## 4 Proposed Method
\begin{tabular}{l l} Parameters & \\ \(\alpha\) & Emission factor--fuel consumption per liter. \\ \(\beta\) & Emission factor for electricity consumption. \\ \(E\) & Electricity consumed. \\ \(\tau_{vsk_{p}}\) & Binary parameter that takes a value of 1 if job sequence \(v\) allows the loading or unloading of goods at berth \(k\) in period \(s\) and a value of 0 otherwise. \\ \(\mu_{p_{v}}\) & Binary parameter that takes a value of 1 if job sequence \(v\) must load or unload of goods in port \(p\) within the specified time window and a value of 0 otherwise. \\ \(\omega_{p_{v}}\) & Binary parameter that takes a value of 1 if the completion time of job sequence \(v\) in route r at port p is within the specified time window and a value of 0 otherwise. \\ \(n_{ri}\) & The number of trips required for transport job \(i\) using route \(r\). \\ \(\mu_{v}\) & Binary parameter that takes a value of 1 if the start time of job sequence \(v\) in route \(r\) is within the time windows of job sequence \(v\) and a value of 0 otherwise. \\ \(\omega_{v}\) & Binary parameter that takes a value of 1 if the completion time of job sequence \(v\) in route \(r\) is within the time windows of job sequence \(v\) and a value of 0 otherwise. \\ \(e_{p_{v}}\) & Earliest allowed arrival time for job sequence \(v\) operated in port \(p\). \\ \(l_{p_{v}}\) & Latest allowed arrival time for job sequence \(v\) operated in port \(p\). \\ \(e_{v}\) & Earliest allowed arrival time for job sequence \(v\). \\ \(l_{v}\) & Latest allowed arrival time for job sequence \(v\). \\ \(st_{p_{v}}^{load}\) & Start time for loading products from job sequence \(v\) in port \(p\). \\ \(st_{p_{v}}^{unload}\) & Start time for unloading products from job sequence \(v\) in port \(p\). \\ \(c_{p_{v}}^{cloud}\) & Completion time for loading products from job sequence \(v\) in port \(p\). \\ \(c_{p_{v}}\) & Completion time for unloading products from job sequence \(v\) in port \(p\). \\ \(c_{ij}\) & The amount of fuel used when traveling from node \(i\) to node \(j\). \\ \(t_{ij}\) & The travel time taken when traveling from node \(i\) to node \(j\). \\ \(\eta_{vq}^{load}\) & The service time at job \(i\). Note that \(t_{i}\) is dependent on the types of operation (either non-operation (job \(i\) is depot) or loading or unloading). \\ \(t_{i}\) & where: \\ \(t_{i}=\left\{\begin{array}{ll}0,&\text{ if non -- operation at job $i$ and job $i$ is depot}\\ t_{i}^{i},&\text{ if loading operation only at job $i$}\\ t_{i}^{i},&\text{ if unloading operation only at job $i$}\\ t_{i}^{i}\end{array}\right.\) \\ \(t_{i}^{i}\) & Loading times at job \(i\). \\ \(\eta_{vq}^{load}\) & Binary parameter that takes a value of 1 if large loading occurs at port \(p\) for transport job sequence \(v\) in route \(r\) in period s. \\ \(\eta_{vq}^{unload}\) & Binary parameter that takes a value of 1 if barge unloading occurs at port \(p\) for transport job sequence \(v\) in route \(r\) in period \(s\). \\ \(K_{sp}\) & The number of berths that are available in port \(p\) in period \(s\). \\ \(N\) & The carrier's maximum number of barges \\ \(r_{k_{p}}\) & Time at which berth \(k\) in port \(p\) is ready. \\ \(l_{k_{p}}\) & Latest allowed arrival time for berth \(k\) in port \(p\). \\ Variables & \\ \(COE_{r}\) & The total CO\({}_{2}\) equivalent emissions of route \(r\). \\ \(TT_{r}\) & The total travel time for route \(r\). \\ Decision variables & \\ \(y_{ij,r}\) & 1, if the barge traversed from job \(i\) to job \(j\) in route \(r\). \\ \(y_{ij,r}\) & 0, otherwise. \\ \(x_{r}\) & 1, if route \(r\) is selected. \\ \(0\), otherwise. \\ \end{tabular}   
The proposed method consists of two components: (a) the data preprocessing phase generates all feasible routes, as described in Section 4.1 and (b) the proposed set is solved using a model with a branch-and-cut algorithm and a Pareto frontier is generated using the \(\varepsilon\)-constraint method, as demonstrated in Section 4.2. A flowchart of the proposed method is shown in Figure 3.