# Multi-Attribute Collaborative Optimization for Multimodal Transportation Based on User Preferences
## 5 Case Study
### Decision Result Discussion  
Building upon the aforementioned research, we further delve into the decision-making strategies of different participants with varying preferences. Whether they are managers, carriers, or shippers, we assume that rational decision makers, in the absence of other influencing factors, consistently gravitate towards selecting the transportation option with the lowest cost. However, the other three factors--carbon emissions, transportation risk, and transit time--respectively represent the perspectives of managers, carriers, and shippers. Managers aim to accomplish transportation tasks with the lowest possible carbon emissions, carriers seek to minimize risks encountered during transit, and shippers desire their goods to be delivered as swiftly as possible. To more clearly analyze these three categories of preferences, we have magnified them by selecting three specific transportation  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & **Transportation** & \multirow{2}{*}{**Transportation Mode**} & \multirow{2}{*}{**Cost/CNY**} & \multirow{2}{*}{**Carbon Emission/kg**} & \multirow{2}{*}{**Time/h**} & \multirow{2}{*}{**Risk**} \\  & **Path** & & & & & \\ \hline \multirow{2}{*}{\(1\)} & \multirow{2}{*}{\(1\)} & \multirow{2}{*}{1-2-5-7-11-15} & Railway-Waterway  
scenarios for testing. Scenario 1 mandates strict adherence to carbon emission policies. Scenario 2 involves the transportation of hazardous goods, where the management and control of transportation risks take precedence. Scenario 3 pertains to the transportation of perishable goods, with the primary focus being the control of transit time, and its time window is set within the range of [36,39] hours. \(B(\text{Scenario 1})\), \(B(\text{Scenario 2})\), \(B(\text{Scenario 3})\) each provided their subjective complementary judgment matrices under different scenarios, and the decision-making results under these varying scenarios are presented in Table 5.  
\(B(\text{Scenario 1})= \begin{vmatrix}0.5&0.1&0.2&0.3&0.2&0.3&0.1\\ 0.9&0.5&0.6&0.9&0.6&0.6&0.1\\ 0.8&0.4&0.5&0.9&0.3&0.3&0.1\\ 0.7&0.1&0.1&0.5&0.2&0.2&0.1\\ 0.8&0.4&0.7&0.8&0.5&0.5&0.3\\ 0.7&0.4&0.7&0.8&0.5&0.5&0.3\\ 0.9&0.9&0.9&0.7&0.7&0.5\\ \end{vmatrix} \)  
\(B(\text{Scenario 2})= \begin{vmatrix}0.5&0.1&0.1&0.2&0.3&0.3&0.5\\ 0.9&0.5&0.3&0.7&0.8&0.8&0.9\\ 0.9&0.7&0.5&0.8&0.9&0.9&0.9\\ 0.8&0.3&0.2&0.5&0.7&0.8&0.9\\ 0.7&0.2&0.1&0.3&0.5&0.7&0.9\\ 0.7&0.2&0.1&0.2&0.3&0.5&0.8\\ 0.5&0.1&0.1&0.1&0.2&0.5\\ \end{vmatrix} \)  
\(B(\text{Scenario 3})= \begin{vmatrix}0.5&0.1&0.1&0.7&0.2&0.2&0.3\\ 0.9&0.5&0.5&0.9&0.7&0.7&0.8\\ 0.9&0.5&0.5&0.9&0.8&0.7&0.8\\ 0.3&0.1&0.1&0.5&0.3&0.3&0.6\\ 0.8&0.3&0.2&0.7&0.5&0.4&0.8\\ 0.8&0.3&0.3&0.7&0.6&0.5&0.8\\ 0.7&0.2&0.2&0.4&0.2&0.2&0.5\\ \end{vmatrix} \)  
As evident from the aforementioned schemes, different preferences of decision makers lead to distinct optimal schemes. From the perspective of carbon emission control, Scheme 2 boasts the lowest carbon emissions and is ultimately selected. When considering risk \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenarios** & **Scenario 1** & **Scenario 2** & **Scenario 3** \\ \hline \multirow{5}{*}{\(W\)} & \(\omega_{1}=0.2187\) & \(\omega_{1}=0.2918\) & \(\omega_{1}=0.7246\) \\  & \(\omega_{2}=0.4692\) & \(\omega_{2}=0.1275\) & \(\omega_{2}=0.0145\) \\  & \(\omega_{3}=0.2025\) & \(\omega_{3}=0.2307\) & \(\omega_{3}=0.1140\) \\  & \(\omega_{4}=0.1096\) & \(\omega_{4}=0.3500\) & \(\omega_{4}=0.0469\) \\ \hline \multirow{5}{*}{\(Z\)} & \(z(x_{1})=0.7717\) & \(z(x_{1})=0.7248\) & \(z(x_{1})=0.7522\) \\  & \(z(x_{2})=0.9684\) & \(z(x_{2})=0.9239\) & \(z(x_{2})=0.8481\) \\  & \(z(x_{3})=0.9661\) & \(z(x_{3})=0.9674\) & \(z(x_{3})=0.8369\) \\  & \(z(x_{4})=0.7894\) & \(z(x_{4})=0.7817\) & \(z(x_{4})=0.7548\) \\  & \(z(x_{5})=0.9026\) & \(z(x_{5})=0.8403\) & \(z(x_{5})=0.8185\) \\  & \(z(x_{6})=0.5731\) & \(z(x_{6})=0.7450\) & \(z(x_{6})=0.8085\) \\  & \(z(x_{7})=0.8648\) & \(z(x_{7})=0.7960\) & \(z(x_{7})=0.8562\) \\ \hline \hline \end{tabular}
\end{table}