# Research of Vulnerability for Fresh Agricultural-Food Supply Chain Based on Bayesian Network

Authors: Juan Yang; Haorui Liu
Journal: Mathematical Problems in Engineering
 (2018)

---

## Abstract

Unbalanced supply and demand, bottleneck of transport capacity, seasonal cycle, and other factors lead to fragile supply chain of fresh agricultural products led by the platform, impeding smooth operation of the supply chain and even causing disruption risk. This paper studies the short-term and long-term vulnerability of the platform leading fresh agricultural product supply chain under the influence of logistics capital flow and information flow, defines its structure and the meaning of its vulnerability, analyzes the vulnerability of each link, and finds out the existing weak links in the supply chain through empirical research. The probability of accident is quantitatively analyzed by using the Bayesian Network. Firstly, the bow-tie model is used to identify the cause and consequence of the accident, and then it is transformed into the Bayesian Network model; then, the “Precursor Incident” information and prior probability are introduced to derive the posterior accident occurrence probability, and the probability of accident occurrence changing with time is quantitatively analyzed; finally, the dynamic risk calculation of fresh agricultural product trading center dominated by a certain platform was carried out. The results show that, with the increase of supply chain operation time and Precursor Incident, the probability of short-term supply chain vulnerability and accident risk present a significant increase trend, while the probability of long-term supply chain vulnerability and accident risk present a significant decrease trend. Therefore, it is suggested that enterprises should establish a dynamic risk evaluation system to monitor and predict the probability of event vulnerability, pay attention to “Precursor Incident,” and take measures to reduce it, such as effective integration of supply chain principal information, timely improvement of information integrated technologies, and comprehensive training on food safety and moral credibility.


---

## Body

## 1. Introduction

The perishability, nonstandard, seasonal, regional, and periodicity of fresh agricultural-food (FAF) is different from the particularity of industrial products, and the degree of organization of agricultural production and logistics operation is too low, the degree of information integration is not high, the cold chain infrastructure is weak, and the quality traceability system is lacking, resulting in the shortage of supply chain system of fresh agricultural products in China [1].The circulation of fresh agricultural products not only involves the survival of hundreds of millions of farmers, but also relates to the quality of life of the masses, and has become a social hot issue concerning the national economy and the people’s livelihood. At present, the development of the supply chain model of fresh agricultural products based on market platform in China is rooted in the macro background of Chinese agriculture. Summary of literature on supply chain vulnerability is listed in Table1.Table 1
Summary of literature on supply chain vulnerability [3–7].
Keyword Research contents Author Vulnerability of supply chains The concept was first put forward as a kind of “random disturbance” Svessen, 2006 The concept of distinguishing between supply chain vulnerability and risk Juttner, 2003 Identify supply chain risk and create flexible supply chain Waters, 2007 Review the meaning of supply chain vulnerability Briano, 2009  Factors affecting vulnerability Unpredictability and uncertainty of supply and demand Christopher Including war, strike, and other external motivations Colema, 2006 External vulnerability drivers such as complexity and uncertainty of demand forecasting Edmund, 2001 Selection and supply risk management among different suppliers Micheli, 2008 Response mechanism of external supply chain risk Suresh 7 factors including globalization of supply chain and fluctuation of demand, and propose 3P management principles Ning Zhong The prevalence of OEMs, the decrease in the number of suppliers, etc. Liu Xilong The increasing trend of supply chain management and the effect of uncertainty risk on supply chain Liu Yanping Methods to reduce supply chain risk such as multi-purchasing and robust supply chain construction Chen Changbin Impact of complex environments Du Zhiping  Industry supply chain productability Node importance, supplier quality and production synergy efficiency Yu Kunpeng Agricultural products Analyzing the causes of supply chain maladjustment of agricultural products, establishing strategic partnership, information sharing and perfecting benefit distribution mechanism. Du Zhao Wei, Liu Shunyi, 2007 coal Using Fault Tree Analysis Method and Bayesian Network Model to calculate the network parameters of supply chain vulnerability Liu Jia, Shi Liwei, 2016


### 1.1. Characteristics of China’s Platform Dominated Fresh Agricultural Products Supply Chain

China’s fresh agricultural product circulation system is different from the European and American countries’ agricultural product supply chain. The former needs to undertake the function of horizontal cross-regional material allocation and faces a larger consumer market, while the latter has obvious blockization characteristics, and there is a lack of tight connectivity between blocks. The agricultural products wholesale trading platform with extensive participation has a high flexibility to adjust the supply and demand of agricultural products, and the platform-driven (PD) mode has more value-added services and development potential. Therefore, the smooth operation of the platform-led fresh agricultural product supply chain (referred to as “PD-FAF-SC”) has far-reaching significance for ensuring the sustainable development of China’s fresh agricultural products circulation and related industries.The vulnerability of FAF-SC is mainly reflected in the following aspects: first is the fragility of cooperative relationship. As a supplier, the farmers usually adopt a random way to establish cooperative relations with the platform enterprises, the cooperative relationship is unstable, and the quantity and quality of agricultural products supply are always confronted with interference and fluctuation. The second is the vulnerability of natural factors. Agricultural products are greatly affected by the production environment; natural disasters easily break the FAF-SC. Third is the fragility of the transportation system. At present, there exist certain contradictions between the diversity and uncertainty of demand for fresh agricultural products and regional characteristics of production, the imperfection of modern logistics system, and the biological properties of fresh agricultural products (high water content, short shelf life, perishable, etc.), and circulation transactions between different regions put forward higher requirements for transportation efficiency and preservation conditions. Fourth, restricted by the natural production time and seasonal characteristics of agricultural products, there is a delay between decision-making information and production cycle, which increases the production risk and affects the stability of FAF-SC and agricultural product market.With the rapid development of China’s fresh agricultural products industry, FAF-SC is not only a product material chain connecting suppliers, producers, and consumers, but also a process of processing, packaging, and transportation of fresh agricultural products in the supply chain. The value-added chain increases its value; the continuous extension of the chain increases the probability of risk occurrence and increases the vulnerability.At present, researches on dynamic evaluation of supply chain vulnerability are concentrated, but in the selection of vulnerability index and the comprehensive dynamic resilience analysis, in the process of evaluation, the selection of vulnerability status monitoring index is easily influenced by subjectivity, and the quantification of index also depends on the knowledge and experience of valuator, resulting in poor objectivity of evaluation results. In addition, in the mathematical method applied by comprehensive elastic dynamic evaluation, the dynamic impact of potential vulnerability in supply chain management on the resilience of supply chain is not taken into account. In the process of supply chain management, vulnerability event and security event are collectively referred to as “Precursor Incident,” which is an effective indicator to predict the possibility of risk occurrence [2]. As evidence information in Bayesian networks, “Precursor Incident” is used to calculate dynamic vulnerability.Therefore, this paper takes into full consideration the dynamic impact of Precursor Incident on vulnerability, introduces bow-tie model and Bayesian Network (hereinafter referred to as BN) model, and establishes a dynamic vulnerability evaluation model. Taking the accident scenario of the platform-dominated fresh agricultural product supply chain as an example, the dynamic change trend of vulnerability with time is analyzed, and the reduction of the vulnerability is sought to improve the effective measures of the supply chain resilience.


### 1.2. Theoretical Model of PD-FAF-SC Vulnerability Assessment

On the basis of the research mentioned in Table1, this study uses Bayesian network for quantitative analysis and builds the model as shown in Figure 1.Figure 1
Theoretical model of PD-FAF-SC vulnerability assessment.Figure1 shows that the vulnerability assessment of the traditional fresh agricultural products trading platform is mainly based on the transaction data of the trading platform, such as supply and demand status, the number of registered trading members, the history of transaction accidents, the loss rate, and the transaction amount. Because of the restriction of less dimension and small coverage group, it is difficult to evaluate the vulnerability of FAF-SC accurately by trading platform data. The PD-FAF-SC vulnerability assessment under big data uses other relevant data on the supply chain platform to innovate the defects of traditional evaluation system. In addition to supply and demand data, PD-FAF-SC vulnerability indicators under big data also make use of natural disasters on supply chain platform, climate change, agricultural production factors, market platform infrastructure and management, cold chain logistics, supply and marketing models, relevant industry policy information, and the bullwhip effect of the supply chain to cross-reproduce the vulnerability of PD-FAF-SC.Based on previous research experience, this paper adds platform management information that can affect the PD-FAF-SC vulnerability assessment status, such as transaction cycle, test data, food mileage, information security traceability of information, and expected loss to evaluate the vulnerability status of the platform’s FAF-SC. Multidimensional data can intersect the vulnerability of PD-FAF-SC, but it also complicates the operation. The improper evaluation model can easily lead to the distortion of evaluation results due to the interference of “data noise.” The existence of “black box” requires the selection of appropriate PD-FAF-SC vulnerability assessment method.A quantitative model is analyzed for calculating the vulnerability of PD-FAF-SC under the influence of logistics, capital flow, and information flow. This paper first proposes the structure of the upper, middle, and lower reaches of PD-FAF-SC. The combination of fault tree and Bayesian network is used to analyze the short-term and long-term vulnerability of the supply chain to obtain the risk transfer process and its influencing factors and quantitatively calculate the results and through the empirical research to find out the weak link of PD-FAF-SC [8].The Bayesian network can completely describe the substitution of conditional probability to logic gate. The application of conditional probability method can make full use of the historical data and the prior probability of PD-FAF-SC to improve the accuracy of vulnerability. Using Bayesian network quantitative methods to analyze the vulnerability of PD-FAF-SC is more helpful to analyze the weak links in the actual operation while conducting in-depth research on the influencing factors and risk transmission links of its operation mechanism and vulnerability. Some reasonable suggestions are put forward to solve the problems such as unbalanced supply and demand of fresh agricultural products, and difficulties in continuous supply under seasonal consumption peaks or emergency management conditions caused by information asymmetry, natural disasters, food safety, etc.


