## 4 Performance Evaluation of Proposed Scheme
### Simulation Results  
We implemented a decision-making framework for multimodal transportation systems by combining DEA and an MDP. The process begins by computing DEA efficiency scores \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Trucks** & **Transportation Mode and Values** & \\  & **Rail** & **Ship** & **Air** \\ \hline Activation cost of supplier per vehicle (IQD) & [26,700–32,040] & [26,26–32,040] & [26,700–30,260] & [20,000–26,700] \\ Variable transportation cost of shipment per km & [13.35–15.13] & [6.23–13.35] & [2.67–8.9] & [0.445–1.335] \\   per vehicle (IQD) & [0.15–0.18] & [0.07–0.17] & [0.02–0.04] & [0.005–0.02] \\ Carbon emissions per kilometer per weight for & & [40–70] & [40–70] & [45–60] & [15–40] \\ transportation mode m & & [18,000–20,000] & [18,000–20,000] & [20,000–22,000] & [18,000–20,000] \\ Total volume capacity of a vehicle/container in kg & & & & \\ Maximum iterations & & & & \\ Average customer demand & & & & \\ Customer demand variance & & & & \\ Supplier capacity for the final product & & & & \\ The production cost of the final product & & & & \\ Carbon emissions for the final product & & & & \\ Supplier risk & & & & \\ Supplier/plant/customer locations & & Randomly distributed & & \\ Weight of the final product & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of different transportation modes [2, 12–14]. for each DMU in the multimodal transportation network. The DEA efficiency scores capture the performance of each DMU in terms of infrastructure cost, fuel consumption, number of employee, passenger capacity, freight capacity, and CO2 emissions. Subsequently, we formulated an MDP to optimize decision-making in the transportation network. The MDP considers three actions, each corresponding to a specific strategy or transportation mode. The rewards for these actions are influenced by the DEA efficiency scores, infrastructure costs, and CO2 emissions. The objective is to find an optimal policy that balances efficiency with the associated costs and emissions. The MDP is solved iteratively using policy iteration, where the policy is evaluated and improved until convergence. Figure 2 depicts the DEA efficiency score for 13 transportation modes, i.e., A: Truck, B: Rail, C: Ship, D: Air, E: Truck + Rail, F: Truck + Ship, G: Truck + Air, H: Rail + Ship, I: Rail + Air, J: Ship + Air, K: Truck + Rail + Ship, L: Truck + Rail + Air, M: Truck + Rail + Ship + Air. It is quite evident from Figure 2 that transportation modes C, F, J, and K outperform all other modes keeping in view the demographical landscape of Iraq. Depending on the type of shipment/cargo, the combination of truck, rail, and sea is more suitable for Iraq, as indicated by DEA efficiency score. In Figure 3, the MDP rewards for 13 distinct transportation modes are presented, illustrating the nuanced evaluation of each mode's performance within the multimodal transportation system. Each transportation mode is represented by a stacked bar showing the division of MDP rewards for three different actions. The rewards are derived from the integration of DEA efficiency scores, signifying the overall effectiveness of each mode based on predefined objectives. The normalization of rewards ensures a consistent and comparable scale, allowing for a meaningful analysis of the relative performance of different transportation modes. This figure provides a visual representation of how the multimodal transportation system is assessed holistically, considering factors such as infrastructure cost, fuel consumption, and employee-related metrics. Figure 3: MDP reward for different actions taken for 13 transportation modes. Figure 2: DEA efficiency score of different transportation modes. Figure 4 offers valuable insights into the decision-making process by showcasing the actions taken against the optimal transportation policy for each DMU. The optimal policy is determined through the combination of DEA efficiency scores and MDP rewards, resulting in a strategic approach to mode selection for each DMU.