After the outbreak of major emergencies, the scheduling of emergency supplies is the key to the emergency rescue work, and the establishment of appropriate emergency logistics centers plays a crucial supporting role. In order to deal with the problem of emergency facility location and material distribution in urban emergency logistics system, this paper establishes a dual objective mixed integer nonlinear programming (MINLP) model with the objective of minimizing the emergency rescue time and maximizing the satisfaction rate of emergency material demand, designs a genetic algorithm to solve the emergency logistics location and allocation model, and obtains the Pareto optimal solution set of the model. Finally, a case study of COVID-19 epidemic in Beijing-Tianjin-Hebei region was carried out to verify the feasibility and effectiveness of the model and algorithm in the actual application, which can provide reference and suggestions for the location and material distribution of urban emergency logistics centers.

Urban emergency logistics is a kind of logistics activity, where the cities urgently guarantee the logistics demand to reduce their own losses under the influence of sudden natural disasters, major public health events, public security events, large-scale group events, and other emergencies. The emergency logistics centers are important nodes in the emergency logistics network. In order to meet the needs of emergency material demand in major emergencies, the emergency logistics centers will play a role as a place to collect and store rescue materials and carry out a series of work such as transportation, circulation, scheduling, and distribution of materials. In recent years, all kinds of major emergencies have occurred from time to time in many countries and regions in the world, from the Tangshan earthquake to the Wenchuan earthquake, from SARS to avian influenza and now to the global COVID-19 epidemic, and from the “911” incident to the frequent mine accidents in recent years. The outbreak of major emergencies not only pose a serious threat to people's life safety but also bring inconveniences to people's production, life, and commodity circulation, which has a strong impact on social and economic development.

Therefore, when major emergencies break out, how to carry out emergency rescue for the affected people and make them get rapid treatment has become a task of top priority. In this process, ensuring the rapid and effective supply of emergency relief materials is the fundamental guarantee. How to reasonably allocate emergency resources and farthest minimize the losses caused by the disaster is a key problem worthy of consideration in emergency logistics. In the emergency rescue work, the establishment of stable emergency logistics centers will play an indispensable supporting role.

Under the background of the frequent occurrence of various major emergencies in the world, many scholars at home and abroad are devoted to the research of emergency logistics problems such as emergency facility location, material distribution, and emergency logistics network optimization. For example, scholar Ekici combines the epidemic transmission model with facility location and material distribution network, establishes a location optimization model for food distribution, and designs the heuristic algorithm in order to solve the practical problems of Georgia [

Nowadays, the occurrence of emergencies is more and more diversified, and the impact of major emergencies has exceeded people's expectations. Because of its burstiness, unpredictability, wide range of impact, and strong destructiveness, decision makers must complete the dispatch of emergency materials in the shortest time and carry out emergency rescue, material support, and protection of secondary emergencies. Through literature review, it can be seen that in the existing literatures, the research methods of emergency logistics center location and material allocation are constantly optimized, and the models are constantly innovated. Most of the single-objective location models are constructed with the factors of cost, distance, coverage rate, demand satisfaction rate, and so on, or the multiobjective location models are constructed by arranging and combining the above factors, but there are not many articles taking the combination of time and demand satisfaction rate as the multiobjective to construct model. The location of emergency logistics facilities is complex, and the decision makers need to consider a variety of factors. If only one factor is considered without the constraint of another factor, the solution obtained will tend to be extreme. On this condition, the location is usually based on two or more mutually restricted objectives. Therefore, the multiobjective programming model is chosen to solve this problem. And when modeling in the complex situation, the variables include discrete variables and continuous variables and the objective function is nonlinear, so the multiobjective mixed integer nonlinear programming model is selected to solve this problem. In this paper, considering that in the context of some major emergencies (such as SARS), the country will carry out emergency rescue regardless of cost, so the multiobjective mixed integer nonlinear programming model is established with the goal of the minimum demand satisfaction rate and the shortest emergency rescue time. In the normal logistics location model, cost is an important factor. However, in this paper, under the background of major emergencies, especially the major public health events such as SARS and COVID-19, because the delay of emergency material transportation will cause more serious consequences, the cost factor is weakened and first considers the emergency rescue time to maximize the rescue efficiency. In addition, the demand satisfaction rate is not an important factor in the normal logistics location model. If the supply of demand point is far less than the demand, it can be solved by redistribution. While in the emergency location model, considering the urgency of demand, the demand of the demand point should be met as much as possible in the primary distribution. Therefore, at the same time we meet the need of the shortest emergency rescue time and the need of highest satisfaction rate should also be met. Taking the COVID-19 epidemic in Beijing-Tianjin-Hebei region as an example, appropriate number of emergency logistics centers are established within the scope of Beijing-Tianjin-Hebei region and emergency materials allocation is carried out during the outbreak of the epidemic in order to verify the feasibility of the emergency logistics center location allocation model and algorithm, and suggestions are provided for the allocation of emergency materials in each region during the outbreak of major emergencies.

