# Multi-Criteria Decision-Making Techniques for Optimal In-House Storage Location Selection
## 4 Results and Discussion  
This paper addresses an optimal warehouse storage location problem in a brewing company in the Czech Republic. After discussing this with the top management of a brewing company, I found that its name is not mentioned for internal policy reasons. However, it is one of the leaders in producing and distributing alcoholic drinks in the Czech market. The company's significant advantages include high production, service quality, customer satisfaction, professional staff, etc. The case study was realized based on the optimal warehouse storage location in Figure 1.  
To address the previously mentioned issue, four criteria have been chosen as crucial: C1--Warehouse-Location Occupation Costs (CZK)--Cost of one pallet in CZK per day; C2--Loading/Unloading Cost (CZK); C3--Handling Time per Unit (min), and C4--Distance to the given storage location (m). In addition, four possible inside storage locations have been considered as alternatives. The locations are marked as Location A, Location B, Location C, and Location D. When it comes to methods, two of the multi-criteria decision-making (MCDM) methods are employed to tackle the optimal storage location issue--the additive ratio assessment (ARAS) method and the combined compromised solution (CoCoSo) method. Before applying the abovementioned methods, it is necessary to formulate an input data matrix where the alternatives will be compared according to the four previously mentioned criteria. The input data matrix is presented in Table 1.  
After the initial decision-making matrix is formulated, the next step is to apply the ARAS and the CoCoSo methods. The following results of the ARAS method have been reached (Tables 2-7). Figure 1: Optimal warehouse storage location problem description. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) \\ \hline \hline
0—Optimal Value & 4.5 & 23 & 2 & 50 \\ Location A & 7.5 & 23 & 2 & 50 \\ Location B & 6 & 48 & 4 & 150 \\ Location C & 9 & 32 & 3 & 180 \\ Location D & 4.5 & 40 & 5 & 400 \\ Criteria Weights & 0.2857 & 0.2551 & 0.2142 & 0.2448 \\ min/max type & min & min & min & min \\ \(\Sigma\) & 0.8556 & 0.1640 & 1.7833 & 0.0547 \\ \hline \end{tabular}
\end{table} 
Table 1: An Input data matrix. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) \\ \hline Location A & 7.5 & 23 & 2 & 50 \\ Location B & 6 & 48 & 4 & 150 \\ Location C & 9 & 32 & 3 & 180 \\ Location D & 4.5 & 40 & 5 & 400 \\ Criteria value 1 & 4.5 & 23 & 2 & 50 \\ Criteria value 2 & 9 & 48 & 5 & 400 \\ min/max type & min & min & min & min \\ \hline \end{tabular}
\end{table} 
Table 2: Initial Decision-Making Matrix (DMM). \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) \\ \hline
0—Optimal Value & \(\mathbf{0.2597}\) & \(\mathbf{0.2650}\) & \(\mathbf{0.2804}\) & \(\mathbf{0.3655}\) \\ Location A & 0.1558 & 0.2650 & 0.2804 & 0.3655 \\ Location B & 0.1948 & 0.1270 & 0.1402 & 0.1218 \\ Location C & 0.1299 & 0.1905 & 0.1869 & 0.1015 \\ Location D & 0.2597 & 0.1524 & 0.1121 & 0.0457 \\ Criteria Weights & 0.2857 & 0.2551 & 0.2142 & 0.2448 \\ min/max type & min & min & min & min \\ \hline \end{tabular}
\end{table} 
Table 3: Normalized DMM. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) \\ \hline
0—Optimal Value & \(\mathbf{0.0742}\) & \(\mathbf{0.0676}\) & \(\mathbf{0.0601}\) & \(\mathbf{0.0895}\) & \(\mathbf{0.2913}\) \\ Location A & 0.0445 & 0.0676 & 0.0601 & 0.0895 & 0.2617 & 0.8981 & 1 \\ Location B & 0.0557 & 0.0324 & 0.0300 & 0.0298 & 0.1479 & 0.5077 & 4 \\ Location C & 0. The range of storage locations obtained by the ARAS method is presented in Figure 2. It may be noticed that the ARAS method ranked Location A as the best possible solution for storing goods, followed by Location C, Location B, and Location D, respectively.