## 1.1. Characteristics of China’s Platform Dominated Fresh Agricultural Products Supply Chain

China’s fresh agricultural product circulation system is different from the European and American countries’ agricultural product supply chain. The former needs to undertake the function of horizontal cross-regional material allocation and faces a larger consumer market, while the latter has obvious blockization characteristics, and there is a lack of tight connectivity between blocks. The agricultural products wholesale trading platform with extensive participation has a high flexibility to adjust the supply and demand of agricultural products, and the platform-driven (PD) mode has more value-added services and development potential. Therefore, the smooth operation of the platform-led fresh agricultural product supply chain (referred to as “PD-FAF-SC”) has far-reaching significance for ensuring the sustainable development of China’s fresh agricultural products circulation and related industries.The vulnerability of FAF-SC is mainly reflected in the following aspects: first is the fragility of cooperative relationship. As a supplier, the farmers usually adopt a random way to establish cooperative relations with the platform enterprises, the cooperative relationship is unstable, and the quantity and quality of agricultural products supply are always confronted with interference and fluctuation. The second is the vulnerability of natural factors. Agricultural products are greatly affected by the production environment; natural disasters easily break the FAF-SC. Third is the fragility of the transportation system. At present, there exist certain contradictions between the diversity and uncertainty of demand for fresh agricultural products and regional characteristics of production, the imperfection of modern logistics system, and the biological properties of fresh agricultural products (high water content, short shelf life, perishable, etc.), and circulation transactions between different regions put forward higher requirements for transportation efficiency and preservation conditions. Fourth, restricted by the natural production time and seasonal characteristics of agricultural products, there is a delay between decision-making information and production cycle, which increases the production risk and affects the stability of FAF-SC and agricultural product market.With the rapid development of China’s fresh agricultural products industry, FAF-SC is not only a product material chain connecting suppliers, producers, and consumers, but also a process of processing, packaging, and transportation of fresh agricultural products in the supply chain. The value-added chain increases its value; the continuous extension of the chain increases the probability of risk occurrence and increases the vulnerability.At present, researches on dynamic evaluation of supply chain vulnerability are concentrated, but in the selection of vulnerability index and the comprehensive dynamic resilience analysis, in the process of evaluation, the selection of vulnerability status monitoring index is easily influenced by subjectivity, and the quantification of index also depends on the knowledge and experience of valuator, resulting in poor objectivity of evaluation results. In addition, in the mathematical method applied by comprehensive elastic dynamic evaluation, the dynamic impact of potential vulnerability in supply chain management on the resilience of supply chain is not taken into account. In the process of supply chain management, vulnerability event and security event are collectively referred to as “Precursor Incident,” which is an effective indicator to predict the possibility of risk occurrence [2]. As evidence information in Bayesian networks, “Precursor Incident” is used to calculate dynamic vulnerability.Therefore, this paper takes into full consideration the dynamic impact of Precursor Incident on vulnerability, introduces bow-tie model and Bayesian Network (hereinafter referred to as BN) model, and establishes a dynamic vulnerability evaluation model. Taking the accident scenario of the platform-dominated fresh agricultural product supply chain as an example, the dynamic change trend of vulnerability with time is analyzed, and the reduction of the vulnerability is sought to improve the effective measures of the supply chain resilience.


## 1.2. Theoretical Model of PD-FAF-SC Vulnerability Assessment

On the basis of the research mentioned in Table1, this study uses Bayesian network for quantitative analysis and builds the model as shown in Figure 1.Figure 1
Theoretical model of PD-FAF-SC vulnerability assessment.Figure1 shows that the vulnerability assessment of the traditional fresh agricultural products trading platform is mainly based on the transaction data of the trading platform, such as supply and demand status, the number of registered trading members, the history of transaction accidents, the loss rate, and the transaction amount. Because of the restriction of less dimension and small coverage group, it is difficult to evaluate the vulnerability of FAF-SC accurately by trading platform data. The PD-FAF-SC vulnerability assessment under big data uses other relevant data on the supply chain platform to innovate the defects of traditional evaluation system. In addition to supply and demand data, PD-FAF-SC vulnerability indicators under big data also make use of natural disasters on supply chain platform, climate change, agricultural production factors, market platform infrastructure and management, cold chain logistics, supply and marketing models, relevant industry policy information, and the bullwhip effect of the supply chain to cross-reproduce the vulnerability of PD-FAF-SC.Based on previous research experience, this paper adds platform management information that can affect the PD-FAF-SC vulnerability assessment status, such as transaction cycle, test data, food mileage, information security traceability of information, and expected loss to evaluate the vulnerability status of the platform’s FAF-SC. Multidimensional data can intersect the vulnerability of PD-FAF-SC, but it also complicates the operation. The improper evaluation model can easily lead to the distortion of evaluation results due to the interference of “data noise.” The existence of “black box” requires the selection of appropriate PD-FAF-SC vulnerability assessment method.A quantitative model is analyzed for calculating the vulnerability of PD-FAF-SC under the influence of logistics, capital flow, and information flow. This paper first proposes the structure of the upper, middle, and lower reaches of PD-FAF-SC. The combination of fault tree and Bayesian network is used to analyze the short-term and long-term vulnerability of the supply chain to obtain the risk transfer process and its influencing factors and quantitatively calculate the results and through the empirical research to find out the weak link of PD-FAF-SC [8].The Bayesian network can completely describe the substitution of conditional probability to logic gate. The application of conditional probability method can make full use of the historical data and the prior probability of PD-FAF-SC to improve the accuracy of vulnerability. Using Bayesian network quantitative methods to analyze the vulnerability of PD-FAF-SC is more helpful to analyze the weak links in the actual operation while conducting in-depth research on the influencing factors and risk transmission links of its operation mechanism and vulnerability. Some reasonable suggestions are put forward to solve the problems such as unbalanced supply and demand of fresh agricultural products, and difficulties in continuous supply under seasonal consumption peaks or emergency management conditions caused by information asymmetry, natural disasters, food safety, etc.


## 2. Description of PD-FAP-SC Supply Chain Vulnerability Model

Part of fragile factors such as extreme weather and natural disasters in PD-FAF-SC has the characteristics of short-term and rapid risk transmission, which has a deep impact on the upstream, middle, and lower reaches of the supply chain and factors such as economic crisis have a significant and substantive impact on the long-term vulnerability of supply chain. According to the characteristics of PD-FAF-SC, this paper analyzes the short-term and long-term vulnerability to reflect the objectivity and scientific of the research.


### 2.1. Description of Short-Term Vulnerability Model

The short-term vulnerability description of PD-FAF-SC affected by risk factors in a short period of time will occur in the calculation of the probability of operating imbalance or even local fracture. The process of vulnerability transmission is as follows: the upstream link mainly includes farmers and fresh agricultural products circulation processing enterprises and fresh agricultural products suppliers/primary purchasers; since more than 70% of the downstream demand structure of fresh agricultural products is retail, the retail demand for fresh agricultural products has a great impact on supply chain [9]; the middle and lower reaches of the supply chain are simplified as follows: trading market, logistics enterprises, downstream distributors, and retailers of fresh agricultural products; the platform is the main bottleneck of FAF-SC, in which the transfer function connects all the upstream and downstream links.


