# Newsvendor Problem- Normal Distribution

- Author:
- Mike May

- Topic:
- Algebra, Normal Distribution

## Instructions and commentary

The newsvendor problem is a classical problem in operations management and applied economics used to determine optimal inventory levels. It is (typically) characterized by fixed prices and uncertain demand for a perishable product.
We assume that a newsvendor buys a quantity of newspapers with a given price paid and sales price. Based on demand, we compute profit.
For this version of the applet we assume that the demand function is a normal distribution.
In step 1 we set up the parameters of the graph.
High Profit, Low Profit, and High Quantity give the limits of the graph.
The Order Quantity, is limited to being between 0 and High Quantity.
We assume that demand is between 0 and High Quantity.
Dragging the purple Q lets you see the profit or loss for a given quantity of papers sold.
In step 2 we specify the mean and standard deviation of the demand function.
Note that the blue density function is on a different scale.
In step 3 we multiply Probability times Profit to get expected profit at each demand value.
(We lose the most money on a day when the demand is zero, but since that is less likely than an demand of 100, we expect to loos more money on days when demand is 100, than on days when demand is 0.0
In step 4 we add up the expected profit for each demand value for our order size and get the expected profit for the order size.
In step 5 we can drag the order size and get the curve of expected profit as a function of order size.