# Theoretical Framework (Module) for Short-Sea Shipping System Evaluation
## 3 Theoretical Basis of the Evaluation of Short-Sea Shipping Processes
### Mathematical SSS System Model
Therefore, the comparative index (\(K_{L}\)) of SSS system services performed between ports or terminals could be expressed by assessing different factors (Equation (10)):  
Figure 2:0  
where \(\eta_{L}\) is the correlation coefficient for the SSS system services (in a case where similar factors are considered--for example, while analyzing a few ports or terminals--this coefficient could be between 0.97 and 0.99, taking into account that more factors can improve identification of correlation coefficients using matrix systems); \(P_{Li}\), \(T_{Li}\), \(D_{Li}\), \(E_{Li}\), and \(A_{Li}\) are the costs, time, distribution, and energy demand for the SSS services performed within the SSS system; \(P_{0}\), \(T_{0}\), \(D_{0}\), \(E_{0}\), and \(A_{0}\) are the costs, time, distribution, and energy demand for ports or terminals, which can be determined by an expert or by applying other methods; \(k_{P}\) is the weight coefficient of the SSS system services costs (this could be between 0.30 and 0.35 depending on the cargo type); \(k_{T}\) is the weight coefficient of the SSS system services time (this depends on the type of cargo and could be between 0.20 and 0.25); \(k_{D}\) is the weight coefficient for distribution services, which depends on the goods distribution requirements and could be between 0.15 and 0.20; \(k_{C}\) is the weight coefficient of the SSS system services' energy (fuel) demand, which depends on the number of logistics operations and could be between 0.20 and 0.25; and \(k_{Ai}\), \(A_{Li}\), and \(A_{0i}\) are other possible factors and weight coefficients, for example, emissions, cargo weights, and other factors important for the SSS system services cases; the sum of the weight coefficients must be equal to one. The methodologies presented in the sources [29; 30; 31; 32] can be used to calculate emissions. When using alternative transport corridors, mostly using road transport, in Formulas (2) and (5)-(10), instead of the maritime transport part, it is necessary to enter the corresponding elements of the specific transport mode. The calculation of the comparative index (Equation (10)) is based on multi-criteria methods. It can be applied to various tasks, for example, related to freight transportation using the SSS system or other modes of transport, including the environmental impact assessment, if several ports or terminals are involved in freight transportation processes, and the assessment of any transport chain. When applying the above equation, it is necessary to select appropriate weighting factors, which can be calculated using a matrix if a suitable database is available or by using expert methods if there is limited access to real data. For the clarity of the developed model, a flow diagram has been prepared, in which the SSS comparative index and its calculation are based on the assessment of factors (flows), and the stages of the developed method are indicated (Figure 3). For the calculation of the SSS comparative index and the final decision, the most important factors are first evaluated, i.e., transportation costs using the SSS system or other transportation methods, transportation time, distribution possibilities and costs, environmental impact, and possible other factors such as restrictions on crossing state borders, additional possible payments, and the like, using the SSS system or using other transportation methods. At the same time, the correlation coefficient must be evaluated if there are similarities between the factors and the factor weight coefficients. In all cases, regardless of the number of factors, the sum of the factor weight coefficients must be equal to one. If the obtained SSS comparative index is satisfactory, the SSS freight transportation system is recommended. If the obtained SSS comparative index is unsatisfactory, it is necessary to separately evaluate the factors, the possibility of their optimization, and if, after this evaluation, the SSS comparative index is satisfactory, the SSS freight transportation system can be used.