#### 2.1.1. Upstream Planting Links

In the upstream planting process, farmers or enterprises of different forms of fresh agricultural products are included. The strong seasonal fluctuations in the prices of raw materials have been the prominent factors restricting the healthy operation of the fresh agricultural products industry in China in recent years. The failure of farmers’ production decision and the difficulty of raising agricultural resources will also cause a great negative impact on the short-term supply chain and even lead to the sudden interruption of the chain.Agricultural production has a strong dependence on natural conditions. The external environmental risk factors of short-term supply chain include insect disasters, animal and plant epidemics, drought, and other natural disasters [10]. The abuse of production materials such as pesticides, chemical fertilizers, and hormones in the production process of farmers, the risk of production pollution caused by the destruction of cultivated land, and water resources seriously affect the resilience of the supply chain. Events such as lean meat powder, melamine milk powder avian influenza, blue ear disease (PRRS), and banana black poisoning have all exposed the huge risks in the production of fresh agricultural products in China.


#### 2.1.2. Midstream Circulation Links

Cold-chain transportation and platform-oriented and cold-chain distribution are all sublinks of PD-FAF-SC midstream circulation. Meteorological disasters have the greatest restriction on land cold chain transportation, while the cold chain technology and equipment are not mature, the logistics infrastructure is relatively backward, and the transportation organization is not good that causes the fresh agricultural products to not be delivered in time and quality, resulting in a certain degree of harm to the supply chain. In the platform-oriented aspect, the deviation of goods source or scheduling error caused by organization and management errors occurred frequently, and the mismatch between food mileage and cold chain logistics facilities, due to poor communication of information, which leads to platform-led transaction disputes and increases the internal management cost of the platform transaction, hinders the operation of the midstream supply chain, resulting in the phenomenon that agricultural products are stranded and stored, rot is difficult to resell, and the loss rate is high. Short-term supply chain risks include logistics risks and lack of integrity of operators.


#### 2.1.3. Downstream Consumption Links

The consumption of fresh agricultural products is greatly affected by natural and environmental conditions. The short-term supply chain demand risk comes from sudden changes in customer demand. The main influencing factors are price fluctuations, scientific and technological progress, quality and safety rumors, etc., resulting in the disruption of the entire supply chain.


### 2.2. Description of Long-Term Vulnerability Model

Different from the short-term supply chain, some influencing factors may lead to the probability of partial interruption of FAF-SC in a foreseeable and long period of time. According to the scale of the enterprise, the corresponding risk degree, and the environment, the long-term PD-FAF-SC divides the upstream planting link into the large-scale fresh agricultural product planting leading enterprises and the small- and medium-sized fresh agricultural product planting farmers. For the downstream link of the supply chain, in addition to terminal retail, high-value-added food processing enterprises also have a significant demand for fresh agricultural products.


#### 2.2.1. Upstream Planting Links

At present, the scale of fresh agricultural products planting enterprises or farmers in China is on the low side due to the asymmetry of information, and the low degree of organization and industrialization, the production arrangement of farmers has great blindness and the increased market risks. For the small- and medium-sized farmers, affected by the circulation and processing equipment of fresh agricultural products, it is difficult for them to switch their production. Once the risk occurs, it is difficult to enter and exit quickly, which to a certain extent increases the management risk of small- and medium-sized fresh farm produce farmers. China’s fresh agricultural products have a bumper harvest, and the slow sales have become a common phenomenon, which appears almost every year, but only in the reincarnation of varieties, which exposes the huge problem of circulation of fresh agricultural products in China.


#### 2.2.2. The Midstream Circulation Links

The long-distance transportation of Chinese fresh agricultural products and the imperfect characteristics of cold chain transportation facilities hinder the transportation of fresh agricultural products and restrict the development of fresh agricultural products industry for a long time. The low level of informatization of China’s fresh agricultural product market platform affects the sustainable development of long-term PD-FAF-SC. The high investment cost of the platform, the long construction cycle, the high technical requirements of data and information integration, and the inaccurate prediction of cold-chain logistics enterprises are the prominent features of PD-FAF-SC and face certain operational risks.


#### 2.2.3. Downstream Demand and Terminal Consumption Links

From the downstream perspective, affected by the domestic macroscopic control, supply-side reform, and the development of e-commerce, the downstream demand and end-consumption structure of fresh agricultural products have undergone major changes, and the bullwhip effect has increased. Although the terminal direct retailing is still the main consumption mode of fresh agricultural products in China, the green deep processing industry of agricultural products has developed rapidly under the influence of national favourable policies.


## 2.1. Description of Short-Term Vulnerability Model

The short-term vulnerability description of PD-FAF-SC affected by risk factors in a short period of time will occur in the calculation of the probability of operating imbalance or even local fracture. The process of vulnerability transmission is as follows: the upstream link mainly includes farmers and fresh agricultural products circulation processing enterprises and fresh agricultural products suppliers/primary purchasers; since more than 70% of the downstream demand structure of fresh agricultural products is retail, the retail demand for fresh agricultural products has a great impact on supply chain [9]; the middle and lower reaches of the supply chain are simplified as follows: trading market, logistics enterprises, downstream distributors, and retailers of fresh agricultural products; the platform is the main bottleneck of FAF-SC, in which the transfer function connects all the upstream and downstream links.


### 2.1.1. Upstream Planting Links

In the upstream planting process, farmers or enterprises of different forms of fresh agricultural products are included. The strong seasonal fluctuations in the prices of raw materials have been the prominent factors restricting the healthy operation of the fresh agricultural products industry in China in recent years. The failure of farmers’ production decision and the difficulty of raising agricultural resources will also cause a great negative impact on the short-term supply chain and even lead to the sudden interruption of the chain.Agricultural production has a strong dependence on natural conditions. The external environmental risk factors of short-term supply chain include insect disasters, animal and plant epidemics, drought, and other natural disasters [10]. The abuse of production materials such as pesticides, chemical fertilizers, and hormones in the production process of farmers, the risk of production pollution caused by the destruction of cultivated land, and water resources seriously affect the resilience of the supply chain. Events such as lean meat powder, melamine milk powder avian influenza, blue ear disease (PRRS), and banana black poisoning have all exposed the huge risks in the production of fresh agricultural products in China.


### 2.1.2. Midstream Circulation Links

Cold-chain transportation and platform-oriented and cold-chain distribution are all sublinks of PD-FAF-SC midstream circulation. Meteorological disasters have the greatest restriction on land cold chain transportation, while the cold chain technology and equipment are not mature, the logistics infrastructure is relatively backward, and the transportation organization is not good that causes the fresh agricultural products to not be delivered in time and quality, resulting in a certain degree of harm to the supply chain. In the platform-oriented aspect, the deviation of goods source or scheduling error caused by organization and management errors occurred frequently, and the mismatch between food mileage and cold chain logistics facilities, due to poor communication of information, which leads to platform-led transaction disputes and increases the internal management cost of the platform transaction, hinders the operation of the midstream supply chain, resulting in the phenomenon that agricultural products are stranded and stored, rot is difficult to resell, and the loss rate is high. Short-term supply chain risks include logistics risks and lack of integrity of operators.


### 2.1.3. Downstream Consumption Links

The consumption of fresh agricultural products is greatly affected by natural and environmental conditions. The short-term supply chain demand risk comes from sudden changes in customer demand. The main influencing factors are price fluctuations, scientific and technological progress, quality and safety rumors, etc., resulting in the disruption of the entire supply chain.


## 2.1.1. Upstream Planting Links

In the upstream planting process, farmers or enterprises of different forms of fresh agricultural products are included. The strong seasonal fluctuations in the prices of raw materials have been the prominent factors restricting the healthy operation of the fresh agricultural products industry in China in recent years. The failure of farmers’ production decision and the difficulty of raising agricultural resources will also cause a great negative impact on the short-term supply chain and even lead to the sudden interruption of the chain.Agricultural production has a strong dependence on natural conditions. The external environmental risk factors of short-term supply chain include insect disasters, animal and plant epidemics, drought, and other natural disasters [10]. The abuse of production materials such as pesticides, chemical fertilizers, and hormones in the production process of farmers, the risk of production pollution caused by the destruction of cultivated land, and water resources seriously affect the resilience of the supply chain. Events such as lean meat powder, melamine milk powder avian influenza, blue ear disease (PRRS), and banana black poisoning have all exposed the huge risks in the production of fresh agricultural products in China.


