### Mathematical Model
Transportation of 80 TEU between the Klaipeda port container terminal and Kaunas FEZ free economic zone (on average, 50 containers (boxes)) uses one train or one barge, or 50 road trucks between port container terminals and Kaunas FEZ free economic zone or 50 road trucks (voyage) for the \"last mile\" destination between the intermodal terminal or inland waterway cargo loading place and the Kaunas FEZ free economic zone. This means that road transport can deliver cargo \"door-to-door\". Rail transport can deliver cargo from the port to Kaunas intermodal terminal. After that, cargo from the intermodal terminal to Kaunas FEZ Free Economic Zone can be transported by road via \"last mile\" transportation. Inland waterway transport can be used for the containers from the port of Klaipeda to the place of unloading of inland waterway cargo (Kaunas). After that (cargo loading place in inland waterways), the cargo is transported by road from the place of unloading to the Kaunas FEZ Free Economic Zone by road transport for the \"last mile\". Transport modes today mainly use diesel fuel. Meanwhile, some transport modes start use LNG fuel, which has about 15 percent higher energy capacity and is more environmentally friendly. The analysis of differences in the comparative index (\(K_{i}\)) of transport types using Equation (8), based on the theoretical and experimental research results presented in this paper, for transportation between the Klaipeda container terminal and the Kaunas FEZ and using the methodology, is presented in Section 3. Equation (8) for the selected conditions can be written as follows:  
\[K_{i}=\frac{1}{\eta_{k}}(k_{P}\cdot\frac{P_{i}}{P_{0}}+k_{T}\cdot\frac{T_{i}} {T_{0}}+k_{E}\cdot\frac{E_{i}}{E_{0}})\]  
where the weighting factor of transportation costs is taken as 0.5, the weighting factor of transportation time is 0.3, and the energy consumption factor is 0.2. The correlation coefficient is 0.98 (correlation mainly exist in transportation conditions between rail and inland waterway transport). Using diesel and LNG fuel and evaluating the transportation scheme and adjacency matrices shown in Figure 6, the results of the comparative index (\(K_{i}\)) calculation of transport modes are presented in Figure 7.  
The received transport mode energy comparative index shows that containers transportation between the selected container terminal and destination in the free economic zone is more useful for railway or inland waterway transport, including the \"last mile\" destination. Relative (\(\Delta K_{i}\)) is assessed for the selected case study by assessing the cost of transportation, time and fuel consumption, using the real parameters presented in Table 3.  
The obtained results indicate that container transportation between Klaipeda port container terminal and Kaunas FEZ Free Economic Zone is the most acceptable using water or railway transport (difference in relative (\(\Delta K_{i}\)) is up to 35-47%). At the same time, it is necessary to take into account that if containers must be delivered in the shortest possible time, road transport for the direct transportation between regions, ports terminals and cargo recipients/shippers could be used as well. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Transport Mode** & **Number of Real Data (Cases)** & **Relative (\(K_{i}\))** & **Dispersion** & \(\pm\Delta K_{i}\) \\ \hline Road & 53 & 1.0 & 0.034 & 0.18 \\ Railway & 22 & 0.65 & 0.021 & 0.14 \\ Inland waterway & 7 & 0.53 & 0.012 & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative (\(\Delta K_{i}\)) for the selected case study based on collected real data.