## 5 Results  
In this paper, the proposed method was applied to solve the real problem of dry bulk cargo transport on the Chao Phraya River and the anchorage area in the Gulf of Thailand, Thailand. This method was divided into two components: (1) Data pre-processing coded with JavaScript in NetBeans IDE 8.1 was applied to generate routes using the backtracking algorithm. (2) The proposed set covering model was solved using the branch-and-cut algorithm in OpenSolver 2.9.0 with the default settings. The experiments were run on a PC with an Intel(r) Core(tm) i7-6800K CPU 3.40 GHz and 16 GB RAM. The instances and parameters collected from February to May 2020 can be downloaded from [[https://sites.google.com/site/transportationlibrary](https://sites.google.com/site/transportationlibrary)]([https://sites.google.com/site/transportationlibrary](https://sites.google.com/site/transportationlibrary)) (accessed on 20 May 2021). There is a total of 10 nodes in this problem, consisting of nine nodes on the river port and 1 node for the load discharge area, as shown in Figure 5. The location of each node is shown in Table 2.  
In the case studies, each job transported 4000 tons, a volume equal to the capacity of a barge, and each river port had two berths that could operate in parallel. Three real-life instances were tested, as displayed in Table 3.  
Currently, decisions are made concerning ship routing and scheduling for IWT using a heuristic method based on the experience of the planning department staff. The old method where the author obtained information from the case study was able to find only one solution for three testing instances, as shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Testing Instances** & \({}^{1}f_{1}\) & \({}^{2}f_{2}\) \\ \hline
1 & 64,427.55 & 55 \\
2 & 74,107.45 & 55 \\
3 & 83,244.64 & 68 \\ \hline \hline \end{tabular} \({}^{\dagger}f_{1}\) = The total CO\({}_{2}\)e emissions (kgCO\({}_{2}\)e), \({}^{2}f_{2}\) = The total travel time (days).  
\end{table} 
Table 2: Location of each node. Figure 5: Locations of the river port and the anchorage area under study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Location** & **Latitude, Longitude** & **Ready Time** & **Latest Allowed Arrival Time** \\ \hline
1 & (13.4735585, 100.9834660000002) & 1 & 17 \\ \hline
2 & (13.6305239, 100.54398190000006) & 2 & 17 \\ \hline
3 & (13.5234748, 100.26317930000005) & 3 & 18 \\ \hline
4 & (14.0266045, 100.5432292000004) & 4 & 20 \\ \hline
5 & (14.2508489, 100.58231790000002) & 2 & 19 \\ \hline
6 & (14.3180176, 100.5680956999996) & 1 & 17 \\ \hline
7 & (14.4157881, 100.5933291999997) & 2 & 18 \\ \hline
8 & (14.4111553, 100.59306560000005) & 3 & 18 \\ \hline
9 & (14.4772767, 100.6218513) & 3 & 18 \\ \hline
10 & (13.140878, 100.823247) & 0 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Location of each node. In this paper, we present the Pareto solutions obtained from the proposed method, and these are compared with the Pareto solutions obtained from the weighted sum method, as shown in Table 5. Each method was run 10 times to obtain non-dominated solutions. The weights of the weighted sum method were adjusted 10 times, with each adjustment ranging from 0 to 1 and totaling a value of 1 exactly. The Pareto frontier or tradeoff between the total CO2e emissions (\(f_{1}\)) and the total travel time (\(f_{2}\)) obtained with each method was plotted, as shown in Figure 6.  
As shown in Table 5 and Figure 6, we found that the proposed method using the \(\varepsilon\)-constraint method provided more Pareto solutions than the weighted sum method for all instances, namely four, three, and three, respectively. The Pareto frontier clearly indicates that an increase in the total CO2e emissions (\(f_{1}\)) will lead to a decrease in the total travel time (\(f_{2}\)).