In our project we use the sale information of 53 articles of the same group in a supermarket. The information about the number of sold articles and the sales revenues in DM (Deutsche Mark, German currency unit) are given weekly starting September 1994. In addition there are advertising campaigns for articles often combined with temporary price reductions. Such a campaign lasts about two weeks and has a significant influence on the demand on this article. Sale, advertising and price for two different articles are shown in figures 1 and 2.
Figure 1: article 362900 (without advertising)
Figure 2: article 372138 (with advertising)
The aim is to forecast the sale of an article for the next week by neural networks. We use a feedforward multilayer perceptron network (see figure 4) with one hidden layer together with the back-propagation training method [3], [4], [5].
For prediction the past information of n recent weeks is given to the input layer. The only result in the output layer is the sale for the next week. So there is a window of n weeks in the past and one week in the future. Both the input and output together are called a training pair. One training of all training pairs is called an epoch.