## 6 Conclusions  
In this paper, a method to solve the GSRSP-BT while minimizing the total CO2 equivalent emissions and the total travel time is presented. This problem includes finding the ship route and berthing time for each barge to perform loading/unloading operation to avoid time clashes for multiple ports in the bulk cargo industry. The proposed method has two components: (1) A backtracking algorithm is used to create all feasible routes with time windows for each job and for each port. These restrictions serve to screen feasible routes within the various time windows in consideration of the proposed bi-objective set covering model. (2) The proposed bi-objective set covering model is solved using a branch-and-cut algorithm, and the Pareto frontier is generated using the \(\varepsilon\)-constraint method while jointly minimizing the total CO2e emissions and the total travel time objectives. In general, the mathematical model to solve this problem is quite difficult to solve it directly via exact \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Testing Instances** & **1** **HVe** & **2** **HVw** & **HVe-HVw** \\ \hline
1 & 58.51\% & 46.68\% & 11.82\% \\
2 & 58.61\% & 13.47\% & 45.14\% \\
3 & 85.92\% & 49.94\% & 35.97\% \\ \hline \hline \end{tabular} \({}^{\dagger}\)HVe = the hypervolume indicator of \(\varepsilon\)-constraint method, \({}^{2}\) HVw = the hypervolume indicator of weighted sum method.  
\end{table} 
Table 6: The hypervolume indicator of each method. Figure 6: All Pareto solutions: (**a**) the Pareto frontier of instance 1; (**b**) the Pareto frontier of instance 2; (**c**) the Pareto frontier of instance 3.  
methods. Therefore, we present a set covering model that reformulates the constraints to be easier to solve the GSRSP-BT. These constraints have been developed specifically for use with the proposed bi-objective set covering model based on route representation. We outline three testing instances from a real case study of a small company conducting transport using barges in the Gulf of Thailand and the Chao Phraya River. According to the Pareto frontier obtained from the proposed method, an increase in total CO2e emissions lead to a decrease in total travel time. The proposed method could offer various alternatives to control tower (decision-makers) using the Pareto frontier to make decisions and provide an appropriate transportation plan. Decision-makers can choose one of the Pareto solutions as routes and schedules for each barge based on the Pareto frontier to balance the two conflicting objectives at the same time [46]. The comparison of different bi-objective optimization methods shows that the proposed method can generate a variety of different Pareto solutions than the weighted sum method and the proposed method represents a larger value of the hypervolume indicator than the weighted sum method for all instances: 11.82%, 45.14%, and 35.97%, respectively. Moreover, all non-dominated solutions from the Pareto fronts produce better results than the old method for both the total CO2e emissions and the total travel time due to the old method using the heuristic method, which primarily relies on employee routing and scheduling capabilities, which cannot guarantee the quality of solutions. It is clear that the proposed method can be used in real case studies in the Chao Phraya River instead of the old method, which offers only one solution. The Pareto fronts obtained from the proposed method also allow for long-term decisions based on the behavior of these boundaries when conducting a sensitivity analysis. In addition, the proposed bi-objective set covering model can be formulated in spreadsheets and easily integrated with solver software packages, making it easier to implement in real cases. We expect the proposed method to be a problem-solving tool for carriers or control towers looking for an easy and effective approach to solve the GSRSP-BT and causing them to account for environmental impact.