## 3 Results
### Computational Formulations
Substituting into Formula (4) for the coefficient \(x=0.4\) we get Formula (7):  
\[y_{l}(x=0.4)=\int_{0}^{x}(A\times B^{x}+C)dx=2 \tag{7}\]  
The value of the constants \(A\), \(B\), and \(C\) was numerically calculated based on the condition in Formula (8),  
\[max\{x_{1}=\left|\int_{x=0}^{x=0.4}(A\times B^{x}+C)dx-2\right|,\ x_{2}=\int_{ x=0}^{1}(A\times B^{x}+C)dx-6|\to 0 \tag{8}\]  
Calculated function parameters:  
* \(A=2.862\), \(B=2.381\), \(C=1.4448\). Thus, after substituting parameters \(A\), \(B\), and \(C\), the function \(y_{l}\) has the form given in Formula (9):  
\[y_{l}(x)=2.8629\times 2.3811^{x}+1.4448 \tag{9}\]  
5. Function f(x) graph and proposed intervals  
Figure 2 shows the functions that are used to divide the individual levels into which the calculated coefficient values are included. The function f(x) is shown with red color. The area under the curve f(\(x\)), presented by the green curve, is calculated by integrating the function f(\(x\)). Levels are represented by the area under the red curve. The achieved level is the largest integer multiple of the area of size 1 (size of each level), and can be realized on the interval <0, >> (see Figure 3). In addition, individual level sizes are presented in the picture. Figure 3 shows this distribution of the interval between the 6 levels. Level 1 is defined as a controlled process with certified process management, however without digitization and vice versa Level 3 is that the company has controlled processes that are partially automated and connected to an external data source. This point does not mean that the company has all the technologies according to \"Industry 4.0\". It marks the beginning of digitization; 40% of the points is not Industry 4.0, it is just the beginning of digitization. First it is necessary to digitize the company, then it is possible to implement Industry 4.0. 40% is the point from which we start, is not a threshold, it is a border of digitization and it is chosen practically. Table 1 shows the calculated range for the interval <0; 1> for each of the six preparedness levels. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{2}{c}{**Interval Range**} \\  & **From** & **To** \\ \hline
0 & 0 & 0.2176 \\
1 & 0.2176 & 0.4096 \\
2 & 0.4096 & 0.5806 \\
3 & 0.5806 & 0.7342 \\
4 & 0.7342 & 0.8731 \\
5 & 0.8731 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interval range and corresponding levels. Figure 3: Interval distribution for preparedness levels. Figure 2: The value of the readiness level depends on the value of the exponent. Interval limits are designed in accordance with Formulas (5) and (6). An exponential function was chosen to divide the interval <0; 1>. This feature was used mainly to extend the range of intervals for lower levels, i.e., the lower the level, the more points you need to get. This is due to the expected investment intensity for obtaining higher levels of readiness (costs are rising sharply, but the shift is small). For this reason, the linear function was not used. Level 4 and especially level 5 represent the highest readiness and correspond to Industry 4.0. principles. In particular, Level 5 is designed with such a philosophy that it fully fulfills the vision, mission, and assumptions of Industry 4.0. That is, the company has not only partially applied technologies, which can be in level 3 or level 4, but comprehensive coverage of the entire logistics internal area.