## 2.1.2. Midstream Circulation Links

Cold-chain transportation and platform-oriented and cold-chain distribution are all sublinks of PD-FAF-SC midstream circulation. Meteorological disasters have the greatest restriction on land cold chain transportation, while the cold chain technology and equipment are not mature, the logistics infrastructure is relatively backward, and the transportation organization is not good that causes the fresh agricultural products to not be delivered in time and quality, resulting in a certain degree of harm to the supply chain. In the platform-oriented aspect, the deviation of goods source or scheduling error caused by organization and management errors occurred frequently, and the mismatch between food mileage and cold chain logistics facilities, due to poor communication of information, which leads to platform-led transaction disputes and increases the internal management cost of the platform transaction, hinders the operation of the midstream supply chain, resulting in the phenomenon that agricultural products are stranded and stored, rot is difficult to resell, and the loss rate is high. Short-term supply chain risks include logistics risks and lack of integrity of operators.


## 2.1.3. Downstream Consumption Links

The consumption of fresh agricultural products is greatly affected by natural and environmental conditions. The short-term supply chain demand risk comes from sudden changes in customer demand. The main influencing factors are price fluctuations, scientific and technological progress, quality and safety rumors, etc., resulting in the disruption of the entire supply chain.


## 2.2. Description of Long-Term Vulnerability Model

Different from the short-term supply chain, some influencing factors may lead to the probability of partial interruption of FAF-SC in a foreseeable and long period of time. According to the scale of the enterprise, the corresponding risk degree, and the environment, the long-term PD-FAF-SC divides the upstream planting link into the large-scale fresh agricultural product planting leading enterprises and the small- and medium-sized fresh agricultural product planting farmers. For the downstream link of the supply chain, in addition to terminal retail, high-value-added food processing enterprises also have a significant demand for fresh agricultural products.


### 2.2.1. Upstream Planting Links

At present, the scale of fresh agricultural products planting enterprises or farmers in China is on the low side due to the asymmetry of information, and the low degree of organization and industrialization, the production arrangement of farmers has great blindness and the increased market risks. For the small- and medium-sized farmers, affected by the circulation and processing equipment of fresh agricultural products, it is difficult for them to switch their production. Once the risk occurs, it is difficult to enter and exit quickly, which to a certain extent increases the management risk of small- and medium-sized fresh farm produce farmers. China’s fresh agricultural products have a bumper harvest, and the slow sales have become a common phenomenon, which appears almost every year, but only in the reincarnation of varieties, which exposes the huge problem of circulation of fresh agricultural products in China.


### 2.2.2. The Midstream Circulation Links

The long-distance transportation of Chinese fresh agricultural products and the imperfect characteristics of cold chain transportation facilities hinder the transportation of fresh agricultural products and restrict the development of fresh agricultural products industry for a long time. The low level of informatization of China’s fresh agricultural product market platform affects the sustainable development of long-term PD-FAF-SC. The high investment cost of the platform, the long construction cycle, the high technical requirements of data and information integration, and the inaccurate prediction of cold-chain logistics enterprises are the prominent features of PD-FAF-SC and face certain operational risks.


### 2.2.3. Downstream Demand and Terminal Consumption Links

From the downstream perspective, affected by the domestic macroscopic control, supply-side reform, and the development of e-commerce, the downstream demand and end-consumption structure of fresh agricultural products have undergone major changes, and the bullwhip effect has increased. Although the terminal direct retailing is still the main consumption mode of fresh agricultural products in China, the green deep processing industry of agricultural products has developed rapidly under the influence of national favourable policies.


## 2.2.1. Upstream Planting Links

At present, the scale of fresh agricultural products planting enterprises or farmers in China is on the low side due to the asymmetry of information, and the low degree of organization and industrialization, the production arrangement of farmers has great blindness and the increased market risks. For the small- and medium-sized farmers, affected by the circulation and processing equipment of fresh agricultural products, it is difficult for them to switch their production. Once the risk occurs, it is difficult to enter and exit quickly, which to a certain extent increases the management risk of small- and medium-sized fresh farm produce farmers. China’s fresh agricultural products have a bumper harvest, and the slow sales have become a common phenomenon, which appears almost every year, but only in the reincarnation of varieties, which exposes the huge problem of circulation of fresh agricultural products in China.


## 2.2.2. The Midstream Circulation Links

The long-distance transportation of Chinese fresh agricultural products and the imperfect characteristics of cold chain transportation facilities hinder the transportation of fresh agricultural products and restrict the development of fresh agricultural products industry for a long time. The low level of informatization of China’s fresh agricultural product market platform affects the sustainable development of long-term PD-FAF-SC. The high investment cost of the platform, the long construction cycle, the high technical requirements of data and information integration, and the inaccurate prediction of cold-chain logistics enterprises are the prominent features of PD-FAF-SC and face certain operational risks.


## 2.2.3. Downstream Demand and Terminal Consumption Links

From the downstream perspective, affected by the domestic macroscopic control, supply-side reform, and the development of e-commerce, the downstream demand and end-consumption structure of fresh agricultural products have undergone major changes, and the bullwhip effect has increased. Although the terminal direct retailing is still the main consumption mode of fresh agricultural products in China, the green deep processing industry of agricultural products has developed rapidly under the influence of national favourable policies.


## 3. Dynamic Bayesian Network Model Based on Bow-Tie Model

Bow-tie model is an accident causality analysis method integrating fault tree and event tree analysis method, which can comprehensively analyze the causes and consequences of an event and clearly and intuitively describe the occurrence sequence of the accident and the logical relationship between each event [11, 12].BN has the advantages of describing common cause failure, polymorphism, and uncertainty logical relations and has developed mature auxiliary calculation software, which is applied to probability calculation and quantitative risk evaluation, and the theoretical basis is Bayesian conditional probability computational formula [13],(1)PA∣B=PB∣APAPBwhere PA is the prior probability, PA∣B is the posterior probability, PB is the evidence factor, and PB∣A is the likelihood function.


### 3.1. Dynamic Vulnerability Assessment Based on “Precursor Incident”

On the basis of the above theory, a dynamic vulnerability analysis model based on bow-Bayesian network is established, as shown in Figure2.Figure 2
Flow chart of dynamic vulnerability assessment based on the bow-Bayesian network model.In bow-tie model, the left side of the critical event is the fault tree, whose elastic barrier is used to prevent accidents. On the right is the event tree, whose resilience barrier is used to reduce the severity of accident consequences. Firstly, we screen the event scenarios that need to be analyzed, analyze the causes, consequences, and top events according to the supply chain structure and nodes, and describe them with the bow-tie model. Secondly, the bow-tie model is transformed into a Bayesian network model in accordance with certain rules, and the prior probability is input. According to the practical supply chain platform record, the Precursor Incident information is input into the Bayesian network model, and the results of dynamic vulnerability assessment can be calculated. The model can be dynamically updated continuously on the basis of the change of time and the increase of evidence information. The key point of model analysis is that the bowtie model is transformed into BN, and the dynamic vulnerability is calculated according to the Precursor Incident.


### 3.2. The Transformation of Bowtie Model to Bayesian Network Model

As the root node and intermediate node of the BN model, the basic and intermediate events of the fault tree have a directed edge from the base event to the intermediate event. Each resilience barrier of the event tree is represented as a node in the BN model, and all resilience barrier nodes that affect the severity of consequences should point to consequence nodes. The risk probabilities for the basic events in the model come from the CFSA database [14] and Table 2.Table 2
CPT between resilience nodes.
Supply chain vulnerability Supply chain disruption Supply chain sustainability Short-term vulnerability 0.99 0.01 Long-term vulnerability 0.02 0.98According to Bayesian formula (1), the posterior distribution PA∣B is proportional to the product of the prior distribution PA and the likelihood function PB∣A, Beta distribution is selected as the prior distribution of the Bayesian network model for dynamic vulnerability assessment, and binomial distribution function is selected as the likelihood function, assuming that the vulnerability probability of each node obeys binomial distribution.Suppose that a nodexi in the Bayesian network model obeys the Betaa,b distribution, i.e.,(2)Px=Γa+bΓaΓbxa-11-xb-1∝xa-11-xb-1If the “Precursor Incident” information shows that the vulnerability data Data=d1,d2,⋯,di of a node, di=1(resilience) or 0(inresilience) obeys Bernoulli distribution, δ=∑i=1ndi, then the following equation is available.(3)Px∣D=PD∣xPxPD∝PD∣xPx∝xδ1-xn-δxa-11-xb-1∝xa+δ-11-xb+n-δ-1According to (3), the posterior distribution satisfies Betaa+δ,b+n-δ; thus it can be seen that both the prior distribution and the posterior distribution satisfy Beta distribution, which shows that Beta distribution has good transitivity, and with the increase of sample number, the influence degree of prior probability gradually decreases. Parameters a and b can be obtained by fitting of historical data, or directly given on the basis of the expert experience. In summary, it can be seen from the analysis that the posterior distribution of node vulnerability can be calculated by using “Precursor Incident” information as evidence information, and then the dynamic vulnerability evaluation results can be obtained.


