Final answer:
The reorder point for the restaurant to maintain a 90% service level is 257.72 gallons, calculated by adding the mean demand during the lead time (240 gallons) to the safety stock (17.72 gallons), based on a standard deviation of 13.84 gallons during the lead time.
Step-by-step explanation:
To determine the reorder point for the restaurant with a 90% service level, we need to calculate the amount of oil that they will need during the lead time, taking into account the variability of their daily demand. Since the daily demand for oil is normally distributed with an average (mean) of 20 gallons and a standard deviation of 4 gallons, and the lead time is 12 days, we first calculate the mean demand during the lead time by multiplying the average daily demand by the number of lead time days:
Mean demand during lead time = Average daily demand × Lead time
Mean demand during lead time = 20 gallons/day × 12 days = 240 gallons
Next, we need to find the safety stock that corresponds to the desired service level. To maintain a 90% service level, we use the standard normal distribution to find the Z-score that corresponds to 90%. We find that the Z-score for a 90% service level is approximately 1.28.
Then, we need to calculate the standard deviation during the lead time, which is the daily standard deviation multiplied by the square root of the number of lead time days:
Standard deviation during lead time = Daily standard deviation × √(Lead time)
Standard deviation during lead time = 4 gallons/day × √(12 days) = 4 gallons/day × 3.46 = 13.84 gallons
Finally, the reorder point is the sum of the mean demand during the lead time and the safety stock, which is calculated by multiplying the Z-score by the standard deviation during lead time:
Safety stock = Z-score × Standard deviation during lead time
Safety stock = 1.28 × 13.84 gallons = 17.72 gallons
Reorder point = Mean demand during lead time + Safety stock
Reorder point = 240 gallons + 17.72 gallons = 257.72 gallons
Therefore, the reorder point to maintain a 90% service level, rounded to two decimal places, is 257.72 gallons.