To determine the number of hamburgers UAHH should order, we need to calculate the reorder quantity based on the desired service level and current inventory. We’ll use the following approach:

1. Identify the Z-score for the service level: For a 95% service level, the corresponding Z-score is approximately 1.645.

2. Calculate the safety stock: The safety stock ensures that UAHH meets the 95% service level. It can be calculated as: $\text{Safety Stock} = Z \times \sigma$ where:

   • $Z = 1.645$ (from the Z-score for 95% service level),
   • $\sigma = 50$ (standard deviation of demand).

3. Calculate the reorder point (ROP): The reorder point combines the safety stock and the average daily demand: $\text{ROP} = \text{Average Daily Demand} + \text{Safety Stock}$ where:

   • Average Daily Demand = 685 hamburgers.

4. Determine the order quantity: To determine how many hamburgers to order, we calculate: $\text{Order Quantity} = \text{ROP} - \text{Current Inventory}$

Step-by-Step Solution:

1. Calculate Safety Stock

$\text{Safety Stock} = 1.645 \times 50 = 82.25 \approx 82$

2. Calculate Reorder Point (ROP)

$\text{ROP} = 685 + 82 = 767$

3. Determine Order Quantity

$\text{Order Quantity} = 767 - 820 = -53$

Since the result is negative, UAHH currently has more inventory on hand (820) than needed for the reorder point (767). This means no additional order is needed today.

Would you like further details on any of these calculations, or do you have any other questions?

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Related Questions

1. What happens to the order quantity if the desired service level is increased to 98%?
2. How would the order quantity change if the daily demand standard deviation increased to 60?
3. What effect would an increase in daily demand to 750 hamburgers have on the reorder point?
4. How can UAHH adjust its safety stock if it wants to reduce holding costs?
5. What is the impact of varying lead times on inventory management for high-demand items?

Tip

Always consider both the average demand and variability in demand when setting reorder points to balance service level and inventory costs.