### 3.3. Short-Term Vulnerability Model of PD-FAF-SC

#### 3.3.1. Short-Term Vulnerability Model

According to the analysis of vulnerability characteristics, the design of fault tree event of PD-FAF-SC short-term vulnerability is described. The vulnerability is defined as the top event of the fault tree, and the intermediate event is used to describe the vulnerability of upstream, middle, and downstream supply chain operations, using logic OR gate and AND gate to construct the fault tree structure as shown in Figures3–5 [15]. The English UP in upstream planting is Upper planters, the English PD in the platform leading UP is Platform-driven, and other similarities are no longer explained.Figure 3
Fault tree of short-term vulnerability of PD-FAF-SC upstream planting links.Figure 4
Fault tree of short-term vulnerability of PD-FAF-SC midstream transport links.Figure 5
Fault tree for short-term vulnerability of PD-FAF-SC downstream demand links.


#### 3.3.2. Short-Term Vulnerability Calculation Based on Bayesian Networks

The PD-FAF-SC vulnerability fault tree has 13 minimum cut sets, which areX1,X2,X3,X4, X5,X6,X7, X8,X9, X10, X11,X12,X13, X14, X15,X16,X17,X18, X19,X20,X21, X22,X23,X24, X25, X26,X27, X28,X29,X30,X31,X32.Transform the above PD-FAF-SC fault tree into Bayesian Network structure; the conversion formulas of logic gates “OR” and “AND” are given, respectively, as well as the analysis formulas for calculating the short-term vulnerability of PD-FAF-SC which is constructed by various network parameters.


#### 3.3.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Using Figures3–5, the basic relationship among the top event, the intermediate event, and the bottom event can be given, corresponding nodes are established and linked in the Bayesian network, and the logic gates in the fault tree are converted to conditional probability in Bayesian network. The event occurs when the event is equal to 1, and when the event is equal to 0, the event does not occur [15]. The conversion formula is as shown in formulas (4)-(16):(4)UP=FPS∪PM∪PPE∪X1∪X10PUP=1∣FPS=0,PM=0,PPE=0,X1=0,X10=0=0PUP=1∣else=1(5)FPS=X2∩X3∩X4PFPS=1∣X2=1,X3=1,X4=1=1PFPS=1∣else=0(6)PM=X5∩X6∩X7PPM=1∣X5=1,X6=1,X7=1=1PPM=1∣else=0(7)PPE=X8∩X9PPPE=1∣X8=1,X9=1=1PPPE=1∣else=0(8)MT=CCT∪PD∪CCD∪DP∪X14PMT=1∣CCT=0,DP=0,CCD=0,X14=0,PD=0=0PMT=1∣else=1(9)DP=X11∩X12∩X13PDP=1∣X11=1,X12=1,X13=1=1PDP=1∣else=0(10)CCT=X15∩X16∩X17∩X18PCCT=1∣X15=1,X16=1,X17=1,X18=1=1PCCT=1∣else=0(11)PD=X19∩X20∩X21PPD=1∣X19=1,X20=1,X21=1=1PPD=1∣else=0(12)CCD=X22∩X23∩X24PCCD=1∣X22=1,X23=1,X24=1=1PCCD=1∣else=0(13)DR=X25∪DS∪TCPDR=1∣X25=0,DS=0,TC=0=0PDR=1∣else=1(14)DS=X26∩X27PDS=1∣X26=1,X27=1=1PDS=1∣else=0(15)TC=X28∩X29∩X30∩X31∩X32PTC=1∣X28=1,X29=1,X30=1,X31=1,X32=1=1PTC=1∣else=0(16)SC=US∪MT∪DRPSC=1∣UP=0,MT=0,DR=0=0PSC=1∣else=1In the upper formula, if DR=X25∪DS∪TC represent event X25 or event DS or event TC, the eventDR will occur; PPE=X8∩X9 indicates through the logical AND gate that if event X8 coincides with event X9, the eventPPE will occur. Other cases refer to the explanation.


#### 3.3.4. Short-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The Bayesian network parameters of PD-FAF-SC are determined by the priori probability of each root node and the connection relation, and the probability that the upstream supply is difficult to meet the downstream demand by the influence of the bottom event factor is calculated. Assuming that all root node events in the network are independent of each other, the priori probability when each root node event in the Bayesian network of PD-FAF-SC can be observedθn=PXn=1,1≤n≤32. According to the priori probability of each root node of PD-FAF-SC, the probability of solving each intermediate event is as follows:First, upstream planting links:(17)PFPS=1=∑X2,X3,X4FPS=1∣X2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2PX3PX4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2=1PX3=1PX4=1=θ2θ3θ4This is because PFPS=1∣X2=1,X3=1,X4=1=1PX2=θ2,PX3=θ3,PX4=θ4.Similarly calculated:(18)PPM=1=∑X5,X6,X7PM=1,X5,X6,X7=θ5θ6θ7(19)PPPE=1=∑X8,X9PPE=1,X8,X9=θ8θ9(20)PUP=1=∑FPS,PM,PPE,X1,X10UP=1,FPS,PM,PPE,X1,X10=∑FPS,PM,PPE,X1,X10UP=1FPS,PM,PPE,X1,X10PFPSPPMPPPEPX1PX10=1-1-PFPS=11-PPM=11-PPPE=11-PX11-PX10=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ10Second, the midstream circulation links:(21)PDP=1=∑X11,X12,X13DP=1,X11,X12,X13=θ11θ12θ13(22)PCCT=1=∑X15,X16,X17,X18CCT=1,X15,X16,X17,X18=θ15θ16θ17θ18(23)PPD=1=∑X19,X20,X21PD=1,X19,X20,X21=θ19θ20θ21(24)PCCD=1=∑X22,X23,X24CCD=1,X22,X23,X24=θ22θ23θ24(25)PMT=1=∑X14,DP,CCT,PD,CCDMT=1∣DP,X14,CCT,PD,CCD=1-1-θ141-θ11θ12θ131-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ24Third, downstream demand and end-consumption links:(26)PDS=1=∑X26,X27DS=1,X26,X27=θ26θ27(27)PTC=1=∑X28,X29,X30,X31,X32TC=1,X28,X29,X30,X31,X32=θ28θ29θ30θ31θ32(28)PDR=1=∑X25,DS,TCDR=1,X25,DS,TC=1-1-θ251-θ26θ271-θ28θ29θ30θ31θ32Based on the conditional probability of the intermediate events in the upper, middle, and lower reaches, the probability of the occurrence of PD-FAF-SC short-term vulnerability can be found in (29):(29)PSC=1=∑UP,MT,DRSC=1,UP,MT,DR=1-1-PUP=11-PMT=11-PDR=1=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ101-θ141-θ11θ12θ13×1-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ241-θ251-θ26θ271-θ28θ29θ30θ31θ32


### 3.4. Construction and Calculation of Long-Term Vulnerability Model for PD-FAF-SC

#### 3.4.1. Long-Term Vulnerability Model Construction

In order to distinguish it from the calculation of short-term vulnerability, long-term supply chain vulnerability is represented bySC∗, and similar node links such as upstream planting link are represented by UP∗, etc. As the economic crisis risk factors will have a long-term impact on many aspects of the supply chain, this paper uses the unified Y1. Figures 6–8 show the fault tree structure for long-term vulnerability in the middle and lower reaches of the PD-FAF-SC.Figure 6
Fault tree of long-term vulnerability of PD-FAF-SC upstream planting link.Figure 7
Fault tree of long-term vulnerability of PD-FAF-SC transit links.Figure 8
Fault tree for long-term vulnerability of PD-FAF-SC downstream demand links.


#### 3.4.2. Long-Term Vulnerability Calculation Based on Bayesian Networks

In accordance with the above idea of short-term vulnerability calculation, the fault tree of long-term vulnerability is first transformed into Bayesian network and given parameters settings to construct a quantitative analysis method.