After the outbreak of large-scale major emergencies, a number of emergency logistics centers need to be established rapidly in a region. The relevant departments need to allocate a large number of emergency materials from the material supply points to the emergency logistics centers and then distribute them to the disaster areas, namely, the material demand points. Therefore, a three-level emergency logistics network including material supply points, emergency logistics centers, and material demand points needs to be established, as shown in Figure

How many emergency logistics centers need to be set in the middle of the transportation of emergency materials from the material supply points to the material demand points

Where the emergency logistics centers are set up and to which material demand points it is responsible for transporting

What is the satisfaction rate of emergency material demand at each material demand point

What is the optimal emergency rescue time from material supply points to material demand points

Three-level emergency logistics network.

In order to better construct the model, the following assumptions are put forward:

Not considering the differences of transportation modes of rescue materials, that is, simplifying the types and transportation modes of emergency rescue materials, only considering a single transportation mode (usually road transportation), and meeting the accessibility of vehicle transportation between network nodes;

The material demand of each material demand point does not exceed the material storage of the corresponding emergency logistics center and can jointly be transported by vehicles;

All kinds of emergency materials meet the compatibility of transportation; that is, the situation that different emergency materials cannot be transported at the same time is not considered;

Regardless of the working time limit and vehicle capacity limit of transport vehicles, it is assumed that each material supply point and emergency logistics center has a sufficient number of transport vehicles and sufficient vehicle carrying capacity;

In order to shorten the time of emergency rescue, the emergency logistics centers distribute the emergency materials to the corresponding material demand points as soon as they receive the emergency materials; that is, the turnover time of the emergency materials in the emergency logistics centers is not considered.

Table

Parameter setting.

Implication | |
---|---|

Set of emergency material supply point | |

Set of emergency logistics center | |

Set of material demand point | |

Weight of material demand point | |

Supply capacity of emergency material supply point | |

Position coordinate of emergency supply point | |

Position coordinate of emergency logistics center | |

Position coordinate of emergency demand point | |

Maximum distribution radius of emergency logistics centers | |

Distance between material supply point | |

Distance between emergency logistics center | |

Transportation speed of materials from material supply point | |

Transportation speed of materials from emergency logistics center | |

Transportation time of emergency materials from material supply point | |

Transportation time of emergency materials from emergency logistics center | |

Relative size of emergency logistics center | |

Material demand of emergency demand point | |

Material demand satisfaction rate of emergency demand point | |

Material storage capacity of emergency logistics center | |

Quantity of emergency materials transported from material supply point | |

Quantity of emergency materials transported from emergency logistics center | |

Whether to locate at emergency logistics center | |

Whether to transport the materials from material supply point | |

Whether to transport the materials from emergency logistics center |

Based on the above parameters, the location allocation model of urban emergency logistics center is established as follows:

In the above urban emergency logistics center location allocation model, the objective function (

The following are further explanations of some of the above formulas:

