# Reducing the Total Product Cost at the Product Design Stage
## 3 A Data-Driven Approach to Reducing the Total Product Cost  
### Problem Specification  
The proposed approach allows the decision-maker to identify the prerequisites which must be fulfilled in the phase of project design and prototype tests to reduce the total cost of a new product. A number of admissible variants of the NPD project performance depends on domains of variables and constraints. Relationships between variables can be identified on the basis of previous experiences with similar NPD projects. As a result, parametric models can be used to evaluate the potential of a project (the cost and revenue of a new product), as well as to verify the existence of possible changes in the phase of project design and prototype tests towards reducing the total cost of a new product to the level accepted by the decision-maker. The presented problem can be described throughout the specification of variables, their domains, and constraints. This research proposes the problem formulation in terms of CSP that offers significant flexibility within the addition/removal of variables or constraints, and consequently, a simultaneous recalculation towards finding a new set of available solutions, if there are any. A problem specified in a CSP consists of [51]:  
\[(V,D,C) \tag{1}\]  
where:  
\(V\) is a finite set of \(n\) variables \(\{V_{1},\,V_{2},\,\ldots,\,V_{n}\}\);  
\(D\) is a finite set of discrete domains \(\{D_{1},D_{2},\,\ldots,\,D_{n}\}\) related to variables \(V\);  
\(C\) is a finite set of constraints \(\{C_{1},\,C_{2},\,\ldots,\,C_{m}\}\). Each constraint is treated as a predicate that can be seen as an \(n\)-ary relation defined by a Cartesian product \(D_{1}\times D_{2}\times\ldots\times D_{n}\). The solution to the CSP is a vector (\(D_{1i}\), \(D_{2k}\),..., \(D_{nj}\)) related to the assessment of the values of each variable that satisfy all constraints \(C\). In general, constraints may be specified using analytical and/or logical formulas [51]. The variables refer to the product life cycle and company's resources. A set of variables and constraints has been defined according to the authors' experience. Nevertheless, a literature analysis also indicates the similar specification [25; 37; 52]. To use a parametric approach to cost estimation (\(V_{1}\), \(V_{14}\), \(V_{15}\), \(V_{18}\)), a few variables (\(V_{5}\),..., \(V_{13}\)) are chosen for their relevance to the problem (including strong impact on the cost) and controllable features, i.e., a company can use them to identify a set of their values, which satisfy all constraints and reduce the total product cost. The following set of variables for estimating the product development, production, and after-sales cost has been specified:  
\(V_{1}\)--product development cost (in thousand \(\mathfrak{C}\));  
\(V_{2}\)--production cost (in thousand \(\mathfrak{C}\));  
\(V_{3}\)--after-sales cost (in thousand \(\mathfrak{C}\));  
\(V_{4}\)--unit production cost (in \(\mathfrak{C}\));  
\(V_{5}\)--number of employees involved in product design and prototype tests;  
\(V_{6}\)--duration of product design (in months);  
\(V_{7}\)--number of prototype tests;  
\(V_{8}\)--number of product components;  
\(V_{9}\)--amount of materials used to manufacture a unit of a new product;  
\(V_{10}\)--time needed to manufacture a unit of a new product;  
\(V_{11}\)--time needed to job preparation;  
\(V_{12}\)--number of workplace units in assembling and processing a new product;  
\(V_{13}\)--density of material used to manufacture a unit of a new product;  
\(V_{14}\)--material cost per unit of product;  
\(V_{15}\)--labor cost per unit of product;  
\(V_{16}\)--energy cost per unit of product;  
\(V_{17}\)--overhead cost per unit of product;  
\(V_{18}\)--warranty cost per unit of product;  
\(V_{19}\)--number of sold products (in thousands);\(V_{20}\)--number of defective products (in thousands);  
\(V_{21}\)--number of repairs in the warranty period;  
\(V_{22}\)--product price (in \(\ell\));  
\(V_{23}\)--sales revenue of a new product (in thousand \(\ell\)).