#### 3.4.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Through the fault tree structure of PD-FAF-SC shown in Figures6–8, and referring to the corresponding relationship between nodes, the logic gate in the long-term vulnerability fault tree is transformed into the conditional probability of Bayesian network; see formulas (30)-(40):(30)UP∗=LCE∩SCEPUP∗=1∣LCE=1,SCE=1=1PUP∗=1∣else=0(31)LCE=Y1∪Y2∪Y3∪Y4∪Y5PLCE=1∣Y1=0,Y2=0,Y3=0,Y4=0,Y5=0=0PLCE=1∣else=1(32)SCE=Y1∪Y6∪Y7∪Y8∪Y9∪Y10PSCE=1∣Y1=0,Y6=0,Y7=0,Y8=0,Y9=0,Y10=0=0PSCE=1∣else=1(33)MT∗=DP∗∪CCT∗∪PD∗∪CCD∗PMT∗=1∣DP∗=0,CCT∗=0,PD∗=0,CCD∗=0=0PMT∗=1∣else=1(34)DP∗=Y11∪Y12PDP∗=1∣Y11=0,Y12=0=0PDP∗=1∣else=1(35)CCT∗=Y1∪Y13PCCT∗=1∣Y13=0,Y1=0=0PCCT∗=1∣else=1(36)PD∗=Y14∪Y15∪Y16∪Y17PPD∗=1∣Y14=0,Y15=0,Y16=0,Y17=0=0PPD∗=1∣else=1(37)CCD∗=Y1∪Y18∪Y19PCCD∗=1∣Y1=0,Y18=0,Y19=0=0PCCD∗=1∣else=1(38)DR∗=RE∩FDEPDR∗=1∣RE=1,FDE=1=1PDR∗=1∣else=0(39)RE=Y1∪Y20∪Y21∪Y22∪Y23∪Y24PRE=1∣Y1=0,Y20=0,Y21=0,Y22=0,Y23=0,Y24=0=0PRE=1∣else=1(40)FDE=Y1∪Y25∪Y26∪Y27∪Y28PFDE=1∣Y1=0,Y25=0,Y26=0,Y27=0,Y28=0=0PFDE=1∣else=1The relationship between “OR” and “AND” gates indicates that the long-term vulnerability fault tree of PD-FAF-SC is expressed as formula (41):(41)SC∗=UP∗∪MT∗∪DR∗PSC∗=1∣UP∗=0,MT∗=0,DR∗=0=0PSC∗=1∣else=1


#### 3.4.4. Long-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The long-term vulnerability assessment of PD-FAF-SC uses the priori probabilityρN=PYN=1, 1≤N≤28, which can be observed at the occurrence of each root event in Bayesian network, and the probability relations between each node to calculate the probability of long-term vulnerability step by step.First, upstream planting links:(42)PLCE=1=∑Y1,Y2,Y3,Y4,Y5PLCE=1,Y1,Y2,Y3,Y4,Y5=1-∏j=151-ρj(43)PSCE=1=∑Y1,Y6,Y7,Y8,Y9,Y10PSCE=1,Y1,Y6,Y7,Y8,Y9,Y10=1-1-ρ1∏j=6101-ρj(44)PUP∗=1=∑LCE,SCEPUP∗=1,LCE,SCE=1-∏j=151-ρj1-1-ρ1∏j=6101-ρjSecond, the midstream circulation links:(45)PDP∗=1=∑Y11,Y12PDP∗=1,Y11,Y12=1-1-ρ111-ρ12(46)PCCT∗=1=∑Y1,Y13PCCT∗=1,Y1,Y13=1-1-ρ11-ρ13(47)PPD∗=1=∑Y14,Y15,Y16,Y17PPD∗=1,Y14,Y15,Y16,Y17=1-∏j=14171-ρj(48)PCCD∗=1=∑Y1,Y18,Y19PCCD∗=1,Y1,Y18,Y19=1-1-ρ11-ρ181-ρ19(49)PMT∗=1=∑DP∗,CCT∗,PD∗,CCD∗PMT∗=1,DP∗,CCT∗,PD∗,CCD∗=1-1-ρ12∏j=11191-ρjThird, downstream demand and end-consumption links:(50)PRE=1=∑Y1,Y20,Y21,Y22,Y23,Y24PRE=Y1,Y20,Y21,Y22,Y23,Y24=1-1-ρ1∏j=20241-ρj(51)PFDE=1=∑Y1,Y25,Y26,Y27,Y28PFDE=1,Y1,Y25,Y26,Y27,Y28=1-1-ρ1∏j=25281-ρj(52)PDR∗=1=∑RE,FDEPDR∗=1,RE,FDE=1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρjAccording to the conditional probability of the above three types of events, the probability of the long-term vulnerability SC∗ of the top event PD-FAF-SC can be obtained as follows:(53)PSC∗=1=∑UP∗,MT∗,DR∗PSC∗=1,UP∗,MT∗,DR∗=1-1-1-∏j=151-ρj1-1-ρ1∏j=6101-ρj×1-ρ12∏j=11191-ρj×1-1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρj


## 3.1. Dynamic Vulnerability Assessment Based on “Precursor Incident”

On the basis of the above theory, a dynamic vulnerability analysis model based on bow-Bayesian network is established, as shown in Figure2.Figure 2
Flow chart of dynamic vulnerability assessment based on the bow-Bayesian network model.In bow-tie model, the left side of the critical event is the fault tree, whose elastic barrier is used to prevent accidents. On the right is the event tree, whose resilience barrier is used to reduce the severity of accident consequences. Firstly, we screen the event scenarios that need to be analyzed, analyze the causes, consequences, and top events according to the supply chain structure and nodes, and describe them with the bow-tie model. Secondly, the bow-tie model is transformed into a Bayesian network model in accordance with certain rules, and the prior probability is input. According to the practical supply chain platform record, the Precursor Incident information is input into the Bayesian network model, and the results of dynamic vulnerability assessment can be calculated. The model can be dynamically updated continuously on the basis of the change of time and the increase of evidence information. The key point of model analysis is that the bowtie model is transformed into BN, and the dynamic vulnerability is calculated according to the Precursor Incident.


## 3.2. The Transformation of Bowtie Model to Bayesian Network Model

As the root node and intermediate node of the BN model, the basic and intermediate events of the fault tree have a directed edge from the base event to the intermediate event. Each resilience barrier of the event tree is represented as a node in the BN model, and all resilience barrier nodes that affect the severity of consequences should point to consequence nodes. The risk probabilities for the basic events in the model come from the CFSA database [14] and Table 2.Table 2
CPT between resilience nodes.
Supply chain vulnerability Supply chain disruption Supply chain sustainability Short-term vulnerability 0.99 0.01 Long-term vulnerability 0.02 0.98According to Bayesian formula (1), the posterior distribution PA∣B is proportional to the product of the prior distribution PA and the likelihood function PB∣A, Beta distribution is selected as the prior distribution of the Bayesian network model for dynamic vulnerability assessment, and binomial distribution function is selected as the likelihood function, assuming that the vulnerability probability of each node obeys binomial distribution.Suppose that a nodexi in the Bayesian network model obeys the Betaa,b distribution, i.e.,(2)Px=Γa+bΓaΓbxa-11-xb-1∝xa-11-xb-1If the “Precursor Incident” information shows that the vulnerability data Data=d1,d2,⋯,di of a node, di=1(resilience) or 0(inresilience) obeys Bernoulli distribution, δ=∑i=1ndi, then the following equation is available.(3)Px∣D=PD∣xPxPD∝PD∣xPx∝xδ1-xn-δxa-11-xb-1∝xa+δ-11-xb+n-δ-1According to (3), the posterior distribution satisfies Betaa+δ,b+n-δ; thus it can be seen that both the prior distribution and the posterior distribution satisfy Beta distribution, which shows that Beta distribution has good transitivity, and with the increase of sample number, the influence degree of prior probability gradually decreases. Parameters a and b can be obtained by fitting of historical data, or directly given on the basis of the expert experience. In summary, it can be seen from the analysis that the posterior distribution of node vulnerability can be calculated by using “Precursor Incident” information as evidence information, and then the dynamic vulnerability evaluation results can be obtained.


## 3.3. Short-Term Vulnerability Model of PD-FAF-SC

### 3.3.1. Short-Term Vulnerability Model

According to the analysis of vulnerability characteristics, the design of fault tree event of PD-FAF-SC short-term vulnerability is described. The vulnerability is defined as the top event of the fault tree, and the intermediate event is used to describe the vulnerability of upstream, middle, and downstream supply chain operations, using logic OR gate and AND gate to construct the fault tree structure as shown in Figures3–5 [15]. The English UP in upstream planting is Upper planters, the English PD in the platform leading UP is Platform-driven, and other similarities are no longer explained.Figure 3
Fault tree of short-term vulnerability of PD-FAF-SC upstream planting links.Figure 4
Fault tree of short-term vulnerability of PD-FAF-SC midstream transport links.Figure 5
Fault tree for short-term vulnerability of PD-FAF-SC downstream demand links.


