## 4 Performance Evaluation of Proposed Scheme
### Simulation Results
This figure provides a clear visualization of how the proposed framework guides decision-makers in choosing transportation modes that balance efficiency, cost-effectiveness, and environmental considerations. It serves as a practical tool for stakeholders to understand the recommended actions based on the integrated evaluation, facilitating informed and data-driven decision-making in the complex landscape of multimodal transportation. The actions represented by 0, 1, and 2 in Figure 4 correspond to different strategies regarding the selection of transportation modes for each DMU. Action 0: Maintain Status Quo/No Change signifies that, according to optimal policy, the decision is to continue with the existing transportation modes and strategies without making any significant alterations. It suggests that the current combination of transportation modes for the DMU is considered optimal based on the integrated evaluation of DEA efficiency scores and MDP rewards. In view of the foregoing, Action 1: Explore New Transportation Modes reflects a more radical decision by exploring new transportation scenarios. This action implies a willingness to experiment with alternative modes of transportation, aiming to discover more efficient, cost-effective, or sustainable options. It suggests a forward-looking and innovative stance toward enhancing the overall transportation strategy. Moreover, Action 2: Adjust Transportation Strategy represents a decision to modify the contemporary transportation strategy for the DMU. This adjustment could involve changes in the mix of transportation modes, possibly emphasizing more efficient, cost-effective, or environmentally friendly modes based on dynamic evaluation. It indicates a proactive approach to optimize the transportation strategy in response to evolving conditions. Figure 5 presents a comparative analysis among the proposed methods, Multicast Routing with Multiple QoS Parameters (MRMQoS), and the Minimum Cost Steiner Tree Model (MCSTM) concerning cost, delay, profit, computational time, and CO\({}_{2}\) emissions needed for multicast tree construction. The MCSTM model establishes a minimum cost Steiner tree without considering the total delay and profit associated with the resulting tree. It is noteworthy that the proposed method exhibits a total cost approximately 29% higher than that of MRMQoS, and the delay is nearly 26% less than that of MCSTM. However, MRMQoS shows an 8.3% higher profit compared to our proposed method, while our proposed scheme exhibits an 11.7% higher profit compared to MCSTM. In terms of computational time, our method achieves an average CPU time, positioned between MCSTM and MRMQoS. Specifically, the CPU time of MCSTM is about 1.6% better than our proposed scheme, and our proposed scheme shows a 9.5% improved computational time in comparison to MRMQoS (given that our approach is based on determining the  
Figure 4: Actions against optimal transportation policy for each DMU. relative efficiency of arcs before solving the integer model). It is pertinent to mention that our proposed method generates reasonably cost-effective multicast trees while exhibiting average delay and profit, thus contributing to an overall superior performance compared to MRMQoS and MCSTM. In terms of CO\({}_{2}\) emissions, the proposed model consistently outperforms the other models. For instance, in a network of size 15, the proposed model demonstrated significantly lower CO\({}_{2}\) emissions (2173 units) compared to MRMQoS (3200 units) and MCSTM (4200 units). This trend persisted across various network sizes, with the proposed model consistently exhibiting reduced CO\({}_{2}\) emissions in comparison to both MRMQoS and MCSTM. The percentage decrease in CO\({}_{2}\) emissions achieved by the proposed model is 7.26%  
Figure 5: Comparison of proposed model, MRMQoS, and MCSTM in terms of cost, delay, profit, and CPU time against network size. (**a**) Cost, (**b**) Delay, (**c**) Profit, (**d**) CPU time, and (**e**) CO\({}_{2}\) emissions.