An emergency supplies scheduling for chemical industry park: based on super network theory

In a concentrated area of chemical industry parks (CIPs), emergency relief efficiency is not only affected by the rescue capability of themselves, but also their coordination relationships with other CIPs. Previous studies focus on the location of resource warehouse and the scheduling of logistics transportation, in the relief process after unexpected events, but rarely integrate them ideally in practice. This paper utilizes the super network theory to propose a regional emergency scheduling model to improve collaboration efficiency among primary relief centers (PRC), local relief centers (LRC), and CIPs. So, the proposed super network model fills the research gap of only considering emergency logistic supply chain and provides decision scheme regarding the emergency material dispatch plan. We developed a modified projection algorithm to solve the scheduling problem by turning it to a variational inequality and compare the performance under several disaster scenarios. The practicability of the model is proved by the result of the numerical example given.


Introduction
The emergence of chemical industry parks (CIPs) is the embodiment of development of industrialization processes, with the centralized layout of CIPs, the possibility of major contingency increases. Once an accident occurs, it is easy to produce domino effect and secondary disasters if it is not disposed timely. For example, one factory's fire at Tianjin Port in China on August 12, 2015, triggered two shocked explosions that not only caused serious casualties and economic losses but also resulted in an extremely negative social impact (Zhao 2016). Natural hazards, such as earthquakes, floods, and geomagnetic storms, are also major latencies in CIPs. All hidden dangers are considered low probability but high-consequence events with significant social impact (Celano & Dolšek 2020;Reniers et al. 2005), and thus, providing quick response and improving emergency dispatching capability for the aftermath of an incident in CIPs present considerable challenges (Du et al. 2020a, b).
Regardless the rich literature on emergency response problems, demander, supplier, and distributer usually defined in general relief scheduling problems (Sheu 2007), and the locations and capabilities of resource providers are key components in managing response efforts after a disaster (Fiedrich et al. 2000;Li et al. 2014). In concentrated areas of CIPs, suppliers are not predetermined, and all agents within zones deployed their own relief resources; they are potentially not only the ones that demand for relief resources but also the supplies providers or the transfer station. Emergency relief cooperation has been proven to be effective and essential given the complexity of a relief network, which involves materials, traffic, and information, among stakeholders (Groothedde et al. 2005). The cluster of CIPs magnify the possibility of risk, but in turn, it also provides a geographical basis for the construction of a regional emergency linkage mechanism. This study aims to determine the optimal allocation with limited emergency resources immediately considering the supply and demand for emergency supplies, and the similarity among all the CIPs. On this basis, a relationship network for CIPs is defined.

3
Specifically, three questions will be answered: (a) How are the interaction effects of complex networks presented and how does network interaction affect scheduling decision? (b) How are rescue points selected under various cases based on the existing distribution of CIPs and other relief centers (RCs)? (c) How can the total emergency operating cost be minimized to meet the demand?
This study presents the formal modeling of large scheduling portfolios for different disaster scenarios by introducing super network theory, which has been applied to express knowledge networks, logistics networks, and emergency management (Nagurney et al. 2002;Zhao et al. 2017;Zhu and Cao 2012). Compared with other research tools, the advantage of applying super network theory to solve the problem of cross-regional emergency resource scheduling is that the properties of other dimensions can be mapped onto the benchmark attribute network structure under the premise of selecting the optimal resource allocation to achieve the goal of overall highly efficient rescue operation. Super network theory is one of the most appropriate methods used to address the multi-network problem (Nagurney et al. 2007). According to Nagurney et al. (2007), super network is a network with higher dimension than the average network; the properties of other dimensions can be mapped onto the benchmark attribute network structure under the premise of selecting the optimal resource allocation. It is propitious to the coordination of a regional emergency and the cooperation of multiple agents to extract representative networks from complex rescue networks. From the operational perspective, we need to determine which of the available agents should be considered in the response according to their capacity, category, proximity, and relation to the emergency site(s).
Considering the multidimensionality involved in the actual rescue process, two types of sub-networks, namely, the relationship network and resources flow network, are designed using the proposed super network theory. The resources' flow network, which can be constructed by agents and transportation paths, is common sense in emergency logistic study. The relationship network, however, the line is just an insubstantial affiliation between two relief agents. In fact, this affiliation enhanced as geographic distance decreased, and it also strengthened as similarity of industry mode, for example, the relationship between biological chemistry and petrochemical chemistry, weakened notably than that between two petrochemical industries. In comparison with single physical network, decision to deploy regional resources relied on the two networks is more realistic and reliable.
The main difference between this study and those considered for emergency logistic scheduling in previous literature is that this method involves a super network, which is combined by the relation network and resource flow network, thereby considering resource diversity and agents heterogeneity. It helps to establish a regional coordination mechanism to make resource dispatching in line with the actual situation. The remaining parts of this study are organized as follows. Section "Related work" presents the literature review on emergency scheduling models. Sections "Problem description" and "Materials and methods" formulate the problem and provide details of our modeling technique, and section "Solution approach" explains the methodology developed to solve the super network problem. Sections "Case study" and "Result" demonstrate the case study used to test the model and discuss the computational results, and finally the conclusions and the suggested possible extensions of the current work are presented in section "Discussion".

