# Scheduling Optimization of Mobile Emergency Vehicles Considering Dual Uncertainties
## 1 Introduction  
In recent years, the frequency and destruction range of sudden natural disasters have been increasing. Large-scale road damage and mass casualties are not uncommon. In disaster-affected areas, there is always an urgent need for a large number of emergency supplies and various rescue services in a short period of time. During a disaster, how to schedule emergency supplies and services more quickly and efficiently to the affected areas is the core task of emergency management. However, since traditional emergency vehicles are only used to support the operation mode of the vehicle, it has been challenging to meet the demand for emergency material distribution and rescue. Transportation path damage, demand fluctuations, and other uncertainties further limit traditional emergency services. The introduction of mobile emergency facilities, which can accurately carry out various emergency measures in a short time, has become the first choice to enhance the response capability of emergency services. As the carrier of all kinds of emergency engineering equipment, the mobile emergency vehicle has the advantages of variable flexibility and precision positioning. It not only supports emergency response plans and executes emergency services quickly but also provides quick feedback after emergency results. In addition, the scheduling model of mobile emergency vehicles can more effectively deliver emergency supplies and extra equipment to implement rescue missions. Most scholars define emergency vehicle scheduling as a branch problem of the emergency logistics network optimization system. Thus, based on different research perspectives, current studies can be divided into three categories: emergency scheduling with uncertainty factors, scheduling optimization with uncertainty emergency scenarios, and mobile emergency routing considering uncertainty. In terms of emergency scheduling with uncertainty factors, [PERSON] [1] introduced post-disaster emergency demand location uncertainty as a characteristic of the emergency vehicle distance minimization model and obtained the optimal routing for relief logistics with changing demand. Focusing on minimizing the vehicle waiting time and total system cost, [PERSON] [2] conducted risk-averse optimization of the disaster relief facility location and solved the problem of reasonable vehicle allocation with stochastic demand. Taking the risk of transportation materials as a starting point, [PERSON] [3] proposed an inventory location model with a variable-weighted algorithm for flammable, explosive, toxic, and harmful emergency materials. Paying attention to fuzzy information and road network damage risk, [PERSON] [4] proposed a multi-period optimization model of emergency material allocation under uncertain conditions. The model improved the rescue effect, minimized disaster losses, and achieved a reasonable allocation of emergency materials. Aiming at the open location-routing problem of green multi-facilities, [PERSON] [5] paid attention to the restrictions of emergency demand changes and traffic conditions on vehicle types and then obtained the vehicle routes with minimized pollution. By summarizing the previous research results and evaluating the reliability of the emergency logistics network with an expert group, [PERSON] [6] demonstrated that the emergency logistics coordination system and the emergency material supply system have higher uncertainty risks than the emergency distribution system and information system. In terms of scheduling optimization with uncertainty emergency scenarios, [PERSON] [7] proposed a scenario tree based on conditional probability to define the correlation between primary and secondary disasters, which reduced the analysis difficulty in unifying the scale and level of disasters and the possibility of secondary disasters. Henceforth, more scholars began to study the dual uncertainty in all kinds of emergency scenarios, but only a few preliminary research results were obtained.