An efficient preprocessing of the data is necessary to input it into the net. All information must be scaled to fit into the interval . 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 a 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:
Because all the considered articles belong to one product group, we have quite a constant sales volume of all products. An increasing sale of one article in general leads to a decrease of the 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 and the i-th net adapts the sale behaviour of article i. Therefor we have a training set with the following pairs (see figure 3):
To forecast the unkown 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: