## 3 Case Study
### Selection of Representative Products  
By using the clustering technology, the products were classified pursuant to their production mode into 96 groups. A two-dimensional ABC analysis was used [18] on criteria of product size and frequency of production. With the help of the employees, the products were divided into three main families and designated:  
* Product (Table 1),
* Supplier product (Table 2),
* Module (Table 3).  
The products were classified into 18 groups based on the quantity of produced products. Table 1 shows the data on the quantities produced in the period from 2012 to 2015.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **2012** & **2013** & **2014** & **2015** & **Sum** \\ \hline Product 1 & 1 & 5 & 3 & 6 & 15 \\ \hline Product 2 & & & & 0 \\ \hline Product 3 & 1 & & & 1 \\ \hline Product 4 & & 3 & & 3 \\ \hline Product 5 & 1 & 3 & 4 & 2 & 10 \\ \hline Product 6 & 3 & 6 & & 1 & 10 \\ \hline Product 7 & 4 & 1 & 1 & 3 & 9 \\ \hline Product 8 & 1 & & 1 & 2 \\ \hline Product 9 & 1 & 1 & 1 & 3 \\ \hline Product 10 & 3 & 2 & 5 & 1 & 11 \\ \hline Product 11 & & 1 & & 1 \\ \hline Product 12 & & & & 0 \\ \hline Product 13 & 2 & & & 2 \\ \hline Product 14 & & & & 0 \\ \hline Product 15 & & 1 & 1 \\ \hline Product 16 & & 1 & & 1 \\ \hline Product 17 & & & & 0 \\ \hline Product 18 & & & & 0 \\ \hline Sum & 17 & 23 & 16 & 13 & 69 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Quantities of the products produced in the period 2012–2015.  
For a further analysis, five families were selected from the entire family of products (18 products) The selection was based on experience and the quantities of products these families cover: Product 1, Product 5, Product 6, Product 7 and Product 10.  
Suppliers supply a large quantity of various products (supplier products--77 families) for the analysed final product, yet many of them appear rarely. Table 2 shows the 10 most frequent products from suppliers, which are used for the analysis.  
Additionally, a module was selected that is integrated into all products (products from suppliers excluded). The modules differ only in size but are treated separately, because a buyer does sometimes not need it or orders it separately. As they are all practically only scaled versions of Module 1, weights were introduced on the basis of size/mass. A representative product of the module family was determined, which is shown in Table 3.  
As a representative product, only one module is selected, the weight of which comes closest to the average weight of the module. In this case, Module 7 with weight 20 came closest to the average  
\begin{table}
\begin{tabular}{c c c c} \hline
**Name** & **Quantity** & **Per Month** & **Per Year** \\ \hline Suppl. product 1 & 236 & 4.917 & 59.00 \\ \hline Suppl. product 2 & 86 & 1.792 & 21.50 \\ \hline Suppl. product 3 & 87 & 1.813 & 21.75 \\ \hline Suppl. product 4 & 85 & 1.771 & 21.25 \\ \hline Suppl. product 5 & 83 & 1.729 & 20.75 \\ \hline Suppl. product 6 & 37 & 0.771 & 9.25 \\ \hline Suppl. product 7 & 32 & 0.667 & 8.00 \\ \hline Suppl. product 8 & 31 & 0.646 & 7.75 \\ \hline Suppl. product 9 & 266 & 5.542 & 66.50 \\ \hline Suppl. product 10 & 30 & 0.625 & 7.50 \\ \hline \end{tabular}
\end{table}
Table 2: Most frequent products from suppliers in the period 2012–2015.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Module Type** & **Quantity** & **Weight** & **Factor \(\times\) Weight** \\ \hline Module 1 & 4 & 2 & 8 \\ \hline Module 2 & 2 & 4 & 8 \\ \hline Module 3 & 9 & 6 & 54 \\ \hline Module 4 & 5 & 8 & 40 \\ \hline Module 5 & 3 & 12 & 36 \\ \hline Module 6 & 3 & 16 & 48 \\ \hline Module 7 & 5 & 20 & 100 \\ \hline Module 8 & 11 & 24 & 264 \\ \hline Module 9 & 9 & 32 & 288 \\ \hline Moduleweight of the module which amounts to 18.3. A weight function method was used to determine all representative products of the selected families.