### Mathematical Model
At the same time, due to required transhipment between inland waterways (railways) transport mode and road transport, the following items need to be considered: \"last mile\" distance, additional time, costs. Energy demand and other items, such as environmental impact [46; 47; 48; 49]. Transport modes and transhipment points during transportation process between the seaport and final cargo destination are presented in Figure 6.  
Transhipment at the intermodal terminal or at the inland waterway barges loading and storage site by a mobile crane with 15 movements per hour and average engine power of about 500 kW should be considered when calculating the total transport time, costs and energy demand. The adjacency matrix of the graph at Figure 6 for the transportation time in hours in case of transportation of 80 TEU (on average, delivery of 50 boxes using one train or one barge, or 50 road trucks), taking into account the conditions mentioned above, could be made as follows:  
\[A_{T}= \begin{bmatrix}0&9&12&37&0&0\\ 9&0&3&28&0&0\\ 12&3&0&25&0&0\\ 150&28&25&0&25&28\\ 21&0&0&25&0&3\\ 18&0&0&28&3&0\end{bmatrix} \]  
Using the dispersion method (Formulas (17)-(19)), experiments on the real transportation time have shown that differences in the road transport reach up to 7-8%, mainly due to traffic conditions in city areas. Differences in railway transport reach up to 5-7% in the event of good planning, and differences in inland waterway transport can reach up to 10%, mainly due to departure issues from the port area. Figure 6: Transport modes and transhipment points adapted in the case study. The adjacency matrix of the graph at Figure 6 for the transportation costs in EUR in case of transportation of 80 TEU (on average, delivery of 50 boxes using one train or one barge, or 50 road trucks), could be made as follows:  
\[A_{P}=\left[ \begin{array}{cccccc}0&4000&6500&9000&0&0\\ 4000&0&2500&5000&0&0\\ 6500&2500&0&2500&0&0\\ 12,500&5000&2500&0&2500&5000\\ 7500&0&0&2500&0&2500\\ 5000&0&0&5000&2500&0\end{array} \right]\]  
The adjacency matrix of the graph in Figure 6 for the total engines power in kW (on average, delivery of 50 boxes using one train or one barge, or 50 road trucks), could be made as follows:  
\[A_{N}=\left[ \begin{array}{cccccc}0&2500&250&200&0&0\\ 2500&0&250&200&0&0\\ 2750&250&0&200&0&0\\ 200&350&200&0&200&450\\ 600&0&0&200&0&250\\ 400&0&0&450&250&0\end{array} \right]\]  
The adjacency matrix of the graph in Figure 6 for the fuel consumption in kg (on average, delivery of 50 boxes using one train or one barge, or 50 road trucks) for transportation of 80 TEU could be made as follows:  
\[A_{K}=\left[ \begin{array}{cccccc}0&3600&3720&4320&0&0\\ 3600&0&120&720&0&0\\ 3720&120&0&600&0&0\\ 4800&720&600&0&600&720\\ 1200&0&0&600&0&120\\ 1080&0&0&720&120&0\end{array} \right]\]  
Presented in this section, the adjacency matrix, sometimes called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices. For a simple graph with no self-loops, the adjacency matrix must have zero on the diagonal. The solution of the presented adjacency matrices for a specific transport corridor or a specific type of transport is carried out by adapting them to specific conditions and applying standard solutions of such a matrix [41; 43]. The comparative results of the solutions of the indicated matrixes in this section are presented in Figure 7.  
Experiments on the real fuel consumption in analyzed transport corridors have shown that differences in the road transport reach up to 5-12%, mainly due to traffic conditions;  
Figure 7: Transport mode energy comparative index (K) for the transportation of 80 TEU between Klaipeda container terminal and Kaunas FEZ free economic zone by different transport roads using diesel and LNG fuels. differences in railway transport reach up to 6-11% in case of good planning and differences in inland waterway transport reach up to 10%, mainly due to maneuvering of the ship.