### 3.3.2. Short-Term Vulnerability Calculation Based on Bayesian Networks

The PD-FAF-SC vulnerability fault tree has 13 minimum cut sets, which areX1,X2,X3,X4, X5,X6,X7, X8,X9, X10, X11,X12,X13, X14, X15,X16,X17,X18, X19,X20,X21, X22,X23,X24, X25, X26,X27, X28,X29,X30,X31,X32.Transform the above PD-FAF-SC fault tree into Bayesian Network structure; the conversion formulas of logic gates “OR” and “AND” are given, respectively, as well as the analysis formulas for calculating the short-term vulnerability of PD-FAF-SC which is constructed by various network parameters.


### 3.3.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Using Figures3–5, the basic relationship among the top event, the intermediate event, and the bottom event can be given, corresponding nodes are established and linked in the Bayesian network, and the logic gates in the fault tree are converted to conditional probability in Bayesian network. The event occurs when the event is equal to 1, and when the event is equal to 0, the event does not occur [15]. The conversion formula is as shown in formulas (4)-(16):(4)UP=FPS∪PM∪PPE∪X1∪X10PUP=1∣FPS=0,PM=0,PPE=0,X1=0,X10=0=0PUP=1∣else=1(5)FPS=X2∩X3∩X4PFPS=1∣X2=1,X3=1,X4=1=1PFPS=1∣else=0(6)PM=X5∩X6∩X7PPM=1∣X5=1,X6=1,X7=1=1PPM=1∣else=0(7)PPE=X8∩X9PPPE=1∣X8=1,X9=1=1PPPE=1∣else=0(8)MT=CCT∪PD∪CCD∪DP∪X14PMT=1∣CCT=0,DP=0,CCD=0,X14=0,PD=0=0PMT=1∣else=1(9)DP=X11∩X12∩X13PDP=1∣X11=1,X12=1,X13=1=1PDP=1∣else=0(10)CCT=X15∩X16∩X17∩X18PCCT=1∣X15=1,X16=1,X17=1,X18=1=1PCCT=1∣else=0(11)PD=X19∩X20∩X21PPD=1∣X19=1,X20=1,X21=1=1PPD=1∣else=0(12)CCD=X22∩X23∩X24PCCD=1∣X22=1,X23=1,X24=1=1PCCD=1∣else=0(13)DR=X25∪DS∪TCPDR=1∣X25=0,DS=0,TC=0=0PDR=1∣else=1(14)DS=X26∩X27PDS=1∣X26=1,X27=1=1PDS=1∣else=0(15)TC=X28∩X29∩X30∩X31∩X32PTC=1∣X28=1,X29=1,X30=1,X31=1,X32=1=1PTC=1∣else=0(16)SC=US∪MT∪DRPSC=1∣UP=0,MT=0,DR=0=0PSC=1∣else=1In the upper formula, if DR=X25∪DS∪TC represent event X25 or event DS or event TC, the eventDR will occur; PPE=X8∩X9 indicates through the logical AND gate that if event X8 coincides with event X9, the eventPPE will occur. Other cases refer to the explanation.


### 3.3.4. Short-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The Bayesian network parameters of PD-FAF-SC are determined by the priori probability of each root node and the connection relation, and the probability that the upstream supply is difficult to meet the downstream demand by the influence of the bottom event factor is calculated. Assuming that all root node events in the network are independent of each other, the priori probability when each root node event in the Bayesian network of PD-FAF-SC can be observedθn=PXn=1,1≤n≤32. According to the priori probability of each root node of PD-FAF-SC, the probability of solving each intermediate event is as follows:First, upstream planting links:(17)PFPS=1=∑X2,X3,X4FPS=1∣X2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2PX3PX4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2=1PX3=1PX4=1=θ2θ3θ4This is because PFPS=1∣X2=1,X3=1,X4=1=1PX2=θ2,PX3=θ3,PX4=θ4.Similarly calculated:(18)PPM=1=∑X5,X6,X7PM=1,X5,X6,X7=θ5θ6θ7(19)PPPE=1=∑X8,X9PPE=1,X8,X9=θ8θ9(20)PUP=1=∑FPS,PM,PPE,X1,X10UP=1,FPS,PM,PPE,X1,X10=∑FPS,PM,PPE,X1,X10UP=1FPS,PM,PPE,X1,X10PFPSPPMPPPEPX1PX10=1-1-PFPS=11-PPM=11-PPPE=11-PX11-PX10=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ10Second, the midstream circulation links:(21)PDP=1=∑X11,X12,X13DP=1,X11,X12,X13=θ11θ12θ13(22)PCCT=1=∑X15,X16,X17,X18CCT=1,X15,X16,X17,X18=θ15θ16θ17θ18(23)PPD=1=∑X19,X20,X21PD=1,X19,X20,X21=θ19θ20θ21(24)PCCD=1=∑X22,X23,X24CCD=1,X22,X23,X24=θ22θ23θ24(25)PMT=1=∑X14,DP,CCT,PD,CCDMT=1∣DP,X14,CCT,PD,CCD=1-1-θ141-θ11θ12θ131-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ24Third, downstream demand and end-consumption links:(26)PDS=1=∑X26,X27DS=1,X26,X27=θ26θ27(27)PTC=1=∑X28,X29,X30,X31,X32TC=1,X28,X29,X30,X31,X32=θ28θ29θ30θ31θ32(28)PDR=1=∑X25,DS,TCDR=1,X25,DS,TC=1-1-θ251-θ26θ271-θ28θ29θ30θ31θ32Based on the conditional probability of the intermediate events in the upper, middle, and lower reaches, the probability of the occurrence of PD-FAF-SC short-term vulnerability can be found in (29):(29)PSC=1=∑UP,MT,DRSC=1,UP,MT,DR=1-1-PUP=11-PMT=11-PDR=1=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ101-θ141-θ11θ12θ13×1-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ241-θ251-θ26θ271-θ28θ29θ30θ31θ32


## 3.3.1. Short-Term Vulnerability Model

According to the analysis of vulnerability characteristics, the design of fault tree event of PD-FAF-SC short-term vulnerability is described. The vulnerability is defined as the top event of the fault tree, and the intermediate event is used to describe the vulnerability of upstream, middle, and downstream supply chain operations, using logic OR gate and AND gate to construct the fault tree structure as shown in Figures3–5 [15]. The English UP in upstream planting is Upper planters, the English PD in the platform leading UP is Platform-driven, and other similarities are no longer explained.Figure 3
Fault tree of short-term vulnerability of PD-FAF-SC upstream planting links.Figure 4
Fault tree of short-term vulnerability of PD-FAF-SC midstream transport links.Figure 5
Fault tree for short-term vulnerability of PD-FAF-SC downstream demand links.


## 3.3.2. Short-Term Vulnerability Calculation Based on Bayesian Networks

The PD-FAF-SC vulnerability fault tree has 13 minimum cut sets, which areX1,X2,X3,X4, X5,X6,X7, X8,X9, X10, X11,X12,X13, X14, X15,X16,X17,X18, X19,X20,X21, X22,X23,X24, X25, X26,X27, X28,X29,X30,X31,X32.Transform the above PD-FAF-SC fault tree into Bayesian Network structure; the conversion formulas of logic gates “OR” and “AND” are given, respectively, as well as the analysis formulas for calculating the short-term vulnerability of PD-FAF-SC which is constructed by various network parameters.


## 3.3.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Using Figures3–5, the basic relationship among the top event, the intermediate event, and the bottom event can be given, corresponding nodes are established and linked in the Bayesian network, and the logic gates in the fault tree are converted to conditional probability in Bayesian network. The event occurs when the event is equal to 1, and when the event is equal to 0, the event does not occur [15]. The conversion formula is as shown in formulas (4)-(16):(4)UP=FPS∪PM∪PPE∪X1∪X10PUP=1∣FPS=0,PM=0,PPE=0,X1=0,X10=0=0PUP=1∣else=1(5)FPS=X2∩X3∩X4PFPS=1∣X2=1,X3=1,X4=1=1PFPS=1∣else=0(6)PM=X5∩X6∩X7PPM=1∣X5=1,X6=1,X7=1=1PPM=1∣else=0(7)PPE=X8∩X9PPPE=1∣X8=1,X9=1=1PPPE=1∣else=0(8)MT=CCT∪PD∪CCD∪DP∪X14PMT=1∣CCT=0,DP=0,CCD=0,X14=0,PD=0=0PMT=1∣else=1(9)DP=X11∩X12∩X13PDP=1∣X11=1,X12=1,X13=1=1PDP=1∣else=0(10)CCT=X15∩X16∩X17∩X18PCCT=1∣X15=1,X16=1,X17=1,X18=1=1PCCT=1∣else=0(11)PD=X19∩X20∩X21PPD=1∣X19=1,X20=1,X21=1=1PPD=1∣else=0(12)CCD=X22∩X23∩X24PCCD=1∣X22=1,X23=1,X24=1=1PCCD=1∣else=0(13)DR=X25∪DS∪TCPDR=1∣X25=0,DS=0,TC=0=0PDR=1∣else=1(14)DS=X26∩X27PDS=1∣X26=1,X27=1=1PDS=1∣else=0(15)TC=X28∩X29∩X30∩X31∩X32PTC=1∣X28=1,X29=1,X30=1,X31=1,X32=1=1PTC=1∣else=0(16)SC=US∪MT∪DRPSC=1∣UP=0,MT=0,DR=0=0PSC=1∣else=1In the upper formula, if DR=X25∪DS∪TC represent event X25 or event DS or event TC, the eventDR will occur; PPE=X8∩X9 indicates through the logical AND gate that if event X8 coincides with event X9, the eventPPE will occur. Other cases refer to the explanation.


