Emergency logistics vehicle routing optimization based on insufficient supply

. In the face of various emergencies, emergency logistics vehicles are required to meet the needs of the affected areas in a short enough time. However, due to the suddenness of the incident and the shortage of relief supplies, it is necessary to further consider how to optimize the route of emergency vehicles in case of insufficient supply. In this paper, when the supply point is insufficient, the emergency vehicle routing can be optimized in the shortest possible time and at the same time to meet the requirements of the disaster site. By establishing the corresponding mathematical model and using the genetic algorithm to solve the relevant examples, the new solution is provided for the emergency logistics vehicle routing problem when the relief materials are insufficient. According to the analysis results of the example, the effectiveness of the optimization method is further demonstrated, and theoretical support is provided for relevant decision makers.


Introduction
With the various major natural disasters that have emerged in recent years, the economic development of the region and even the economic development of the country have been greatly affected. In the event of a major natural disaster, how to rescue the disaster relief site in a short period of time is very important, so the status of emergency logistics is increasingly prominent.
How to quickly and efficiently deliver relief supplies to disaster-stricken areas in the face of unexpected events is an important challenge for emergency logistics. At the same time, due to the suddenness of the incident, it is difficult for relief materials to meet the needs of all disaster-affected sites. How to plan the route of emergency logistics vehicles and the quantity of materials at the disaster site is a problem that emergency logistics often encounters under realistic conditions. Based on the background of major natural disasters and the shortage of relief materials, this paper constructs a corresponding vehicle routing optimization model. Under the constraints of vehicle load and reasonable distribution of rescue materials, the genetic algorithm is used to study the optimal path of emergency vehicles when the relief materials are insufficient.

Emergency logistics overview
Emergency logistics is a special logistics activity [1] generally refers to the emergency protection of the needs of materials, personnel and funds at the disaster site in order to response emergencies such as serious major natural disasters, military conflicts and so on. As with ordinary daily logistics, emergency logistics is also based on logistics efficiency. The difference is that in addition to logistics efficiency, general logistics also emphasizes logistics efficiency. Emergency logistics is to achieve logistics benefits through logistics efficiency.
After the emergency occurs, the relief materials need to be delivered to the disaster area in the shortest possible time, and the path optimization of the emergency logistics vehicles is a key issue to be considered. Optimizing the route of emergency logistics vehicles, the reasonable distribution of relief materials within the specific time window of the disaster-stricken point can be achieved, and the rescue pressure of the disaster-stricken point can be greatly reduced.

Research on path optimization of emergency logistics vehicles
At present, relevant scholars at home and abroad have already had rich research results on emergency logistics path planning. For example, Zhao et al. (2010) [2] studied the optimization of the route of the emergency aid delivery vehicle with time window, and used the ant colony algorithm to solve the constructed model; Sascha et al. (2012) [3] studied the dynamic path optimization of emergency logistics vehicles under the condition of deterministic demand, which is different from the traditional static planning; Alberto et al. (2014) [4] studied the location and vehicle routing problems in emergency logistics in the context of drug distribution; Cheng Birong et al. (2016) [5] aimed at the shortage of emergency supplies in critical rescue period, an optimization model of emergency logistics vehicle routing problem under stochastic demand environment is established, and a solution method based on genetic algorithm is designed; Wu Xinsheng et al. (2018) [6] introduced two groups of In the context of major natural disasters, this paper aims at the problem of insufficient relief materials, and aims to minimize the maximum value of the difference between the time and the risk of the two disaster-affected points. The model is constructed under the constraint of time window and using genetic algorithm to solve the model. In contrast, there are some innovations in the objective function.

Related assumptions and models 2.1 Model description
In this paper, if a major natural disaster occurs in a certain area, it is necessary to timely deliver relief materials to each affected area. The location of the relief supplies distribution center is known and fixed, but there is a shortage of relief supplies. The distribution center has a certain number of emergency vehicles available for rescue, each vehicle is exactly the same, and has a certain load limit. There are multiple disaster sites, and the location of each disaster site and the demand for relief supplies are known. Under the goal of minimizing the delivery time and the minimum value of the difference between the demand and the rate of the two disaster-affected points, how to optimize the load and delivery path of the emergency vehicle, and let each disaster-stricken point receive relief materials in a short period of time as fair as possible is the focus of this study.

Variable definitions
Based on the questions raised in this study, the following related variables are defined: When the decision variable is 1, it means that vehicle K comes from point i to point j .