Related work
With the development of the chemical industry in China, enormous hazardous materials (i.e., toxic, flammable, or explosive substances) are inevitably involved in manufacturing processes; these materials can potentially lead to major environmental accidents, such as chemical leakage, fire, explosion, or toxic material proliferation, causing catastrophic effects and leading to heavy casualties and tremendous property losses (Georgiadou et al. 2010;Zhou and Liu 2012;Fan 2014). Research on rescue scheduling problem is abundant, and many decision models have been developed to solve various rescue scheduling problems, including the ones in the context of chemical accidents (Baser and Behnam 2020;Duan and He 2015;Li et al. 2014;Liu et al. 2017), as well as the ones for large-scale natural hazards (Wex et al. 2014), which may trigger "domino accident" -means that one disaster leads to another (Khan and Abbasi 2001). There are numerous concealed threats in CIPs because of the varieties of hazards and pollution sources that are intensively distributed in such areas.
Emergency relief network, as a logistics network, is an essential conveyor of tangible materials between suppliers and receivers and has been widely discussed in most literature (Sheu 2007;Fiedrich et al. 2000;Chang et al. 2007;Feng et al. 2020). For example, Li et al. (2014) developed a multi-objective emergency rescue model considering a single demand site and multiple supply site for allocating maritime emergency resources effectively during chemical spill or leakage accidents. The work of Horner and Downs (2010) has demonstrated a GIS-based spatial model based on the capacitated warehouse/production-distribution systems for scheduling relief goods to people in need. Du et al. (2020a, b) proposed a mathematical model considering the disaster scenarios and characteristics of emergency resources to cope with allocating and scheduling of resources for CIPs accidents. They evaluated the total number of fatalities and the amount of losses caused by domino effects as optimal objectives, and the heuristic algorithm was used to test the conducted numerical case study. Emergency cooperation had been verified as superior way to response to cross-regional emergency (Fu and Piplani 2004;Chen et al. 2016). Wang et al. (2013) indicated that existing enterprises information system cannot flexibly adapt to turbulent and dynamic environment. Green and Kolesar (2004) pointed out that regional coordination is an important development direction in the future. Evidently, Groothedde et al. (2005) demonstrated that interoperable networks of cities can effectively reduce logistics costs while maintaining service levels. Kapucu et al. (2010) suggested that the investment in community capacity at the local and state level should be increased, and the cooperation among local, state, and federal agencies of the resources should be considered. The literature addressed that various aspects of relief agent coordination are elicited attention on humanitarian relief (Hackl and Pruckner 2006;Balcik et al. 2010). Humanitarian relief environments engage many sector companies, each of which may have different interests, capacity, and logistics expertise. Typically, no single actor has sufficient resources to respond effectively to a major disaster.
Emergency scheduling coordination for chemical contingency of CIPs is a complicated task due to the diversity of pollution conditions (Liu et al. 2017). So, emergency resources scheduling is difficult to assess accurately with qualitative and quantitative information because of inherent and highly uncertainty and imprecision (Zhang et al. 2012). Fang et al. (2021) introduced entropy concept and proposes a method to process multi-source data such as satellites, hospitals, asylums, and mobile phones for improving the reliability and accuracy of forecasted demands of medical resources. A new methodology based on system management and operational research was proposed by Kourniotis et al. (2001); this method aims to improve effective chemical emergency management. Protective actions for decisionmaking in nuclear or chemical plants have been extensively recorded in the literature (Hedemann-Jensen 2004;Du et al. 2020a, b), but few studied concentrated areas with chemical risks, such as CIPs clusters. Therefore, improving existing scheduling model to accommodate the special characteristic of CIPs has more practical significance in urban areas. In addition to the flow of resources, transportation and information network exist among different agents (Fang et al. 2021). Meanwhile, the relationships between two CIPs can also be built by natural (e.g., geographical distance, grade of connecting roads) and social (e.g., similarity of stored resources, cooperation, and trade) characteristics.
Most existing studies recognize that super network theory is suitable for describing and representing different attributes (Yamada et al. 2011;Zhao et al. 2017;Zhu and Cao 2012). Nagurney et al. (2002) first applied the concept of super networks to a supply chain. In subsequent studies (Nagurney et al. 2007), they constructed a super network model to analyze interactions and relationships between the global supply chain and international financial networks. Cruz and Liu (2011) analyzed the effects of social relationship levels on a multi-stage supply chain network, in which multiple decision makers are associated at different tiers. Although there is little literature of super network on relief study, the super network method has been determined to be favorable in solving the problem of cross-regional emergency coordination.

