Question

Daily demand for a product is normally distributed with a mean of 100 and a standard deviation of 12, The lead time is normally distributed with a mean of 5 days and a standard deviation of 1.5 days.

a) What is the ROP to satisfy a %90 probability of not stocking out?

b) What is the safety stock?

c) What is the probability of stocking out if the manager has decided to kee

Answer 1

The student's questions pertain to ROP, safety stock, and the probability of stocking out. The calculations use the mean and standard deviations of product demand and lead time, applying concepts from the normal distribution.

Step-by-step explanation:

The student is asking about calculations related to inventory management, specifically determining the reorder point (ROP), safety stock, and the probability of stocking out for a product with demand that follows a normal distribution. The corresponding values for mean daily demand, standard deviation of daily demand, mean lead time, and standard deviation of lead time have been provided.

Calculation Steps:

1. To calculate the ROP, we need to calculate the lead time demand and then add safety stock to it. This involves finding the z-score that corresponds to the desired service level (in this case, a 90% probability of not stocking out).
2. The safety stock is determined by multiplying the z-score (for the desired service level) by the standard deviation of the lead time demand.
3. If a different reorder point is chosen by the manager, the probability of stocking out can be assessed by looking at how far the new ROP deviates from the one calculated for a 90% no-stock-out probability.