Final answer:
The store's reorder point (ROP) is 13,700 bags after considering the demand during the lead time and safety stock to cover 99% demand. With 25,000 bags in stock, they currently have more than enough to satisfy the ROP, and therefore do not need to order more chocolates at this time.
Step-by-step explanation:
The Colorado candy store needs to calculate how many bags of rocky chocolates should be ordered to meet the 99% demand by the time the next shipment arrives. To find this, we need to determine the reorder point (ROP), considering the lead time and the demand variability. The demand during the lead time (DLT) is the average demand per day multiplied by the lead time in days:
DLT = Average demand/day × Lead time days
DLT = 2,000 bags/day × 5 days
DLT = 10,000 bags
To cover 99% of the demand during the lead time, we apply the z-score for the 99% confidence interval, which is approximately 2.33 (from the standard normal distribution table), to the standard deviation and the square root of the lead time in days:
Safety stock = z × standard deviation × √(lead time days)
Safety stock = 2.33 × 800 bags × √(5 days)
Safety stock = 2.33 × 800 bags × 2.236
Safety stock ≈ 3,700 bags (rounded)
Therefore, the reorder point (ROP) is:
ROP = Demand during lead time + Safety stock
ROP = 10,000 bags + 3,700 bags
ROP = 13,700 bags
Since the store currently has 25,000 bags in stock, we subtract the ROP from the current inventory to determine how many bags need to be ordered:
Bags to be ordered = ROP - Current stock
Bags to be ordered = 13,700 bags - 25,000 bags
As the store already has more than enough stock to cover the ROP, no additional chocolates need to be ordered at this time.