An efficient preprocessing of the data is necessary to input it into the net.
Due to our implementation of the back-propagation algorithm all information must be scaled to 
.
We assume that the necessary information is given for T weeks in the past.
With the following definitions
we have decided to use the following inputs for each article i and week t:
For each article i and recent week t we use the three-dimensional vector:
For a week t in the future the vector is reduced by the unknown sale:
To predict the sale for one article within a week t, we use a window of the last n weeks. So we have the following input vector for each article i:
We have quite a constant sales volume of all products, because all the considered articles belong to one product group. An increasing sale of one article in general leads to a decrease of other sales. Due to this, we concatenate the input vectors of all p articles to get the vector given to the input layer:
The sale of article i within week t (
) is the requested nominal value
in the output layer that has to be learned by one net for this 
vector.
So we have p nets where the i-th net adapts the sale behaviour of article i.
Therefore we have a training set with the following pairs (see figure 1):
To forecast the unknown sale 
for any article i within a future week T+1 we give
the following input vector to the trained i-th net:
The output value of this net is expected to be the value 
,
which has to be re-scaled to the value for the sale of article i within week T+1:
