key: cord-0909149-60udag0r authors: Yang, Yun; Ma, Changxi; Ling, Gang title: Pre-location for temporary distribution station of urban emergency materials considering priority under COVID-19: A case study of Wuhan City, China() date: 2022-03-25 journal: Physica A DOI: 10.1016/j.physa.2022.127291 sha: 92258a2c29aba70e3cc9ab6983fd9f5e21fa17fd doc_id: 909149 cord_uid: 60udag0r In order to avoid the huge hidden dangers caused by emergencies, it is particularly vital to make a reasonable pre-location and layout of emergency logistics facilities. A multi-objective pre-location model of temporary distribution station for emergency materials was built, which considered the problems of information shortage and uncertain demand after the incident with minimum time, maximum time satisfaction, minimum delivery cost and psychological trauma to the masses. The priority of candidate points was solved by comprehensive evaluation methods, the nominal demand of served points was estimated by triangular fuzzy number theory (TFN), and the location model was solved by non-dominated sorting genetic algorithm. In addition, the optimal schemes without priority and considering it were compared and analyzed, the practicability of the model is verified by concrete examples. The results show the time and cost reduction of 7.754% and 25.651%, an increment of total satisfaction value of the scheme considering location priority. Therefore, the model and algorithm provide theoretical support and practical ideas for solving the location problem, which can better complete the task of the location problem for temporary distribution stations of urban emergency materials. The location theory of distribution center (DC) was first put forward by Alfred Weber in 1929. In the logistics system, the DC is in a crucial hub position, and the location for DC can optimize the whole logistics system. Actually, the location of logistics facilities aims to improve the efficiency of the logistics system by means of determining the geographical locations of distribution centers, warehouses and production facilities. At present, a great deal of research has been done on the location of logistics facilities and fruitful results have been achieved, they mainly focusing on: Liu et al. studied the three-level optimal location allocation of transportation centers, processing plants and distribution centers in the supply chain network, and established a robust 0-1 mixed integer optimization model based on uncertain transportation costs and customer demands [1] . The optimal layout of transportation network hubs was of great practical significance for improving transportation efficiency. Therefore, Wang et al. established a location model with the objective of minimizing transportation network cost and solved it by genetic algorithm, the experiment showed that this model can effectively enhance the transportation efficiency of agricultural products [2] . And also, Wu and Yang put forward a bi-level programming model which combined the location optimization with the traffic distribution to realize the pre-location of manufacturing J o u r n a l P r e -p r o o f Journal Pre-proof industry under the economic globalization [3] . Wang et al. proposed a method based on generalized cell mapping to solve the distribution of the exit position of weak noise excitation system on the basis of probability evolution analysis [4] . Wang et al. proposed an extended evacuation field model to determine the best location [5] . WALTER and GUTJAHR developed a location model of relief allocation in a biobjective optimization model and innovated a new algorithm to solve it [6] . Only a few papers considered quantitative and qualitative factors, thus, Ozgen and Gulsun combined the possibility linear programming and fuzzy analytic hierarchy process to study the multi-objective multi-facility location problem with limited capacity [8] . Elevli deeply discussed the location decision of logistics freight center based on fuzzy PROMETHEE method [11] . Besides, Shishebori and Babadi proposed a mixed integer linear programming model for the network design of medical service (MS) center location considering uncertain parameters [14] . Also, Liu [18] [19] [20] . MURAT and NOVRUZ developed a new mutation operator to heighten the performance of genetic algorithm [22] . Ortiz-Astorquiza et al. conducted a comprehensive review of multi-level facility location issues and expanded several classic facility location issues. Different from other facilities location, in order to minimize the number of residents who were not serviced, Chen et al. considered limited rational choice behavior of residents and established a location model based on limited rational choice behavior, they also designed simulated annealing algorithm and genetic algorithm [24, 25] . For the sake of effectively dealing with all kinds of natural or social emergencies, it is particularly pivotal to strengthen the emergency management system. As an essential infrastructure of the emergency management system, the emergency materials J o u r n a l P r e -p r o o f Journal Pre-proof reserve is of great significance in strengthening response efficiency and reducing disaster losses. Under the environment of risk, emergency multi-objective location is an NP-hard problem with high complexity of objectives and constraints. As soon as this kind of traffic problem is put forward, it has been widely concerned by scholars. Since then, the location and optimization of emergency logistics facilities have become more significant, also, more research results have been obtained in recent years. Sudtachat et al. put forward a relocation strategy to elevate the performance of (Emergency Medical Service, EMS) system and verified it with an example [33] [34] [35] . There was once an earthquake in Turkey, KILCI et al. set up a positioning system model of temporary shelter area after the earthquake according to real cases, and Peker et al. also took Turkey as an example to analyze the location of logistics center based on ANP /BOCR. GHASEMI et al. proposed a multi-objective, multi-commodity, multi-cycle and multi-vehicle location-allocation model for emergency supplies based on the evacuation planning after the earthquake and considering uncertain factors. After sudden public events, limited transportation resources must be used to transport a large number of patients to medical facilities, the