# Demand Prediction Using a Soft-Computing Approach: A Case Study of Automotive Industry
## 4 Application
### Qualitative and Quantitative Data Integration Using Narx  
Forecasting demand is a fundamental activity in the planning process, this support the entire supply chain, from suppliers to marketing and consumption. Companies tend to use tools applied to generation the future sales projections through the past data implementation with the aim of generating possible future values. It is usually used mathematical techniques and classical statistics and even some hybrid methods such as ARIMA among the most used.  
The proposed methodology is contemplated the artificial neural networks application that belongs to the machine learning area that derives from computer science. This can be understood as the mathematical aspect inspired by the human being learning processes. These tools are have countless applications, from the pattern analysis processes or classification to the projection's generation. This is widely applied in the planning process and they go on to generate relevant results for the people who manage the companies.  
Study envisages integrating two variables in the process forecasting the demand. First variable corresponds to the historical data, the sales records, billing, production, etc., and the second are the staff working opinions with fuzzy logic. This study that includes two input variables is chosen the implementation of NARX that was derived from the structure ARX with the modification activation function types non-linear, as show in the Figure 5[67].  
This tool can generate projections to one or more future periods. This network is also characterized by integrating two activation functions, linear and non-linear, as show in the Figure 6.  
Figure 5: Integration of historical data and experts judgements in ARX, external variable.  
Figure 6: Integration of historical data and experts judgements in NARX, closed-loop network.  
This application can be made to a future period, in which historical data are implemented. Multiple periods are also projected when the neural network is closed-loop in which they are trained with output values, as show in the Figures 6 and 7.  
The final methodology stage includes the integration of the data obtained from the fuzzy analysis Table 2 and the historical sales records that includes 168 periods, from 2005 to 2018 corresponding to the data from [68]. The data are processed using \(X/Xmax\).  
The study included experimentation through a nonlinear autoregressive network with exogenous inputs (NARX) and Nonlinear autoregressive (NAR) neural network and hold statistical model from which the following results are obtained.  
The information implementation from different sources allows generating a robust, flexible and adaptable tool to changes, as show in the Tables 3 and 4. This research shows that NARX allows that fuzzy analysis is integrated and make appropriate adjustments in the weightings and training, this allows to generate an efficient forecast with low error level.  
Therefore, the methodology is capable of generating a tool that contributes to the work plan in organizations and individual suppliers. It is important to say that the tools focused mainly on a single variable, also the new technologies allow the application of hybrid tools in a wide variety of industries.