Related assumptions
(1) Vehicles k starts from the distribution center, and eventually returns to the distribution center;(2) There is no difference in the types of relief materials delivered, and there is no need to distinguish between materials;(3) A vehicle can transport supplies for multiple disaster sites, and each disaster relief site is serviced by only one vehicle;(4) The vehicle must meet the time window of the disaster site during the delivery process;(5) The amount of materials required for each disaster site is greater than the vehicle capacity.

Model building
Equation (1) is the objective function of the model, which consists of two parts: the delivery time and the maximum value of the difference between the requirements of the two disaster-affected points. Equation  (4) and (5) indicate that the emergency vehicle k arrives at the disaster site i from the disaster site j .
Equation (6) indicates the proportion of the supply of the disaster site i to meet the demand. Equation (7) indicates that the time when the vehicle arrives at the disaster site j is the sum of the time when the emergency vehicle leaves the disaster site i and the travel time between the two disaster sites. Equation (8) indicates that the time from the disaster site i to the disaster site j is the distance between the two disaster sites divided by the vehicle speed. Equation (9) represents the time window constraint of each disaster site.

Algorithm description
Various types of algorithms applied to the vehicle routing problem, different algorithms have their own characteristics, for example, the Tabu search algorithm [7] can avoid the criterion of stopping with local optimum; The calculation process of simulated annealing [8] has a simple calculation process and is suitable for parallel processing, but at the same time, the convergence speed is slow, the execution time is long, the performance of the algorithm is related to the initial value and the parameters are sensitive; the genetic algorithm [9] finds the optimal solution by imitating the choice of nature and the mechanism of inheritance. The search starts from the group and has potential parallelism, which can simultaneously compare multiple individuals. Therefore, combined with the relevant characteristics of emergency logistics, this paper will apply genetic algorithm to solve the vehicle routing planning of emergency logistics.

Solution process
The solution process of the genetic algorithm [10] is as follows: (1) Initialization a. Combine the actual, select a relatively suitable coding scheme, and convert the variable with certain characteristics into the corresponding chromosome, that is, the numeric string. In general, choose binary encoding.
b. Set the appropriate parameters, including the group size (M), crossover probability c P , and mutation probability m P .
c. Further determine the fitness function ( ) fx.
(2) Form an initial group (including M individuals). In the slope slip surface search problem, the analyzed possible slip surface group is taken as the initial group. the corresponding digit string will be inverted, that is, the binary code of the chromosome is changed to a number 0 to 1, and 1 becomes 0. After a round of initialization and selection, crossover, and mutation, a new population is created. The new evolutionary round will continue to a certain number and be repeated, and finally the optimal chromosome will be the solution to the problem.

Case analysis
According to the model constructed above and the specific example for further verification, in this example, it is assumed that there is one distribution center and 10 disaster sites in the disaster area, the coordinates of each point and the corresponding specific information are as table 1 shows.
According to the specific data in Table 1, the position distribution map shown in Figure 1 is obtained. From the distribution center in Figure 1 and the location of each demand site, the distribution center is located in the central area of the demand site, and the location of each demand site is distributed around the distribution center, which can further judge the distribution of the distribution center and the demand site.
In the distribution center, there are 5 distribution vehicles, each of which is exactly the same. The maximum load is 10t, the speed of the emergency vehicle is V=40km/h, and the corresponding objective function is α=β=0.5.
Based on the established model, the genetic algorithm is used to perform MATLAB programming, and finally the results shown in Table 2 are obtained: According to Table 2, the path of each vehicle is shown in the position map as shown in Figure 2. According to the result of the vehicle route, the vehicles in the distribution center are fully utilized, starting from the distribution center, and returning to the distribution center after each disaster site. The resulting vehicle route meets the needs of each demand site to a certain extent, and saves rescue time.

Conclusion
This paper mainly studies the vehicle routing problem of emergency logistics. When the relief materials are difficult to meet the needs of all demand sites, the relief materials will be distributed to all disaster sites as soon as possible and fair. This study first establishes a vehicle routing model when the materials are insufficient. The distribution time is as short as possible, and the maximum value of the difference between the demand and the rate of the two disaster-affected points is as small as possible, solving the optimal vehicle routing under certain constraints. In the process of solving with a specific example, the genetic algorithm is used to further solve the model. The final example analysis shows that the model in this paper is effective and feasible.
As an important part of emergency rescue, emergency logistics still needs to be improved in some places, especially under the influence of big data and Internet of Things, intelligent logistics including emergency rescue has emerged [11] , so emergency logistics learning and research is a long process. In the theoretical study of emergency logistics, it is necessary to further contact with the actual situation, and the combination of theory and practice can solve the problems related to emergency rescue more efficiently.