# Indexing Model Based on Vector Normalization Available for Value Engineering in Building Materials
## Case Study
### Calculating Cost Score  
In VE, the cost evaluation consists of initial cost and running cost and analyzes LCC. The initial cost, the construction cost, is the direct construction cost. Direct construction cost consists of material cost, labor cost and expenses. The LCC analysis results are used as cost scores. In VE, the initial cost is the construction cost, and the construction stage is set as the present point in the LCC analysis. Therefore, the construction cost itself becomes the present value. The running cost is the future cost of maintenance in the process of using the building after completing construction. It is divided into the cost that is repeated every year (recurring cost) and costs which are not required to be repeated every year but at a certain time (non-recurring cost). The running cost is equivalent to the construction cost at the same point in time when using the present value method. At this time, in order to convert future costs to present value, it is necessary to consider the change in value of money with time. The real discount rate is the rate of change in the cost value over time. The real discount rate is calculated using the nominal discount rate and the inflation rate as shown in Equation (7) below. Recurring cost is converted into present value using Equation (8), and non-recurring cost is converted into present value using Equation (9). \[i_{r}=\left\{(1+i_{n})/(1+f)\right\}-1 \tag{7}\]  
\[RPV=\left\{(1+i_{r})^{m}-1\right\}/\left\{i\times(1+i_{r})^{m}\right\}\times RC \tag{8}\]  
\[NPV=\left\{i\times(1+i_{r})^{n}\right\}\times NC \tag{9}\]  
where \(RPV\) is the present value of the recurring cost, \(NPV\) is the present value of the non-recurring cost, \(RC\) is the recurring cost, \(NC\) is the non-recurring cost, \(m\) is the period of occurrence of recurring cost, \(n\) is the time of occurrence of non-recurring cost, \(i_{r}\) is the real discount rate, \(i_{n}\) is the nominal discount rate, and \(f\) is the inflation rate. As shown in Table 4, the initial cost and the running cost of the original design and the alternative design were compared and analyzed. The initial construction cost of vibration reduction and laminate flooring of the original design was W36,666,000. The initial cost of conductive tile and art deco tile, which are the components of the alternative design, were W5,990,906 and W13,599,762, respectively. According to the client's request, 50 years are applied for the life cycle of the building and the real discount rate is 3%. The LCC was then analyzed. The LCC of the original design was W70,615,530 and the LCC of the alternative design was W54,658,790. Therefore, it is analyzed that when changing to the alternative design, 29% was saved. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Names of Items**} & \multirow{2}{*}{**Weight**} & \multicolumn{2}{c}{**Original Design**} & \multicolumn{2}{c}{**Alternative Design**} \\ \cline{3-6}  & & **Grade** & **Score** & **Grade** & **Score** \\ \hline Convenience of outside circulation & 41.5\% & 5 & 2.074 & 5 & 2.074 \\ Durability (Endurance limit) & 21.9\% & 5 & 1.096 & 7 & 1.534 \\ Ease of maintenance & 21.2\% & 5 & 1.059 & 6 & 1.270 \\ Hazard Prevention (Fire and disaster) & 10.3\% & 5 & 0.517 & 7 & 0.724 \\ Usage of environmental-friendly materials & 5.1\% & 5 & 0.255 & 7 & 0.357 \\ Total & 100 & - & 5.000 & - & 5.959 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Function score calculation data.