Question

Problem: You want to optimize the quantity of product shipped to your 11 retail stores from your four distribution centers to minimize the cost. However, you do not know what demand will be at your retail stores. You have some idea of expected demand (mean) and the dispersion (standard deviation) and

1) Want to estimate what your maximum expected costs will be 70% of the time? 2) You want to know the probability of costs being no more than $50,000?

Answer 1

Most of the data is not provided.

However, for estimating what your maximum expected costs will be 70% of the time, the formula that can be used is:

Unit rate*Estimated demand = Mean demand + Normsinv(0.70)*standard deviation.

This will give the estimate of maximum expected costs at 70% of time.

b)

Similarly for estimating probability of costs being no more than $50,000, the following formula can be used:

Probability = Normsdist(((50000/unit rate) - Expected demand)/standard deviation)