Problem description
Without losing generality, primary relief centers (PRCs), local relief centers (LRCs), and CIPs coexist in a large region, and each agent preserves relief resources stocks and finds a balance between reducing cost and addressing potential damages. All agents will cooperate to deal with an emergency in the spirit of humanitarianism. Every CIP may suffer an unexpected disaster. Once a contingency outbreak at a CIP, it becomes the demand point in the network, whereas other emergency agents become rescue points or transfer points, depending on their relationship to the demand point. As shown in Fig. 1, the emergency relief network of a certain region consists of rescue points, transfer points, and demand points.
The current work solves the dispatching and cooperation problem when a major accident occurred at some CIPs in reginal. Similar to the sequence of events for standard emergency medical system calls discussed by Fitzsimmons (1973), Fig. 1 depicts the process of a two-level supply chain network for CIPs. The first level is related to the processing of LRCs, unaffected CIPs play the part of rescue points and provide relief resources to demand points, and the second level involves two routines, the establishment of PRCs and other unaffected CIPs as rescue points directly to demand points or indirectly deliver resources to transfer points. For small-scale disasters, the first level of relief system starts with directly transportation to affected CIPs; the suppliers are selected from LRCs and unaffected CIPs. If a calamity is particularly serious, the rescue cover of first level may be insufficient to satisfy the demands and to support all emergency logistics operation. At this point, the second level relief system is implemented; more PRCs, LRCs, and unaffected CIPs are involved in the emergency relief network considering the relationship loosely.
Our analytical model makes several key assumptions that are predicated upon the real-life operation of emergency resource scheduling when disasters occurred at CIPs. This study focuses on a resource scheduling problem in which the demand points and supply points are not fixed and multitype relationships are existed. We assume that LRCs can be 1 3 selected as rescue or transfer points within a region, but PRCs and unaffected CIPs can only be candidate sets for rescue points. In addition, taking into account the diversity of materials, each demand point k requires two types of resources in this context: professional relief supplies (e.g., firefighting equipment and life-saving/defending equipment) and daily necessities (e.g., drinking water, food). Moreover, there is a little difference of context of relief for CIPs from the general relief scheduling problem; that is, all points in the region have resources stocks including CIPs themselves, such that they may become rescue points. Particularly, the reserved resources of a park can meet a part of needs under emergency.

Modelling emergency resource scheduling based on super network
From the operational perspective, we need to determine which of the networks should be considered in the relief process. According to the "Related work section" and the multidimensionality involved in the actual rescue process, two types of sub-networks, namely, the logistics network and relationship network, are proposed. Logistics network is a resource flow network which acts as the first sub-network. In this way, the basic nodes, lines, and spatial structure are constructed. The question that comes with is what affects the resources dispatching between two nodes of logistics network. Notably, there are still many factors that include but not limited to spatial accessibility of from origin to destination, demand for resources of each disaster locations, available supplies, and so on. So a "relationship network" is proposed and alliance with logistics network to develop a super network nested structure. The relationship network means a network composed of nodes and their relations that specifically embodied as spatial distance and similarity of reserved resources in this model.
The constructed super network is shown in Fig. 2, where the solid line in the resource flow network shows the amount of delivery resources between two emergency agents and the solid line in the relationship network shows the degree of social relationship between two emergency agents. The points linked by one dotted line indicates that they are the same one but means different in the two networks.