decisions about where to send patients are usually made by the on-site respondents in an ad hoc manner [40] [41] [42] . And, Mills et al. formulated two heuristic strategies on this issue [43] . Behnam [54] [55] [56] . In order to effectively deal with all kinds of natural or social emergencies, it is particularly important to strengthen the emergency management system. As an important infrastructure of the emergency management system, the emergency materials reserve is of great significance in improving response efficiency and reducing disaster losses. Wang joined the UAV system in the process of studying similar problems, which provided certain reference for the construction of emergency logistics service facilities for similar problems [59] . Based on the above research results, it can be found that the priority of logistics distribution center is neglected in most existing studies, only the location factor is considered in the study of site-path optimization. In fact, there are many factors influencing the location of emergency logistics distribution center, such as the environment of demand point, road condition, society and history, among which social factors include population density, economic development level and medical condition. In view of these, this paper will use the comprehensive evaluation methods to evaluate the priority of alternative logistics distribution sites considering the influence of various factors. The essence of the research is a multi-objective optimization problem of prelocation for urban emergency logistics facilities. The non-dominant sorting genetic algorithm is adopted to solve the mathematic model of this problem, and an example is given to verify model. At the same time, the optimal location scheme considering the priority is compared with the scheme without considering the priority. The content structure of this paper is as follows: Section 1 studies the research of Euclidean distance is used as the distance in this paper. 6) Every demand point must be completely covered. 7) The position coordinates of candidate points are known. Penalty cost function with time window constraint of receiving materials for demand points: Establish a function of minimizing dispatch cost: , , As the model established in this paper is nonlinear, which cannot be solved by conventional genetic algorithm, the non-dominated sorting genetic algorithm is tried to solve the problem. Genetic algorithm (GA) was first proposed by Professor J. Holland of Michigan University in 1975. Non-dominated sorting genetic algorithms (NSGA) was put forward by Srinivas and Deb in 1995, which is an algorithm based on Pareto optimal concept. Three basic operators of this method are as follows. ① Selection operator: Roulette wheel selection mechanism is adopted. The fitness function is shown in Fig. 2 . We suppose that the fitness value of () xi ② Crossover operator: The uniform crossover method is used for crossover operation. ③ Mutation operator: The method of random mutation site is used for antibody mutation. It is common knowledge that genetic algorithm belongs to heuristic algorithm, and heuristic algorithm is more suitable for practical problems. Therefore, the genetic algorithm will be adopted to solve the pre-location optimization problem of emergency material distribution center with superior universality and robustness. The flow of multi-objective genetic algorithm is shown in Fig.3 . (1) Major parameters of I-GRA code 40 11 Finally, the priority selection sequence of temporary distribution stations for emergency supplies was obtained: 2→4→1→5→10→9→6→3→7→8. Table 4 . (1) Pre-location scheme of urban emergency logistics facilities The control parameters of multi-objective genetic algorithm are set as follows: the population size is 200, the mutation probability is 0.9, the crossover probability is 0.8, and the maximum number of iterations is 500. fig. 4 -a corresponding to the pre-location optimal scheme, which selects the number of 7 candidate points, i.e., candidate point 2, Pre-location optimal scheme Table 9 below. Table 11 . dp.4+ dp.13+ dp.8+ dp.2+ dp.1+ dp.7 cp. j =cp.4 dp.11 cp. j =cp.1 dp.10+ dp.6 cp. j =cp.5 dp.3+ dp.12 cp. j =cp.10 [1] (cos ) total ft  =13342.2 [2] (cos ) total ft  =9919.700 -25.651% It can be gained from Table 12 that the time cost of the scheme with consideration of the priority is slightly reduced by 7.754%, the total time satisfaction value is increased by 2.299%, and the total cost is reduced by 25.651%. Therefore, consideration of the location priority can not only lessen the cost, but also heighten the time satisfaction value to some extent in practice, which indicates the scheme with the location priority is better. To sum up, the pre-location of emergency logistics plays a significant role in dealing with emergencies. This paper establishes a pre-location mathematical model in conformity with the characteristics of the location for emergency logistics facilities. Firstly, the priority of each candidate point is evaluated by means of comprehensive evaluation methods in accordance with the factors concerning pre-location to be considered. Then, a multi-dimensional objective optimization model with time window constraints is established, which is solved by non-dominated sorting genetic algorithm. Finally, the validity and feasibility of the model & algorithm are verified by a case study of a pre-location problem for urban emergency materials distribution station in Wuhan, Hubei Province. Furthermore, a comparative analysis of the optimal pre-location schemes with a consideration of priority or not shows that the scheme considering priority is better, which takes the form of the time reducing by 7.754%, the cost decreasing by 25.651% and the total satisfaction improved by 2.299%. Consequently, the research provides theoretical support and practical ideas for the solution of the location problem of urban emergency logistics facilities. (1) Minimize the delivery time: The delivery of relief supplies is an exceedingly pivotal link in the rescue work after a disaster, one minute earlier the arrival of relief supplies may arrest more deaths and economic losses. Besides, total cost minimization corresponds to economic logistics. Therefore, this paper builds a mathematical model in conformity with timeliness, which can be better applied to practice. 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