# Scheduling Optimization of Mobile Emergency Vehicles Considering Dual Uncertainties
## 2 Model Construction
### Mobile Emergency Vehicle Scheduling Model Considering Dual Uncertainties  
Although different disaster scenarios cannot affect the underlying logic standard of mobile emergency vehicle scheduling, all kinds of external conditions still influence the scheduling scheme design of mobile emergency vehicles. Moreover, the particular risk of each sudden disaster will affect the decision preference of the mobile emergency vehicle scheduling model. With reference to the modeling processes by [PERSON] (2018) and [PERSON] (2018), the overall scheduling factors of mobile emergency vehicles from the emergency center to the disaster area are explored based on Section 2.1. Considering the dual uncertainties, the scheduling optimization model for mobile emergency vehicles focuses on scheduling mobile emergency vehicles to disaster areas for providing emergency services. The objective of the model is not only to find the balance point between the scheduling time advantage and the cost advantage of a mobile emergency vehicle so as to maximally protect the lives and properties of the affected people but also to achieve a win-win situation of timely rescue and effective control of emergency costs. Since the mobile emergency center has the characteristics of rapid planning, fast feedback, and flexible assignment, the cost of the front-end transfer and replenishment of mobile emergency vehicles can be ignored. Thus, the scheduling model of mobile emergency vehicles must consider the behavior of mobile emergency vehicles only after leaving the emergency center. Furthermore, when finding the optimal value of the total objective function, the total scheduling cost \(C\) and the total time \(T\) of mobile emergency vehicles should be considered with equal importance. Here, the total emergency cost \(C\) consists of the fixed cost \(C_{1}\), transportation cost \(C_{2}\), preparation cost \(C_{3}\) and penalty cost \(C_{4}\). The fixed cost \(C_{1}=\sum_{f}f_{i}X_{i}\) denotes the construction cost and various preparation costs of the mobile emergency center for mobile emergency service. The transportation cost \(C_{2}=\sum_{i\
eq k}\left(z_{ij}^{k}\eta_{ij}^{k}i_{ij}^{k}+z_{ij}^{u}\eta_{ij }^{u}c_{ij}^{u}\right)\) includes the total cost of emergency material distribution and emergency rescue vehicles transferring from the mobile emergency center to the demand point. The initial cost \(C_{3}=\sum_{ju}j_{i}^{u}\) refers to the additional cost consumed in the early stages when emergency rescue vehicles arrive at the disaster area and carry out various rescue work according to the on-site rescue needs. The penalty cost \(C_{4}=\sum_{jku}\left(\theta_{j}^{k}\lambda_{j}^{k}+\theta_{j}^{u}\lambda_{j}^ {u}\right)\) represents the direct and indirect losses caused by the failure of various emergency supplies or rescue services to reach the demand point. As for the total emergency time \(T\), it is composed of transportation time \(T_{1}\), development time \(T_{2}\) and punishment time \(T_{3}\). The transportation time \(T_{1}=\sum_{ijk}z_{ij}^{k}\eta_{ij}^{k}+\sum_{ju}z_{ij}^{u}\eta_{ij}^{u}\) refers to the cumulative transportation time of emergency material distribution and emergency rescue vehicles. The development time \(T_{2}=\sum_{i\
eq u}z_{ij}^{u}\eta_{j}^{u}\) refers to the cumulative preparation time for rescue work after the arrival of emergency rescue vehicles at the demand point. The penalty time \(T_{4}=\sum_{jku}\left(\theta_{j}^{k}\lambda_{j}^{k}+\theta_{j}^{u}\lambda_{j}^ {u}\right)\) is similar to the penalty cost and constrains the model development with the goal of efficient scheduling and meeting the emergency demand as much as possible. The scheduling optimization model of mobile emergency vehicles is described by Formulas (4)-(14).