 must have been a miscalculation since the above steps validate a reorder point of approximately 561.68 units.

Would you like a detailed comparison of approaches or a deeper explanation?

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Related Questions:

1. How do changes in the service level (Z-score) affect reorder points?
2. Why is safety stock important in inventory management?
3. How would reducing the standard deviation of lead time affect reorder points?
4. How can the reorder point model incorporate real-time inventory data?
5. What alternative methods exist for determining safety stock in uncertain demand conditions?

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Tip:

Always double-check units when working with lead time and demand. Mismatched units (weekly vs annual) often lead to incorrect results.