### Mathematical Model
The transportation time function (\(T\)) for a specific quantity of cargo units can be expressed as follows:  
\[T=\frac{1}{\eta_{i}}[(T_{T}+\frac{S_{1}}{v_{M1}}+0,5\cdot T_{IT})\cdot N_{TUI 1}+(0,5\cdot T_{IT}+\frac{S_{2}}{v_{M2}}+T_{F})\cdot N_{TUI2}+\ldots] \tag{3}\]  
where: \(T_{T}\)--transport unit time in port terminal; \(S_{1}\)--distance between port terminal and final destination or intermodal terminal; \(v_{M1}\)--average transport mode speed between original cargo transportation place and final destination place or intermodal terminal; \(T_{IT}\)--transport unit full operation time in intermodal terminal; \(S_{2}\)--distance between intermodal terminal and final destination place; \(v_{M2}\)--average transport mode speed between intermodal terminal and final destination place; \(T_{F}\)--average operation time of one transport unit in final destination place; \(+\ldots\) --other possible elements, such as waiting convoy time during oversize cargo transportation, and so on. Energy consumption function (\(E\)) for a specific quantity of cargo units can be expressed as follows:  
\[E=\frac{1}{\eta_{i}}[(E_{T}+E_{M1}+0,5\cdot E_{IT})\cdot N_{TUI1}+(0,5\cdot E _{IT}+E_{M2}+E_{F})\cdot N_{TUI2}+\ldots] \tag{4}\]where: \(E_{T}\)--energy demand in original (port) terminal for the loading/unloading transport unit; \(E_{M1}\)--energy demand on the first chain part for the transport mode unit (transportation from/to the port to/from the intermodal terminal or inland waterway unloading/loading place or the final destination when using a \"door to door\" system); \(E_{IT}\)--energy demand in an intermodal terminal or in inland waterway unloading/loading place for one transport unit (for an intermodal terminal or unloading/loading place operations); \(E_{M2}\)--energy demand on the second chain part for the transport mode unit (transportation from/to intermodal terminal or inland waterway unloading/loading place to/from final destination); \(E_{F}\)--energy demand in final destination for unloading/loading operations; +... -- other possible elements, such as additional energy consumption due to additional waiting time, bypass some transportation corridor sections, and so on. Given the average vehicle engine power during the journey, the driving distance and the average driving speed, the total energy used can be calculated using the following formula:  
\[E=N_{TM}\frac{S}{v} \tag{5}\]  
where: \(N_{TM}\)--average vehicle engine power; \(S\)--driving distance; \(v\)--average driving speed. The amount of energy needed by the terminal equipment can be calculated using the average power of the equipment's motor and the working time. Transport requires engines that are powerful enough; for example, sea ships consume a lot of fuel. Ships use a lot of fuel while sailing and use a little less when they are at ports or anchorages, i.e., waiting for access to ports. The amount of fuel consumed by a means of transport is calculated during the voyage or during another period. In general, the engine fuel consumption (\(Q_{f}\)) can be calculated as follows [2,16]:  
\[Q_{f}=\int\limits_{0}^{T}k_{f}\cdot q_{f}\cdot N_{TM}\cdot dt \tag{6}\]  
where: \(k_{f}\) is the coefficient, which depends on the type of engine [2]; \(q_{f}\) is the consumption of fuel for the definite engine (kg/kWh); \(N_{TM}\) is the engine's average power during the working period (kW), which can be calculated using Equation (7):  
\[N_{TM}=\frac{\int\limits_{0}^{t}N_{TMi}\cdot dt}{t} \tag{7}\]  
where: \(N_{TMi}\)--is the instantaneous transport means (equipment) engine power (kW); \(t\)--is the transport means working time in hours. In order to find optimal solutions, evaluation methods with weight coefficients could be used.