Parameters
N All emergency subjects within in region.
U All CIPs within in region. P All primary relief centers within region. L All local relief centers within region.

Other variables
In this model, the objective function (1) minimizes the total cost across rescue points j to demand points k in a network. The objective is to associate the quadratic function with resource flow and relation networks. This choice of objective function is justified by the characteristics of a super network.
As mentioned above, the emergency resource scheduling of CIPs for large emergencies exhibits an evident interrelationship among the emergency subjects in the entire scheduling network, which is denoted as r ab in this model. In general, the distance between emergency subjects is inversely proportional to the amount of resource scheduling, whereas the similarity of reserved resources ( S ij ) among subjects is positively related to scheduling quantity. Assume that the weight of the distance is w in the "relationship". Thus, the relationships among points are shown in Formula (3).

Decision process
This paper aims to solve the scheduling problem of emergency resources for disasters of different scales of CIP and sets trigger thresholds to judge how the two-level disaster relief system responds to small-scale and large-scale disasters. If the affected points cannot afford the relief demand on their own, i.e., d kh − A kh ≥ 0 , then the emergency plan starts first level of relief system for a small-scale emergency scheduling mode ( 1 = 1 ). Furthermore, if demand exceeds the capacity of the selected rescue point, that is, if the second level is triggered, i.e., 2 = 1 , then each demand point may receive resources from subjects in the second level I . PRCs will participate in the relief work in any large-scale disaster considering humanitarian reasons. Let P ⊆ I . Then, all emergency subjects may be selected, and the process is shown in Fig. 3.

The first level
This is subject to the following sets of constraints: In this model, the objective function (4) minimizes the total cost of the first level across rescue points j to demand points k in a network. The constraint set (5) controls the extent of resource transportation limited by road capacity. The constraint set (6) ensures that the total amount of resources delivered to demand point k should meet the requirements. The constraint set (7) implements the conservation of the types of relief materials. The constraint set (8) imposes non-negativity.

The second level
This is subject to the following sets of constraints: The objective function (9) is added directly and indirectly to the scheduling process: the cost of transporting resources from i to j and to demand point k . The structure of the objective function is quadratic. The constraint set (10) controls resource transportation quantity, which is limited by road capacity. The constraint set (11) controls resource delivery to j and k , which is limited by the resources stored at i . The constraint set (12) indicates that the source of relief supplies delivered by j should exceed its thresholds, including its own reserves A j and that transported by i . The constraint set (13) ensures that the total amount of resources delivered to demand point k should (7) ∑ h q jkh = q jk , forallh ∈ H, j ∈ J, k ∈ K satisfy its demand. Similarly, the constraint set (14) implements the conservation of the types of relief supplies, and the constraint set (15) imposes non-negativity.

Solution approach
Variational inequality problem The model constructed above is a convex optimization problem with objective function continuity, and the convex optimization problem has the equivalent conversion relation to the variational inequality problem (VIP). VIP is regarded as an important tool for studying super networks (Nagurney et al. 2002;Raciti 2004), so the abovementioned convex optimization model is transformed into equivalent VIP to solve.
Assuming that there is a point X * ϵK to meet: Then, it holds that X * is a solution of VI: where ∇F(X * ) denotes the gradient of F(•) to the respective components of X , i.e., Convert the established small-scale model, we obtain: where K = {(q jkh , jk , k )|q jkh ≥ 0, ∀j, k} and satisfy K = {(q jkh , jk , k )|u 1 > q jkh ≥ 0; jk ≥ 0;u 3 ≥ k ≥ 0} Convert the established large-scale model, we obtain: ∀i, j, k} and satisfy.
, where {u 1 , u 2 , u 3 } are constants, so F(X) in the VIP(F, K) is a convex function, monotonic and continuous can be guided. It can also prove that the second derivative is bounded, according to the differential mean theorem, that there is a Lipschitz constant ≥ 0 , make it: When the VIP is monotonic and Lipschitz continuous, then the solution of VIP exists and is unique.