In the three-level emergency logistics network established in this paper, the material supply points, emergency logistics centers, and material demand points are all nodes in the network, and the location of nodes is expressed by their geographical coordinates. Therefore, the distance between every two city nodes in formula (

The scope of urban emergency logistics center location studied in this paper is in a region. The transportation of materials from the emergency logistics centers to the material demand points in a region usually uses road transportation. When major emergencies occur in the region, it is necessary to quickly mobilize emergency materials around the region to save the time of material transportation. Road transportation is also the main way to transport materials from the adjoining areas of the region to the emergency logistics centers in the region, so the transportation speed in formulas (

Because the objective function

In addition, in the case of only considering a single mode of transportation (road transportation), assuming that the transportation speed of transport vehicles is same and constant, the problem of minimizing the emergency rescue time can be transformed into the problem of minimizing the sum of the distances from the material supply points to the material demand points. The expression is as follows:

In this paper, the urban emergency logistics center location allocation model under major emergencies is a 0-1 mixed integer nonlinear programming model, which involves a large scale of data, including the population data, location data, demand data of each material demand point, and material reserve data of material supply points. Then, the number and locations of emergency logistics centers are unknown, which means the problem to be solved is a NP-hard problem. After the multiobjective mixed integer nonlinear programming model is established, the computational cost of solving the model is high. As there are many variables and constraints with complex forms, the model is usually transformed into a single-objective programming model and solved by the heuristic algorithm. If the accurate algorithm is used to solve the problem, it will increase the difficulty and cost more time. In the context of major emergency rescue, it is necessary to meet the timeliness requirements and find the near-optimal solution of the model in the shortest time. Therefore, this paper uses the genetic algorithm to solve the model according to the characteristics of the model. In addition, when using the genetic algorithm to solve the model, the unknown variables need to be put into the chromosome codes, which require the real data of variables except those serve as chromosome codes can be collected in the example analysis. And the flow chart of the genetic algorithm is shown in Figure

The number of rows of chromosome corresponds to the number of emergency logistics centers, and the first two columns of chromosome are the locations of emergency logistics center “

Flow chart of the genetic algorithm.

In this paper, we take the first four stages (from the discovery of unexplained pneumonia cases in Wuhan, Hubei Province, on December 27, 2019, to the normalization of national epidemic prevention and control on April 29, 2020—according to <Fighting Covid-19 China in Action>) of COVID-19 epidemic in Beijing-Tianjin-Hebei region as an example to verify the effectiveness of the model and algorithm in the actual major emergencies and take 13 prefecture level cities in Beijing-Tianjin-Hebei region as 13 material demand points

Locations and demand of material demand points.

Material demand point | Geographic coordinate | Weight | Material demand quantity |
---|---|---|---|

Beijing | (39.55, 116.24) | 0.196 | 59300 |

Tianjin | (39.02, 117.12) | 0.142 | 19000 |

Shijiazhuang | (38.02, 114.30) | 0.095 | 2900 |

Tangshan | (39.36, 118.11) | 0.072 | 5800 |

Qinhuangdao | (39.55, 119.35) | 0.029 | 1000 |

Handan | (36.36, 114.28) | 0.087 | 3200 |

Xingtai | (37.04, 114.30) | 0.067 | 2300 |

Baoding | (38.51, 115.30) | 0.086 | 3200 |

Zhangjiakou | (40.48, 114.53) | 0.04 | 4100 |

Chengde | (40.59, 117.57) | 0.033 | 700 |

Cangzhou | (38.18, 116.52) | 0.069 | 4800 |

Langfang | (39.31, 116.42) | 0.044 | 3000 |

Hengshui | (37.44, 115.42) | 0.04 | 800 |

According to the 2019 national economic and social development statistical communique of Beijing, Tianjin, and Hebei Province, the number of permanent residents of 13 prefecture level cities in Beijing-Tianjin-Hebei region by the end of 2019 is obtained as follows: 21.536 million in Beijing, 15.6183 million in Tianjin, 10.3942 million in Shijiazhuang, 7.964 million in Tangshan, 3.1463 million in Qinhuangdao, 9.5497 million in Handan, 7.3952 million in Xingtai, 9.399 million in Baoding, 4.4233 million in Zhangjiakou, 3.5827 million in Chengde, 7.5443 million in Cangzhou, 4.795 million in Langfang, and 4.486 million in Hengshui.

