## 4 Scenario Analysis
### Study Solution and Result Analysis
#### 4.2.2 Sensitivity Analysis  
Path Selection Sensitivity Analysis  
Based on the above analysis, it was determined that the path selection between customer nodes in the study of this problem had a significant impact on the formulation of vehicle paths and the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model Variable** & **Travel Distance** & \
\begin{tabular}{c} **Vehicle Speed or** \\ **Road Congestion** \\ \end{tabular} & **Vehicle Load** &
\begin{tabular}{c} **Fuel Price or** \\ **Driver’s Salary** \\ \end{tabular} \\ \hline Minimum distance & \(\surd\) & & & \\ Shortest time & \(\surd\) & \(\surd\) & & \\ Minimal fuel & \(\surd\) & \(\surd\) & \(\surd\) & \\ consumption & \(\surd\) & \(\surd\) & \(\surd\) & \\ Lowest cost & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Differences among various models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Path and Key Index** & **Minimum Distance** & **Minimum Time** & **Minimum Fuel** & **Minimum Cost** \\ \hline  & 0-9-10-0 & 0-3-1-0 & 0-2-10-0 & 0-8-7-0 \\  & 0-8-7-0 & 0-4-9-0 & 0-4-9-0 & 0-6-2-0 \\ Tour plan & 0-4-3-0 & 0-6-7-0 & 0-6-5-0 & 0-9-5-0 \\  & 0-1-2-0 & 0-8-10-0 & 0-8-7-0 & 0-4-10-0 \\ Total traveled distance (km) & 319.5 & 325.55 & 323.65 & 323.45 \\ Total traveled time (minute) & 424 & 420 & 427 & 429 \\ Total fuel (liter) & 42.63 & 44.95 & 42.61 & 43.84 \\ Total cost (€) & 552.18 & 559.33 & 555.64 & 544.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons of scenarios of \(11\) nodes with different objective functions. four key performance indicators. Therefore, sensitivity analysis was performed on the entire model in the next step when the customer's path selection changed. We reduced the number of paths between nodes to one when the paths were adjusted. In this paper, the path information in the case of label K = A was directly selected, and the calculated result was compared with the optimal path resulting from the processing of the data. Finally, the path change was found, which impacted the four key performance indicators. In the sensitivity analysis of this paper, Java-invoked CPLEX was also employed. The specific results are shown in Table 4.  
Table 4 shows the four key performance indicators under different objective functions when K = A. By comparing this data with the data in Table 3, Figure 3 was obtained. Through analysis of the results shown in Figure 3, it was seen that without considering multi-channels, the results under different objective functions were not perfect. Except for the small difference in performance between the benchmark instance and K = A instance under the minimum fuel consumption indicator, the performance of the main indicators of K = A under the other three performance indicators was not satisfactory. In the two key indicators of time and cost, in particular, the routing formulation without considering multi-paths consumed more time and cost \begin{table}
\begin{tabular}{c c c c c} \hline
**Path and Key Indicators** & **Minimum Distance** & **Shortest Time** & **Minimum Fuel Consumption** & **Lowest Cost** \\ \hline  & 0-210-0 & 0-9-50 & 0-31-0 & 0-9-10-0 \\  & 0-4-9-0 & 0-4-3-0 & 0-4-9-0 & 0-4-3-0 \\ Tour plan & 0-6-50 & 0-6-10-0 & 0-2-5-0 & 0-6-5-0 \\  & 0-8-7-0 & 0-8-7-0 & 0-6-10-0 & 0-8-7-0 \\ Total traveled distance (km) & 328.65 & 326.5 & 354 & 335 \\ Total traveled time (minute) & 451 & 443 & 454 & 450 \\ Total fuel (liter) & 52.28 & 55.17 & 51.62 & 52.15 \\ Total cost (€) & 598.16 & 611.16 & 603.13 & 595.64 \\ \hline \end{tabular}
\end{table} 
Table 4: Scenarios of \(11\) nodes with different objective functions when K = A.  
Figure 3: Channel selection impact on performance indicators. than the benchmark instance. Such results effectively indicate that considering multi-channels has a significant impact on vehicle routing formulation.