## 5 The Model's Implementation
### Experimental Results  
The proposed methodology is evaluated through the case study at a bustling multimodal hub. By examining the specific dynamics and operational characteristics of this hub, this study aims to offer actionable insights and scalable solutions that could be implemented across various nodes in the PI. An analysis is made of the average simulation outcomes of 15 instances for each scenario generated based on the experimental protocol mentioned in Section 5.2. The optimisation results of the GUROBI solver for the objective function are presented in Table 6, and the basic statistical performance in terms of each KPI is presented in Table 7.  
Table 6 demonstrates the relationship between the trucks, containers, and empty space, highlighting how the container arrangements impact the space utilisation efficiency. Increasing the number of trucks generally reduces the amount of empty space, with the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Trucks** & **Number of Containers** & **Empty Space (m)** \\ \hline
30 & 26 & 25.93 \\  & 28 & 25.37 \\  & 30 & 28.74 \\  & 35 & 26.20 \\
35 & 26 & 25.00 \\  & 28 & 25.52 \\  & 30 & 25.60 \\  & 35 & 29.00 \\
40 & 26 & 20.98 \\  & 28 & 22.92 \\  & 30 & 26.80 \\  & 35 & 31.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimisation results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **Number of** & **CO\({}_{2}\) Emissions** & **CO\({}_{2}\) Emissions** & **Trucks Used** \\
**Trucks** & **Containers** & **(Mean)** & **(Std)** & **(Mean)** \\ \hline
30 & 26 & 88.03 & 3.75 & 15.0 \\  & 28 & 125.07 & 12.77 & 16.0 \\  & 30 & 132.47 & 16.48 & 17.0 \\  & 35 & 118.36 & 19.83 & 19.0 \\
35 & 26 & 112.26 & 15.64  
most efficient configuration achieved using 40 trucks and 26 containers (20.98 m). However, scalability challenges emerge as the container numbers increase. Additionally, Table 7 shows that as the number of containers increases, CO2 emissions also rise, with higher variability in the emissions for larger container loads. Additionally, more trucks are required to accommodate additional containers, leading to higher logistical costs and fuel consumption. These trends highlight the need for optimisation strategies to balance the container load, truck usage, and environmental impact. The boxplot presented in Figure 5 provides a detailed analysis of the total CO2 emissions across different configurations of containers and trucks. The data are grouped by the number of containers (26, 28, 30, and 35) and are further categorised by the number of trucks (30, 35, and 40), with each truck configuration represented by a distinct colour. The boxplot analysis reveals stability in the CO2 emissions in the outcomes of the model in efficiently managing the container assignments and routing when the number of trucks matches the number of containers. The even distribution of instances ensures that the truck capacities are fully utilised without excessive underloading or overloading, leading to minimal variations in the emissions across different scenarios. The consistency observed in this configuration also underscores the robustness of the scheduling algorithm in maintaining a balance between the container grouping and truck allocation, thereby achieving the optimal environmental performance. The graph presented in Figure 6 illustrates the cumulative distribution function of CO2 emissions for various container and truck configurations. Each curve represents the emission profile of a particular configuration, providing insights into the variability in and the stability of emissions under different logistical setups. Steeper curves indicate that emissions are tightly clustered around specific values, suggesting lower variability and higher operational stability. On the other hand, flatter curves represent result scenarios with higher variability in the emissions. These scenarios can lead to underutilisation, increasing the sensitivity of emissions to operational changes.