# Comparative Studies of Major Sea Routes
## 3 Theoretical Basis of the Evaluation Sea Routes
### Mathematical Model  
A review of the literature, the available information on the main sea routes and their characteristics, and the navigation of real ships on the main sea routes (the Suez and Panama Canals, the sea route around the African continent, and the Northern and Northwestern Sea routes) were used to develop mathematical models of the efficiency of sea routes. In the development of mathematical models, it was assumed that the largest possible ships navigate specific sea routes. To use the Northern and Northwestern Sea routes requires icebreaker assistance or else ships cannot navigate these sea routes at all. The types of ships and their geometric dimensions depend on cargo flows and transportation distances. Cargo flows focused on the largest possible ship types, oil and oil products, long-distance bulk transport, and containers transported between the main industrial regions (Southeast Asia, North America, and Western Europe). In this way, a mathematical Benchmark model was created that evaluates the main factors: transportation price and time, possible maximum ship parameters (mainly draft), request of transportation energy (fuel), and other possible factors, such as the probability of the restrictions, and can be expressed by the following formula:  
\[I_{T}=\frac{1}{\eta_{T}}\left(k_{P}\frac{P_{T}}{P_{0}}+k_{T}\frac{T_{T}}{T_{0} }+k_{D}\frac{D_{T}}{D_{0}}+k_{E}\frac{E_{T}}{E_{0}}+k_{A}\frac{A_{Ti}}{A_{0i}} \right), \tag{1}\]  
where \(\eta_{T}\)--correlation coefficient; \(P_{T}\)--transportation costs of the analyzed sea routes; \(T_{T}\)--transportation time of the analyzed sea routes; \(D_{T}\)--possible maximum ship draft of the analyzed sea routes; \(E_{T}\)--request of transportation energy of the analyzed sea routes; \(A_{Ti}\)--other possible factors of the analyzed sea routes, including environmental impact; \(P_{0}\), \(T_{0}\), \(D_{0}\), \(E_{0}\), \(A_{0i}\)--ideal (best) sea routes factors; \(k_{P}\), \(k_{T}\), \(k_{D}\), \(k_{E}\), \(k_{A}\)--factor weight coefficients. A general formula for sea transportation can be used to calculate the cost of freight transportation, based on different sources [29; 30]:  
\[P_{T}=P_{OTHC}+P_{BAF}+P_{CAF}+P_{ISPS}+P_{WRS}+P_{CONG}+P_{PORT}+P_{THC}+P_{ DOC}+P_{IMP/EXP}+P_{S/P}+P_{RF} \tag{2}\]where \(P_{OTHC}\)--sea freight factor; \(P_{BAF}\)--bunker adjustment factor; \(P_{CAF}\)--currency correction factor; \(P_{ISPS}\)--the International Ship and Port Facility Security factor; \(P_{WRS}\)--war risk factor; \(P_{CONG}\)--cost of transshipment in ports factor; \(P_{PORT}\)--port dues factor; \(P_{THC}\)--terminal handling fee factor; \(P_{DOC}\)--fee for preparation of documents factor; \(P_{IMP/EXP}\)--export/import tax factor; \(P_{S/P}\)--Panama/Suez Canal Fee factor; and \(P_{RF}\)--fee for connecting the referred container, etc. The cost of transportation, using Formula (2), must be adapted to the specific conditions of transportation; i.e., part of the ingredients presented in Formula (2) can be omitted or supplemented. Transit (transportation) times depend on various factors and, similarly, calculating the cost of transportation can be broken down into various time factors depending on the specific conditions of transportation, such as waiting before entering the Panama or Suez Canals, icebreaker waiting time, etc.