# Transportation and Reserve of Emergency Medical Supplies during Public Health Events
## 3 Materials and Methods
### Allocation and Storage Model of Emergency Medical Materials
#### 3.3.2 Allocation and Storage Model of Emergency Medical Materials  
The purpose of this paper is to study how to optimize the transportation and storage of emergency medical materials at a lower cost based on the requirements of time and demand. Emergency medical materials have the characteristics of various types, large quantities, and high transportation timeliness. However, in public health emergencies, such as epidemics, the demand for emergency medical materials is always uncertain and urgent. Every rescue has a golden age, and timely delivery of emergency medical supplies will greatly protect the lives and health of victims. At the same time, with the gradual development of Internet technology, timely information is the basic requirement, which requires the establishment of a perfect emergency medical materials distribution system to deal with the impact of emergencies. Therefore, in the scheduling and storage model, the most important thing is the urgency of the demand for each demand point, aiming to minimize the comprehensive delay penalty cost of each demand point and to meet the best service time window of each demand point as much as possible. At the same time, according to the characteristic that the demand for emergency medical materials varies greatly in different regions, an emergency medical materials dispatching model based on fuzzy multi-attribute decision-making method is constructed, which can well adapt to the emergency medical materials dispatch requirements in different regions. Taking an emergency medical material distribution center as an example, this paper studies its dispatching problem. When the demand emergency degree is low, the emergency degree level is higher, so it should give priority to meeting its best service time window. Therefore, in order to achieve the goal of minimizing the cost and the shortest response time, a dual-objective function is proposed to reduce the overall running time of the system and reduce the penalty cost of each demand point to achieve the goal of minimizing the cost and the shortest response time. A dual-objective optimization model is established to optimize the distribution route. \(H=\) (0, 1, 2, 3,..., \(h\)) is the demand point, where \(H_{0}\) is the center of the dispatching point of emergency medical supplies. The existing emergency medical materials in the center of the dispatching point is \(V_{0}\). The number of vehicles that can be dispatched is \(K\). The maximum load of a vehicle is \(q_{0}\), and there is no fault problem in the vehicle. \(D\) = {_d_(_a_,_b_} \(|\)_a_,_b_\(\in\)_H_} is the distance set between various demand points, _d_(_a_,_b_) represents the distance from \(a\) to \(b\), \(t_{ab}^{k}\) represents the time it takes for vehicle \(K\) to be dispatched from \(a\) to \(b\), and \(v_{0}\) represents the driving speed of the distribution vehicles. \(C_{0}\) represents the cost per unit distance of vehicle \(K\), \(C_{1}\) represents the start-up cost of vehicle \(K\), \(ET_{a}\) represents the earliest service time acceptable to demand point \(a\), \(RT_{a}\) represents the last service time acceptable to demand point \(a\), \(\Delta_{a}\) represents the assembly time required by demand point \(a\), \(q_{a}\) represents the quantity of emergency medical materials required by demand point \(a\), \(Y_{a}\) represents the total urgency of demand corresponding to demand point \(a\), \(B_{a}\) represents the delay time caused by emergency medical materials reaching demand point \(a\), \(D_{a}\) represents the penalty cost caused by emergency medical materials reaching demand point \(a\), and \(o\) represents the penalty cost per unit time when the latest acceptable service time is exceeded. Set decision variables:  
\(x_{ak}=\left\{ \begin{array}{rl}&1,\text{Materials for demand point $a$ are delivered by vehicle $k$}\\ &0,\text{Materials for demand point $a$ are not distributed by vehicle $k$}\\ \end{array} \right.\)  
\(u_{ak}=\left\{