# Reducing the Total Product Cost at the Product Design Stage
## 4 An Example of Business Analytics for New Product Performance
### Predictive Analytics  
Predictive analytics is concerned with identifying dependencies between variables related to the NPD project and products specification, and the specific cost (including the cost of NPD, material, production, and warranty per unit of product--\(V_{1}\), \(V_{14}\), \(V_{15}\), \(V_{18}\)). These dependencies have been identified using feedforward artificial neural networks (ANNs). The data were divided into two sets--learning (25 cases) and testing (7 cases) to evaluate the quality of an estimating model. In this study, a multilayer ANN was trained using the back-propagation algorithm and weights optimized according to the Levenberg-Marquardt algorithm (LM) and gradient descent momentum with adaptive learning rate algorithm (GDX). The neural network structure was determined in an experimental way, via the comparison of errors in the learning and testing set for the different number of layers and hidden neurons. The mean absolute percentage errors (MAPEs) were calculated as the average of 50 iterations for an ANN structure reaching 50 hidden neurons. Experiments conducted for different number of hidden layers indicate the tendency to overfit the learning data and worse performance in predicting the cost compared to the use of one hidden layer of neurons. Therefore, the architecture of ANNs consists of one hidden layer of neurons. Moreover, the experiment results show that the increase of hidden neurons results in overfitting of an ANN model, and the optimal number of hidden neurons is between 20 and 25. Figure 4 illustrates the comparison of MAPEs calculated in the testing set using the parametric estimation technique (ANNs), analogical estimation technique (AET), and arithmetic average (AVG).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & \(\mathbf{f^{P}}\) & \(\mathbf{f^{R}}\) & \(\mathbf{SF}\) \\ \hline Number of components & 0.75 & 0.82 & 93\% \\ Product size & 0.66 & 0.74 & 92\% \\ Product weight & 0.54 & 0.66 & 88\% \\ Material consumption & 0.82 & 0.75 & 93\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Similarity functions between the past and new product.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product** & **SV (\%)** & \begin{tabular}{c} **NPD Cost** \\ **(Thousands)** \\ \end{tabular} & \begin{tabular}{c} **Material** \\ **Cost** \\ \end{tabular} & \begin{tabular}{c} **Production** \\ **Cost** \\ \end{tabular} & \
\begin{tabular}{c} **Energy** \\ **Cost** \\ \end{tabular} &
\begin{tabular}{c} **Overhead** \\ **Cost** \\ \end{tabular} \\ \hline P2001730 & 91.5 & 183 & 11.83 & 43.59 & 2.25 & 17.52 \\ P2200081 & 89.8 & 210 & 9.77 & 37.90 & 2.21 & 17.52 \\ P2001175 & 89.1 & 156 & 10.63 & 47.18 & 2.32 & 17.52 \\... &... &... &... &... &... \\ \hline \hline \end{tabular}
\end{table}
Table 2: A set of the most similar products.  
The ANNs trained according to the LM algorithm obtained the least MAPEs in the testing set for estimation models regarding the cost of material (\(V_{14}\)), production (\(V_{15}\)), and warranty (\(V_{18}\)), whereas the ANNs trained according to the GDX algorithm for estimating the cost of NPD (\(V_{1}\)). An ANN with the minimal MAPE was used to the specific cost estimation by providing the values of input variables to the trained ANN. The estimated cost of NPD was estimated at 192 thousand \(\epsilon\), the cost of materials per unit of product reaches 12.5 \(\epsilon\), production cost--42.7 \(\epsilon\), and warranty--1.4 \(\epsilon\) per 1000 sold products. There was the two-year projected period of product life cycle, for which the total discounted cost of a new product reaches 1137 thousand \(\epsilon\), and the NPV--420 thousand \(\epsilon\).  
Let us assume that the total product cost does not satisfy the decision-maker who wants to reduce the cost to 1100 thousand \(\epsilon\). To solve this task, the problem is reformulated into the following question: Are there any values of input variables for which the expected total product cost is fulfilled?