Input the set parameters into Matlab and solve the model. Run the algorithm for 20 times, and take the average value of 25.2223 as the approximate optimal solution of the objective function. At this time, the minimum value of the sum of the distances from the material supply points to the material demand points through the emergency logistics centers is 26.1557, and the maximum value of the sum of the demand satisfaction rate of each material demand point is 0.9334. Through 20 repeated calculations and statistical analysis of the calculation results, we can get that the average operation time of the algorithm is 93.454 seconds, and the standard deviation of the calculation results is 0.4156. The results show that the calculation results of the genetic algorithm have a certain stability, and the reliability of the calculation results can be improved by repeated operations.

Because the total supply of emergency materials is less than the total demand, the total demand satisfaction rate is less than 1, the overall demand of Beijing-Tianjin-Hebei region is unsatisfied, and the total demand satisfaction rate is relatively high, slightly less than the ratio of material supply to demand of 0.9446, which reflects the effectiveness of the emergency logistics center location model in material allocation, and the demand satisfaction of each material demand point is shown in Table

Demand satisfaction of material demand points.

Material demand point | Material demand quantity | Material supply quantity | Demand satisfaction rate (%) |
---|---|---|---|

Beijing | 59300 | 56349 | 95.02 |

Tianjin | 19000 | 18323 | 96.44 |

Shijiazhuang | 2900 | 2702 | 93.17 |

Tangshan | 5800 | 5428 | 93.59 |

Qinhuangdao | 1000 | 907 | 90.7 |

Handan | 3200 | 2959 | 92.47 |

Xingtai | 2300 | 2174 | 94.52 |

Baoding | 3200 | 2920 | 91.25 |

Zhangjiakou | 4100 | 3730 | 90.98 |

Chengde | 700 | 621 | 88.71 |

Cangzhou | 4800 | 4399 | 91.65 |

Langfang | 3000 | 2761 | 92.03 |

Hengshui | 800 | 727 | 90.88 |

In addition, it is not difficult to see that the demand satisfaction rate of core cities (Beijing, Tianjin, and so on) is generally higher than that of edge cities (Zhangjiakou, Qinhuangdao, Chengde, and so on), and node cities (Beijing, Tianjin, Xingtai, and Tangshan) as emergency logistics centers have significantly higher demand satisfaction rate than other cities, and cities with higher population density (Beijing, Tianjin, Shijiazhuang, Tangshan, and so on) also have high demand satisfaction rate. Generally speaking, geographical location, traffic conditions, and population density are factors to measure the level of economic development; thus, it can be seen that the emergency materials demand of cities with higher level of economic development is easier to be met when major emergencies occur. According to objective function (

The result shows that the optimal emergency logistics network is shown in Figure

Locations and distribution of emergency logistics centers.

Sites and relative size of emergency logistics centers.

No. | Geographical coordinate | City | Relative size |
---|---|---|---|

1 | (39.55, 116.24) | Beijing | 0.6323 |

2 | (39.02, 117.12) | Tianjin | 0.2185 |

3 | (37.04, 114.30) | Xingtai | 0.0823 |

4 | (39.36, 118.11) | Tangshan | 0.0669 |

Based on this, the urban emergency logistics network in Beijing-Tianjin-Hebei region after the locations of emergency logistics centers is determined under the outbreak of epidemic and is drawn on the map of Beijing-Tianjin-Hebei region (as shown in Figure

Structure of urban emergency logistics network in Beijing-Tianjin-Hebei region.

Distribution of emergency materials.

