Consider the following problem:

Suppose at a retail store the annual demand for a toy is a random variable with a normal distribution of N(600, 100), i.e., with mean of 600 and standard deviation of 100.   Simulate the distribution of sales if 700 units of such a toy is ordered.  What is the expected sales? Also, what is the chance it will have more than 50 units of unsold inventory at the end of the year?

You might think: The expected sales should be 600. That’s because the demand is 600 on the average, right?

Well, think again.

This video below will show you an important managerial lesson: Demand does not equal to sales in many situations.

The reason is that you may not always have enough on hand to sell to the customers. So the expected sales is almost always less than expected demand.

See the following demand for illustrations:

You can download the file here.