## 5 Results and Discussions
### Impact of Lowering Voyage Speed with the Current Number of Vessels  
Table 6 provides the results of lowering voyage speed with the current number of vessels (two large and two small vessels) on the system performance. The column \"Product  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Small Vessel** & **Large Vessel** \\ \hline Number & 2 & 2 \\ \hline Capacity in the specification (TEU) & 650 & 950 \\ \hline Current utilized max capacity (t) & 7444 & 10,880 \\ \hline Average fuel cost per round trip (USD) & a & b \\ \hline \multicolumn{2}{c}{Port dues (USD)} & c & d \\ \hline \hline \end{tabular}
\end{table}
Table 4: Vessel information.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Operations**} & \multicolumn{2}{c}{**Time (h)**} \\ \cline{3-4}  & & **Small Vessel** & **Large Vessel** \\ \hline \multirow{4}{*}{A} & Tugging for arrival & 3 & 3 \\ \cline{2-4}  & Loading & 12 & 16 \\ \cline{2-4}  & Tugging for departure & 3 & 3 \\ \hline \multirow{2}{*}{Sea} & Voyage A\(<\)\(>\)B & 18 (=9 \(\times\) 2) & 18 (=9 \(\times\) 2) \\ \cline{2-4}  & Voyage A\(<\)\(>\)C & 22 (=11 \(\times\) 2) & 22 (=11 \(\times\) 2) \\ \hline \multirow{4}{*}{B, C} & Waiting at B, C & 2 + Gamma(3.86, 1.43) & 2 + Gamma(3.86, 1.43) & 2 + Gamma(3.86, 1.43) \\  & (shape: 3.86, scale: 1.43) & (shape: 3.86, scale: 1.43) \\ \cline{1-1} \cline{2-4}  & Unloading at B, C & 14 & 16 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time duration for operations.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **\# Data Points** & **Mean** & **Std dev.** & **Distribution Expression** & **Square Error** & \(p\)**-Value** \\ \hline \multirow{4}{*}{High-speed Wind} & Interarrival time (day) & 62 & 30.1 & 52.2 & \begin{tabular}{c} 0.999 + Weibull (12, 0.38) \\ (Scale: 12, Shape: 0.38) \\ \end{tabular} & 0.0018 & \(<\)0.005 \\ \cline{2-4}  & Duration (hour) & 63 & 2.76 & 2.5 & \begin{tabular}{c} 0.5 + 15*Beta (0.544, 3.07) \\ (alpha: 0.544, beta: 3.07) \\ \end{tabular} & 0.0071 & 0.238 \\ \hline \multirow{4}{*}{Low Visibility} & Interarrival time (day) & 43 & 34.9 & 59.8 & \
\begin{tabular}{c} 0.999 + Weibull (5.76, 0.259) \\ (Scale: 5.76, Shape: 0.259) \\ \end{tabular} & 0.0016 & \(<\)0.005 \\ \cline{1-1} \cline{2-4}  & Duration (hour) & 44 & 5.5 & 2.93 &
\begin{tabular}{c} 0.5 + 12*Beta (1.4, 1.9) \\ (alpha: 1.4, beta: 1.9) \\ \end{tabular} & 0.0293 & 0.213 \\ \hline \hline \end{tabular}
\end{table}
Table 5: High-speed wind and low visibility data and fitted distribution.  
volume\" gives the produced amounts and transported amounts of products in metric kilo-tonnes (KT). The column \"Costs\" provides total cost and cost breakdown, including rental cost, port dues, and voyage cost. In case C1, the forward and backward speed factors are decision factors determined by the optimization model. Table 6 also includes the results of some examined cases for the voyage speed factors to identify a meaningful pattern.  
Within the considered range of the speeds, all cases could transport more than the target volume (3248 KT), which is 99% of the produced product. As the forward and backward speeds decrease, the total costs decrease proportionally due to lower fuel consumption. The lowest speed with the FS factor of 0.7 and BS factor of 0.7 is the most economical, saving 11% (1,125,620 USD per year) compared with the total cost of case C0. However, there is no meaningful difference between lowering forward and backward speeds: the cost reduction from reducing 0.1 of the FS factor is similar to that obtained by lowering the BS factor by the same amount.