## 5 Examples and Results
### Discussion  
The solution obtained by the above method is often a set of Pareto solution sets, that is, a set of generally incomparable compromise solutions, while the decision process usually needs to provide the decision-maker with the optimal solution choice. The decision-maker's preference weight \(w\) can be introduced to select the optimal solution satisfying the decision-maker from the Pareto solution set.  
\[\text{min}wg^{\prime}+(1-w)f^{\prime}_{r} \tag{29}\]  
where \(g^{\prime}\) and \(f^{\prime}_{r}\) are the normalized objective function values, and different preference weights are selected according to the decision-maker's preference for different objectives to provide the decision-maker with the corresponding most appropriate multi-period allocation scheme of hazardous materials. Figure 9 shows the allocation scheme with the lowest number of reserve points participating in allocation in Sec 1.  
From the perspective of material allocation, the current research mainly focuses on the allocation of hazardous materials in a single period, where the best scheme for the allocation of hazardous materials is found from different perspectives and methods. For example, in literature [10], transportation risk, transportation time, and fuel consumption are considered to find the optimal distribution network. However, from the perspective of supply and demand, the supply and demand relationship will change dynamically in each period. It is not enough to consider only the optimal scheme setting in a single period.  
In order to further compare the impact of single-period and multi-period decision making methods on hazardous material allocation scheme. The proposed method in this paper is compared with the traditional single-period decision making method under different scenarios to calculate the cumulative number of reserve point participating allocation tasks, the cumulative allocation risk, and the comprehensive objective value. The results are shown in Figure 10 and the comprehensive objective value is defined as follows:  
\[E=\ \frac{f-f_{\text{min}}}{2(f_{\text{max}}-f_{\text{min}})}+\frac{g-g_{ \text{max}}}{2(g_{\text{max}}-g_{\text{min}})} \tag{30}\]  
Figure 9: The optimal allocation scheme when \(w=1\) in Sec 1.  
where \(f_{\max}\), \(f_{\min}\), \(g_{\max}\) and \(g_{\min}\) are the maximum and minimum values of the cumulative allocation risk and cumulative number of reserve points participating in the allocation, respectively, in the Pareto solution under the difference scenarios.  
The traditional decision making approach only considers the optimal target of this period when developing the allocation scheme without considering the future allocation of hazardous materials. From the comparison results in Figure 10, it can be seen clearly that the integrated consideration of multiple periods can lead to a safer and more suitable ideal allocation scheme. Moreover, in the scenario of long-term allocation and limited resources, the comparison of the two decision methods becomes more and more obvious. For example, as shown in Figure 10a, the cumulative numbers of reserve points of the two decision making methods are both 6 in Scenario 3; there is no difference between them and the difference is also small in Scenario 1. However, when resources are limited or the number of periods increases, the multi-period decision making method can obtain an allocation scheme with fewer cumulative reserve points participating in allocation, and the difference between them is larger, which can be seen from the comparison results of Scenario 2, Scenario 4, Scenario 5, Scenario 6, Scenario 7, and Scenario 8 in Figure 10a. Therefore, it is very important for the sustainable management of hazardous materials to develop a suitable multi-period allocation scheme of hazardous materials.