# Scheduling Optimization of Mobile Emergency Vehicles Considering Dual Uncertainties
## 4 Analysis of Examples  
In order to verify the adaptability of the mobile emergency vehicle scheduling model for sudden disasters under uncertain conditions, A simulation was conducted by referring to the disaster information related to the \"5.12\" Wenchuan earthquake. It supposes that four mobile emergency centers and 10 disaster areas are utilized for the mobile emergency response system. The four mobile emergency centers were selected and numbered as \(I_{1}-I_{4}\) near the urban transportation hubs of Chengdu City, Guanghan City, Deyang City, and Mianyang City. The 10 heavily affected points, represented by Wenchuan County, Maoxian County, Beichuan County, Mianzhu City, Shifang City, Pingwu County, An County, Pengzhou City, Dujiangyan City, and Qingchuan County, are identified and numbered as \(J_{1}-J_{10}\). The mobile emergency material distribution vehicle can provide three main types of emergency materials: medical, living materials \(K_{2}\), and special materials \(K_{3}\). The mobile emergency rescue vehicle can provide two types of emergency services: excavation and medical rescue services \(K_{5}\). The material capacity of the mobile emergency center is directly related to the city's layout scale, transportation facilities, and economic situation. Therefore, the location and information of each mobile emergency center are shown in Table 2. The material needs in the affected areas directly refer to the official media reports after the Wenchuan earthquake. By taking the severity of the disaster as the primary standard and referring to the urban population density of the disaster area, the demand quantity information for the disaster area is estimated as shown in Table 3. Before the mobile emergency vehicle arrives at the disaster area, the unit transportation cost of the mobile emergency vehicle is positively correlated with the transportation distance and transportation time. Table 4 shows the unit transportation cost and the single transportation time between each demand point. When mobile emergency rescue vehicles arrive at the affected areas, the cost of preparing emergency rescue services is related to the number of services available. The unit preparation cost of \(K_{4}\) and \(K_{5}\) is CNY 800 per item and CNY 1000 per item, respectively. And the unit development time is 15 min per item and 20 min per item, respectively. Figure 4: Chromosome variation. Figure 3: Chromosomal chiasm. Firstly, to verify the model's effectiveness, the genetic algorithm is set with the following conditions: initial population size \(N\)\(=\) 200, the maximum number of iterations \(T_{max}\)\(=\) 40000. According to References [15; 30], the crossover probability and mutation probability are initialized as \(P_{1}\)\(=\) 0.9, \(P_{2}\)\(=\) 0.1. In addition, the optimal values of mobile emergency cost and time are set to \(Z_{\rm C}^{min}\)\(=\) 5612800 and \(Z_{\rm T}^{min}\)\(=\) 1540300, respectively. In the solution process, GA search and convergence speed is fast, showing good stability in several experiments. After 10 experiments under the same conditions, the floating range of the optimal cost value \(Z_{\rm C}^{min}\) is within 20,000, and the floating range of the optimal time value \(Z_{\rm T}^{min}\) is within 5000. When the importance degree of mobile emergency cost and mobile emergency time is set to be the same \(w_{1}=w_{2}\)\(=\) 0.5, the optimal solution of the mobile emergency vehicle scheduling model is \(Z=\) 100.02, \(C=\) 5614400 and \(T=\) 1540300 minutes. In the above process, 107 material distribution vehicles and 37 rescue and rescue vehicles are involved in the mobile emergency work. The average cost of each mobile emergency vehicle is \(\overline{C}\)\(\approx\) 38989, and the average time is \(\overline{T}\)\(\approx\) 10697. It can be seen that although the optimal values of the two single objectives are challenging to achieve at the same time, the multi-objective model can well solve the contradiction between the sub-objectives.