### Mathematical Model
For the graph tree, presented in Figure 2, the sets of vertices and the set of edges can be expressed as follows [41]:  
\[P=\frac{1}{\eta_{i}}[(P_{T}+P_{M1}+0,5\cdot P_{IM})N_{TUI1}+(0,5\cdot P_{IM}+ P_{M2}+P_{F})\cdot N_{TUI2}+\ldots] \tag{2}\]0  
\[P=\frac{1}{\eta_{i}}[(P_{T}+P_{M1}+0,5\cdot P_{IM})N_{TUI1}+(0,5\cdot P_{IM}+ P_{M2}+P_{F})\cdot N_{TUI2}+\ldots] \tag{2}\]1  
\[P=\frac{1}{\eta_{i}}[(P_{T}+P_{M1}+0,5\cdot P_{IM})N_{TUI1}+(0,5\cdot P_{IM}+ P_{M2}+P_{F})\cdot N_{TUI2}+\ldots] \tag{2}\]2 The graph tree for transport modes possible ways: \(v_{1}\)—departure point; \(v_{2},v_{3},v_{5},v_{6}\) —waypoints; \(v_{4}\) —destination point. The incident matrix of all vertices, consisting of connecting direct graph connections provided by the graph tree G, can be presented as follows [42]:  
\[P=\frac{1}{\eta_{i}}[(P_{T}+P_{M1}+0,5\cdot P_{IM})N_{TUI1}+(0,5\cdot P_{IM}+ P_{M2}+P_{F})\cdot N_{TUI2}+\ldots] \tag{2}\]3  
where  
\[a_{ij}=\left\{ \begin{array}{l}1\text{ if }v_{i}\text{ is the initial vertex of }e_{j}\\ -1\text{ if }v_{i}\text{ is the terminal vertex of }e_{j}\\ 0\text{ otherwise.}\end{array} \right.\]  
In this case, study (Figure 2) for possible transport corridors network adjacency matrix can be explained as follows [41]:  
\[A=\left\{ \begin{array}{l}v_{1},v_{2},v_{3},v_{4},\dots\\ v_{2}\\ v_{3}\\ v_{4}\\ \dots\end{array} \right\} \tag{13}\]  
For the graph tree covering the transport corridors network, which is explained in Figure 2, the mentioned matrix in formula (12) can be calculated as follows:  
\[A=\left[ \begin{array}{l}0111\dots\\ 1010\\ 1101\\ 1010\\ \dots\end{array} \right] \tag{14}\]  
Matrix (14) could be used for the calculation of time, costs and energy demand. Finally, the optimum distances, optimal price or minimum energy demand in transport routes in the network could be calculated using the following optimization formula [41; 42; 43]:  
\[f:E\Rightarrow R^{+}, \tag{15}\]  
It is also necessary to find a graph tree \(T=(VE^{\prime})\) price, optimal distance or minimum energy demand \(F(T)\):,  
\[F(T)=\sum_{xy\in E^{\prime}}f(xy), \tag{16}\]  
where: \(f(xy)\)--minimum price, optimal distance or minimum energy demand. Here, the edges \(e=xy\in E\) as minimum price, optimal distance or minimum energy demand could be calculated as follows [41]:  
\[f(e)=\underset{xy\in E}{\min}f(xy), \tag{17}\]  
Based on the proposed graph theory, it is possible to design optimal transport corridors based on transportation time, cost and energy saving (minimum demand) [44; 45]. For the analysis and evaluation of the experimental or collected data distribution, it is proposed to use a dispersion (\(\sigma\)) [18; 20] method to find the possible factors range (band). \[\sigma^{2}=\frac{1}{n-1}\sum_{1}^{n-1}\left(x_{i}-x_{m}\right)^{2} \tag{18}\]Here: \(n\)**--measured quantity (statistics data); \(x_{i}\) measures results; \(x_{m}\)**--mathematics' factor, which can be calculated as follows:  
\[x_{m}=\frac{1}{n}{\sum\limits_{1}^{n}}x_{i}, \tag{19}\]  
Then, the relative transport mode comparative index band (\(\Delta K_{i}\)) can be calculated using the following formula:  
\[\Delta K_{i}=\pm\sqrt{\sigma^{2}}, \tag{20}\]  
The main scientific contribution of the developed methodology is based on using graph theory, multi-criteria and comparative methods. The received tool is more accurate in comparison with existing methods [3; 25; 44; 45; 46] for evaluation of optimal transportation possibilities, including energy demand between regions, ports and consignee locations, for the evaluation. Case Study on the Different Transport Modes between Ports and Consignee Location Evaluation (Lithuania Case)  
Analysis of cargo transportation and use of methodology, presented in Section 3, were performed as practical tasks--optimization of cargo transportation processes between port and consignee locations. For this case study, transportation of containers from (to) Klaipeda port to (from) Kaunas free economic zone was undertaken.