Modified projection algorithm
The modified projection algorithm is a new algorithm based on the projection algorithm, which is more rapid to find the solution and more closely compared with the projection algorithm logic. Algorithm is described as follows: , and L is a Lipschitz constant. The specific iteration steps are as follows: S T E P 1 : I n i t i a l i z e . A s s u m e that:X 0 = (q 0 S T E P 2 : ) ∈ K find the solution of the function:

Case study
A specific site in the Pearl River Delta region in China is selected as the study area. This region, located in the central and southern parts of Guangdong Province, adjacent to Hong Kong and Macao, is known as China's "South Gate". The Pearl River Delta region includes Guangzhou, Shenzhen, and nine other cities, as shown in Fig. 4a. A statement from the "Coordinated Development Plan for Urban Agglomeration in the Pearl River Delta (2004-2020)" indicates that the region has a total population of 42.3 million and covers a total land area of 41,698 km 2 . Various types of highly developed CIPs are concentrated in the Pearl River Delta due to its geographic particularity. We select 10 points, namely, 1 PRC, 2 LRCs, and 7 CIPs, as shown in Fig. 4b.
To facilitate the subsequent expression, we assign a number to each agent as shown in Fig. 1. The pentagram represents the PRC, which is located in Guangzhou; the diamond represents the LRCs in Foshan and Guangzhou; and the other 7 triangles represent the CIPs. The cost function in this section is set in the following form: The required simulation data are standardized to facilitate calculation. The relationship and road capacity among the points are shown in Tables 1 and 2, respectively.
In the model proposed in this work, different scales of disasters will require different rescue points to engage in disaster relief; that is, implementing first level or second level relief system will depend on the disaster scenarios. Thus, in the simulation experiment presented in this section, two cases are presented for testing. Case 1 is small-scale emergency, in which resource demand is lower than that in case 2, which is a large-scale disaster. Unlike in a general emergency scheduling situation, all points have reserves involved in the network under the context of a CIP emergency. The relief resources are assumed to be divided into two categories: daily necessities and professional supplies. The data shown in Table 3 include the demand for resources of the two cases in affected CIPs (assuming that points 5, 6, and 7 suffered from an emergency).

Result
We apply the variational inequality of the modified projection algorithm proposed in "Solution approach" section to simulate the model of emergency resource scheduling is conducted by MATLAB. In case 1, the affected CIPs (demand points) and closely related points can satisfy the demand, and the flow of shipped resources are relatively small; hence, only a few rescue points participate in the relief network. The calculation result is presented in Table 4. In case 2, a large-scale emergency occurs, and considerable demands have to be met. The situation becomes more complicated due to the coordination and interaction among emergency subjects. The first-echelon and second-echelon scheduling results are presented in Table 5 and Table 6, respectively.
The difference in disaster scale results in a significant variation between selected suppliers and flow of rescue 1 3 resources. In case 1, the material demand for each point is the least, and thus, some subjects do not participate in the network. In case 2, the PRC, LRCs, and all unaffected CIPs within a region become members of the relief network to contribute to emergency scheduling work. In two cases, the unaffected CIPs play a very critical role during emergency response, and only a small part of emergency resources came directly from LRC and PRC.
We consider the relationship among emergency subjects in the proposed super network. Thus, making a thorough inquiry "relationship" work to affect the scheduling process will be interesting. To this end, we observe changes in resource flow and total cost by changing the relationship of a specific path under a disaster scenario. Graphs 5, 6 and 7 present each path in the super network and depict the trends of flow and total cost with an increase in path relationship. For agent 1 (Zhaoqing), when its relationship with an affected agent increases, the flow of delivered resources also increases, whereas total cost decreases. For agent 8 (Foshan), when the relationship of paths 8-7 (Foshan to Jiangmen) increases, the total cost decreases significantly faster than those of paths 8-5 and 8-6. For agent 9 (Guangzhou),     Type q 1,5 q 1,6 q 1,7 q 4,5 q 4,6 q 4,7 q 8,5 q 8,6 q 8,7 q 9,5 q 9,6 q 9,7 q 10,5 q 10,6 q 10,7 1 3 when the relationships among paths 9-5, 9-6, and 9-7 are strengthened, the total cost surprisingly increases, and the transferred resources also increase. From the simulation results, we can determine the key paths in the network that contribute to improve rescue effectiveness for practical applications. The development of the relationship between agent 9 (LRC located in Guangzhou) and other CIPs will increase cost, thereby implying that agent 9 is unsuitable for delivering supplies to demand points, at least for agents 5, 6, and 7. By contrast, for Shenzhen (agent 4), strengthening its relationship with agent 7 (Jiangmen) will significantly decrease cost. These results may enlighten managers to adjust their strategies and optimize external relationships with others to achieve the global optimum.
Moreover, we discuss the sensitivity analysis of retention factor of disaster points, as shown in Fig. 8. The total relief cost for agent 6 (Zhongshan) decreases linearly with an increase in retained resources; however, the cost for agent 7 (Jiangmen) and agent 5 (Zhuhai) drops off a cliff when the retention factor approaches 0.2. Evidently, the slack resources of agent 5 and agent 7 after the disaster can greatly reduce the reginal rescue cost. Therefore, it is a wise strategic plan to improve the emergency resources reserves and resilience of Zhuhai and Jiangmen.

