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**:

Mon Jan 15 12:01:43 MET 1996