No. | City | Emergency demand point |
---|---|---|

1 | Beijing | Beijing, Zhangjiakou, Baoding, Langfang |

2 | Tianjin | Tianjin, Cangzhou |

3 | Xingtai | Xingtai, Shijiazhuang, Handan, Hengshui |

4 | Tangshan | Tangshan, Chengde,Qinhuangdao |

It can be seen from Table

It can be seen from Figure

From the above test results, we can see that in the final objective function, the total distance has a greater impact on the result of the objective function, while the total demand satisfaction rate has a smaller impact on the result of the objective function. Among the factors that affect the total distance, the number of emergency logistics centers plays a decisive role. If the number of emergency logistics centers is too small, each emergency logistics center is responsible for more material demand points, and the total distances between the emergency logistics centers and the corresponding material demand points are larger; when the number of emergency logistics centers is too large, the emergency logistics centers to be supplied by the material supply points are more, and the number of paths from the material supply points to the emergency logistics centers increases, so the total distance between the two will become larger. Therefore, the appropriate number of emergency logistics centers should be the Pareto optimal solution between the above two. The following is a sensitivity analysis on the number of emergency logistics centers. The number of emergency logistics centers in the model is changed, and the other parameters are unchanged. The influence of the number of emergency logistics centers on the solution of the objective function is studied so as to obtain the optimal solution of setting several emergency logistics centers in the region. The number of emergency logistics centers is set as 2, 3, 4, and 5, respectively, for testing. The test result is shown in Table

Calculation results of sensitivity analysis of emergency logistics centers number.

Number of emergency logistics centers | 2 | 3 | 4 | 5 |
---|---|---|---|---|

Distance between material supply points and emergency logistics centers | 10.1613 | 13.8857 | 16.0276 | 18.7902 |

Distance between emergency logistics centers and material demand points | 21.3107 | 12.5024 | 10.1281 | 8.7472 |

Total distance | 31.472 | 26.3881 | 26.1557 | 27.5374 |

Emergency logistics center | Beijing, Tianjin | Beijing, Tianjin, Xingtai | Beijing, Tianjin, Xingtai, Tangshan | Beijing, Tianjin, Handan, Baoding, Tangshan |

Site selection of two emergency logistics centers.

Site selection of three emergency logistics centers.

Site selection of four emergency logistics centers.

Site selection of five emergency logistics centers.

The trend of the distances between the three nodes in the emergency logistics network with the variation of emergency logistics centers number.

As can be seen from Table

Under the background of major emergencies, the location problem of urban emergency logistics center is a complex problem with multiple objectives and constraints. In this paper, taking the shortest emergency rescue time and the highest demand satisfaction rate as the objectives, a dual objective location model of emergency logistics center is established and transformed into a single-objective model. A genetic algorithm is designed to solve the model, and an analysis of practical examples is used to verify the feasibility and effectiveness of the model and algorithm. The model has great flexibility and adaptability, and it is suitable for complex problems with multiple objectives, multiple variables, and nonlinear objective function. It is often used in programming problems, such as location-routing problem of logistics. Decision makers can adjust the parameters according to the actual situation to finish the emergency logistics center location and emergency material scheduling. In addition, this paper also considers the population density of the material demand points, the radiation radius of the emergency logistics centers, and other factors, which have important practical significance for decision makers.

The deficiency of this paper is that only a single transportation mode of emergency materials is considered. In the actual situation, there are many kinds of emergency materials and different modes of transportation. Therefore, in the next step of research, we will consider the situation of multiple materials and multimodal transportation and add them to the location model of emergency logistics center so as to select the location of emergency logistics center from a more scientific and realistic angle and improve the quality of the solution.

The number of permanent residents of 13 prefecture level cities in Beijing-Tianjin-Hebei region by the end of 2019 is obtained in the 2019 national economic and social development statistical communique of Beijing, Tianjin, and Hebei Province; the geographical coordinates of 13 cities of Beijing-Tianjin-Hebei region are obtained in Coordinate table of all cities in China.

The authors declare that they have no conflicts of interest.

This study was supported by the fund project of National Natural Science Foundation of China:“Research on collaborative control of urban logistics based on network theory” (61772062).