Final answer:
To determine the safety stock that should be carried, we need to consider the demand during the lead time and the desired service level. The recommended safety stock to be carried is 232 boxes.
Step-by-step explanation:
In order to determine the safety stock that should be carried, we need to consider the demand during the lead time and the desired service level.
First, we calculate the average demand during the lead time. Using the probabilities given, we can calculate:
- Average demand = (0 x 0.2) + (100 x 0.2) + (200 x 0.2) + (300 x 0.2) + (400 x 0.2) = 200 boxes
Next, we calculate the standard deviation of demand. Using the same probabilities and the formula for standard deviation, we can calculate:
- Standard deviation = sqrt(((0-200)^2)x0.2 + ((100-200)^2)x0.2 + ((200-200)^2)x0.2 + ((300-200)^2)x0.2 + ((400-200)^2)x0.2) = 141.42 boxes
Finally, we can calculate the safety stock using the desired service level. For example, if we want a 95% service level, we can consult a standard normal distribution table and find the Z-score for a 95% service level, which is approximately 1.645. Multiplying the Z-score by the standard deviation, we get:
- Safety stock = 1.645 x 141.42 = 232.41 boxes
So, the recommended safety stock to be carried is 232 boxes. This will help prevent stockouts and ensure a high service level to customers.