# Theoretical Framework (Module) for Short-Sea Shipping System Evaluation
## 3 Theoretical Basis of the Evaluation of Short-Sea Shipping Processes
### Mathematical SSS System Model
); \(k_{TD}\) is the cost function coefficient, which depends on the operations which should be carried out during transportation by railways (in case of additional leasing before entering into railway ferries, etc. ); and \(+\cdots\) refers to other possible cost elements such as special requirements for the placement and securing of dangerous goods in vehicles, etc. For the entire load or a unit of it, for example, a unit of a freight vehicle, the energy demand function, which includes the average power used by the main engines of the transport modes, the relative fuel consumption, the types of fuel used, for example, diesel fuel, LNG, and others, (\(E_{L}\)) can be expressed as follows (Equation (8)):  
\[E_{L}=\frac{1}{\eta_{E}}\bigg{(}q_{fS}^{\prime}N_{WS}\frac{S_{S}}{v_{S}}N_{T} +q_{fR}^{\prime}N_{WR}\frac{S_{R}}{v_{R}}N_{T}+q_{fT}^{\prime}N_{WT}\frac{S_{ T}}{v_{T}}N_{T}+\cdots\bigg{)}, \tag{8}\]  
where \(\eta_{E}\) is the correlation coefficient in case of similarities between transport modes' fuel consumption (this could be between 0.97 and 1.0 (in the case where one transport mode is used, this coefficient will be one)); \(q_{fS}^{\prime}\) is the relative fuel consumption of the ship's engine, which is between 0.15 and 0.20 kg/kWh; \(N_{WS}\) is the ship engine's average power during sailing between SSS ports; \(q_{fR}^{\prime}\) is the relative fuel consumption of the road transport engine, which is between 0.12 and 0.18 kg/kWh; \(N_{WR}\) is the road transport unit's average power during a voyage between SSS ports or other locations; \(q_{fT}^{\prime}\) is the relative fuel consumption of the road transport engine, which is between 0.15 and 0.18 kg/kWh; \(N_{WT}\) is the railway transport unit's average power during a voyage between SSS ports or other locations; and \(+\cdots\) is other possible elements, like energy demand during transportation and atypical transportation, for example, special services transportation of dangerous goods, etc. For the transportation of cargo or its unit quantities using the SSS system and other modes of transport, the emissions generated by a specific mode of transport (carbon dioxide,carbon monoxide, sulfur oxides, nitrogen oxides, and particulate matter) depend on the amount of fuel consumed, the average power of the vehicle engines, and their operating time; (\(A_{L}\)) can be expressed as follows (Equation (9)) [12; 13; 19]:  
\[A_{L}=\frac{1}{\eta_{A}}\Big{(}\Delta\text{CO}_{2}q_{f}+\Delta\text{SO}_{x}q_{f }+\Delta\text{CON}_{W}t+\Delta\text{NO}_{x}N_{W}t+\Delta\text{PMN}_{W}t\Big{)}, \tag{9}\]  
where \(\eta_{A}\) is the correlation coefficient in case of similarities between emissions generated (including fuel consumption, as well as the average engine power of the transport mode (this could be between 0.95 and 1.0 (in the case where one type of emission is calculated, this coefficient will be one))); \(\Delta\text{CO}_{2}\) is the CO\({}_{2}\) emission generation coefficient, which depends on the type of fuel (for example, for diesel fuel, on average, this coefficient is 3.2; for LNG fuel, it is 2.7); \(q_{f}\) is the fuel quantity used during the voyage; \(\Delta\text{SO}_{x}\) is the SO\({}_{x}\) emission generation coefficient, which depends on fuel quality (for example, for diesel fuel, this is about 0.001, and for LNG fuel, it is about 0.0); \(\Delta\text{CO}\) is the CO emission generation coefficient, which depends on the engine type and quality, which can be found in the engine specification; N\({}_{W}\) is the average engine power during the voyage; \(t\) is the voyage time; \(\Delta\text{NO}_{x}\) is the NO\({}_{x}\) emission generation coefficient, which depends on the fuel type and engine quality; \(\Delta\text{PM}\) is the PM emission generation coefficient, which depends on the fuel type (for example, for LNG fuel, it is about 0) and engine quality. In order to find optimal solutions, evaluation methods that use weight coefficients could be applied.