Discussion
This work proposed a new mathematical programming approach for the selection of a supply portfolio in a relief supply chain by considering heterogeneity and relationships among CIPs. The well-established resources allocation and scheduling models in post-disaster relief management need to be improved for concentrated CIPs areas. In this work, we construct a super network model for supporting emergency logistics operations in response to large regional natural hazards or chemical accidents.
In the comparison of results of case 1 and case 2, we can find that peer support is the main rescue force after the disaster, which greatly reduces total rescue costs. Therefore, for high-risk agents such as CIPs, it is more reliable and effective to establish a coordinated and joint emergency response mechanism between the parks than relying on local government rescue centers. A lack of coordination among relief agents has been shown to increase inventory costs, extend delivery times, and impair customer service (Simatupang et al. 2002). The proposed super network model of emergency dispatching for CIPs helps the identification of key nodes and edges in an emergency network, which provide a scientific basis for cooperation among CIPs to make emergency scheduling better in responding to cross-regional disasters. In specific applications, by simulating all kinds of disaster events, CIPs can make an optimal emergency logistics planning (optimal types and quantities of resources and optimal distribution route) that improve the relief efficacy.
The main contribution of this research is that the proposed two-level emergency dispatch model based on the super network not only considers the physical distance, but also considers the relationship distance between different subjects, which provides a scientific basis and feasible for the park's regional emergency cooperation. plan. The simulation results confirm that the model can adapt to different disaster scenarios flexibly. A relief system associated with rescue points is automatically selected by identifying the degree of disaster and the amounts of resources required.
In terms of management practice of emergency relief management, established flow-relationship super network in this paper can be a creative method benefits from commercial practices by coordinating stakeholders' relationship, which allow CIPs reserve different and partial resources but get sufficient relief supplies when suffered a huge disaster. Relief agents often fail to make the effort, or simply find it too difficult to collaborate, but for CIPs, they are all potential affected areas; a matter of course, they have incentive to collaborate with each other and may only pay a relatively small cost. The problem of coordination of resource and information flows within and across chain members has been widely addressed in the commercial supply chain (Lee 2000), but this mechanism is not feasible for emergency logistics (Balcik et al. 2010). Therefore, the proposed method is expected not only to aid the design of a suitable emergency scheduling supply network but also to provide recommendations on resource allocation and the establishment of relationships within a network. 1 3 Considerable potential exists to improve the performance of the proposed method. First, the settings of the objective function are worthy of further research. Relief goal should consider other performance indexes, such as transportation time or crowd evacuation (Liu et al. 2021), which is important in emergency scheduling because of the urgency of rescue in CIPs. Second, the quantification of the social relationship is also worth exploring. On the one hand, if the rescue points are selected through the shortest path, which may make the resource traffic beyond the capacity limit caused by congestion, then the actual geographic distance increases. On the other hand, a high similarity of reserved resources is not a good relationship for some required special supplies. Future research can discuss different relationship among CIPs with various types of resources. Finally, another potential area for future research deals with the issue of information availability and accuracy. We are aware of the limitations of our approach in terms of dealing with multiple heterogeneous big data (Fang et al. 2014;Yin et al. 2021). The answers to such questions will contribute importantly to emergency scheduling management in the future.
Funding The writing of this article was supported by the National Natural Science Foundation of China, 72174218.

Data availability
The datasets analyzed during the current study are variability from the corresponding author on reasonable request. Fig. 7 The flow and total cost change with social relationship between LRC 9 (Guangzhou) and demand points. (a) path 9-5, (b) path 9-6 and (c) path 9-7.