## 3.3.4. Short-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The Bayesian network parameters of PD-FAF-SC are determined by the priori probability of each root node and the connection relation, and the probability that the upstream supply is difficult to meet the downstream demand by the influence of the bottom event factor is calculated. Assuming that all root node events in the network are independent of each other, the priori probability when each root node event in the Bayesian network of PD-FAF-SC can be observedθn=PXn=1,1≤n≤32. According to the priori probability of each root node of PD-FAF-SC, the probability of solving each intermediate event is as follows:First, upstream planting links:(17)PFPS=1=∑X2,X3,X4FPS=1∣X2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2,X3,X4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2PX3PX4=∑X2,X3,X4FPS=1∣X2,X3,X4PX2=1PX3=1PX4=1=θ2θ3θ4This is because PFPS=1∣X2=1,X3=1,X4=1=1PX2=θ2,PX3=θ3,PX4=θ4.Similarly calculated:(18)PPM=1=∑X5,X6,X7PM=1,X5,X6,X7=θ5θ6θ7(19)PPPE=1=∑X8,X9PPE=1,X8,X9=θ8θ9(20)PUP=1=∑FPS,PM,PPE,X1,X10UP=1,FPS,PM,PPE,X1,X10=∑FPS,PM,PPE,X1,X10UP=1FPS,PM,PPE,X1,X10PFPSPPMPPPEPX1PX10=1-1-PFPS=11-PPM=11-PPPE=11-PX11-PX10=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ10Second, the midstream circulation links:(21)PDP=1=∑X11,X12,X13DP=1,X11,X12,X13=θ11θ12θ13(22)PCCT=1=∑X15,X16,X17,X18CCT=1,X15,X16,X17,X18=θ15θ16θ17θ18(23)PPD=1=∑X19,X20,X21PD=1,X19,X20,X21=θ19θ20θ21(24)PCCD=1=∑X22,X23,X24CCD=1,X22,X23,X24=θ22θ23θ24(25)PMT=1=∑X14,DP,CCT,PD,CCDMT=1∣DP,X14,CCT,PD,CCD=1-1-θ141-θ11θ12θ131-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ24Third, downstream demand and end-consumption links:(26)PDS=1=∑X26,X27DS=1,X26,X27=θ26θ27(27)PTC=1=∑X28,X29,X30,X31,X32TC=1,X28,X29,X30,X31,X32=θ28θ29θ30θ31θ32(28)PDR=1=∑X25,DS,TCDR=1,X25,DS,TC=1-1-θ251-θ26θ271-θ28θ29θ30θ31θ32Based on the conditional probability of the intermediate events in the upper, middle, and lower reaches, the probability of the occurrence of PD-FAF-SC short-term vulnerability can be found in (29):(29)PSC=1=∑UP,MT,DRSC=1,UP,MT,DR=1-1-PUP=11-PMT=11-PDR=1=1-1-θ11-θ2θ3θ41-θ5θ6θ71-θ8θ91-θ101-θ141-θ11θ12θ13×1-θ15θ16θ17θ181-θ19θ20θ211-θ22θ23θ241-θ251-θ26θ271-θ28θ29θ30θ31θ32


## 3.4. Construction and Calculation of Long-Term Vulnerability Model for PD-FAF-SC

### 3.4.1. Long-Term Vulnerability Model Construction

In order to distinguish it from the calculation of short-term vulnerability, long-term supply chain vulnerability is represented bySC∗, and similar node links such as upstream planting link are represented by UP∗, etc. As the economic crisis risk factors will have a long-term impact on many aspects of the supply chain, this paper uses the unified Y1. Figures 6–8 show the fault tree structure for long-term vulnerability in the middle and lower reaches of the PD-FAF-SC.Figure 6
Fault tree of long-term vulnerability of PD-FAF-SC upstream planting link.Figure 7
Fault tree of long-term vulnerability of PD-FAF-SC transit links.Figure 8
Fault tree for long-term vulnerability of PD-FAF-SC downstream demand links.


### 3.4.2. Long-Term Vulnerability Calculation Based on Bayesian Networks

In accordance with the above idea of short-term vulnerability calculation, the fault tree of long-term vulnerability is first transformed into Bayesian network and given parameters settings to construct a quantitative analysis method.


### 3.4.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Through the fault tree structure of PD-FAF-SC shown in Figures6–8, and referring to the corresponding relationship between nodes, the logic gate in the long-term vulnerability fault tree is transformed into the conditional probability of Bayesian network; see formulas (30)-(40):(30)UP∗=LCE∩SCEPUP∗=1∣LCE=1,SCE=1=1PUP∗=1∣else=0(31)LCE=Y1∪Y2∪Y3∪Y4∪Y5PLCE=1∣Y1=0,Y2=0,Y3=0,Y4=0,Y5=0=0PLCE=1∣else=1(32)SCE=Y1∪Y6∪Y7∪Y8∪Y9∪Y10PSCE=1∣Y1=0,Y6=0,Y7=0,Y8=0,Y9=0,Y10=0=0PSCE=1∣else=1(33)MT∗=DP∗∪CCT∗∪PD∗∪CCD∗PMT∗=1∣DP∗=0,CCT∗=0,PD∗=0,CCD∗=0=0PMT∗=1∣else=1(34)DP∗=Y11∪Y12PDP∗=1∣Y11=0,Y12=0=0PDP∗=1∣else=1(35)CCT∗=Y1∪Y13PCCT∗=1∣Y13=0,Y1=0=0PCCT∗=1∣else=1(36)PD∗=Y14∪Y15∪Y16∪Y17PPD∗=1∣Y14=0,Y15=0,Y16=0,Y17=0=0PPD∗=1∣else=1(37)CCD∗=Y1∪Y18∪Y19PCCD∗=1∣Y1=0,Y18=0,Y19=0=0PCCD∗=1∣else=1(38)DR∗=RE∩FDEPDR∗=1∣RE=1,FDE=1=1PDR∗=1∣else=0(39)RE=Y1∪Y20∪Y21∪Y22∪Y23∪Y24PRE=1∣Y1=0,Y20=0,Y21=0,Y22=0,Y23=0,Y24=0=0PRE=1∣else=1(40)FDE=Y1∪Y25∪Y26∪Y27∪Y28PFDE=1∣Y1=0,Y25=0,Y26=0,Y27=0,Y28=0=0PFDE=1∣else=1The relationship between “OR” and “AND” gates indicates that the long-term vulnerability fault tree of PD-FAF-SC is expressed as formula (41):(41)SC∗=UP∗∪MT∗∪DR∗PSC∗=1∣UP∗=0,MT∗=0,DR∗=0=0PSC∗=1∣else=1


### 3.4.4. Long-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The long-term vulnerability assessment of PD-FAF-SC uses the priori probabilityρN=PYN=1, 1≤N≤28, which can be observed at the occurrence of each root event in Bayesian network, and the probability relations between each node to calculate the probability of long-term vulnerability step by step.First, upstream planting links:(42)PLCE=1=∑Y1,Y2,Y3,Y4,Y5PLCE=1,Y1,Y2,Y3,Y4,Y5=1-∏j=151-ρj(43)PSCE=1=∑Y1,Y6,Y7,Y8,Y9,Y10PSCE=1,Y1,Y6,Y7,Y8,Y9,Y10=1-1-ρ1∏j=6101-ρj(44)PUP∗=1=∑LCE,SCEPUP∗=1,LCE,SCE=1-∏j=151-ρj1-1-ρ1∏j=6101-ρjSecond, the midstream circulation links:(45)PDP∗=1=∑Y11,Y12PDP∗=1,Y11,Y12=1-1-ρ111-ρ12(46)PCCT∗=1=∑Y1,Y13PCCT∗=1,Y1,Y13=1-1-ρ11-ρ13(47)PPD∗=1=∑Y14,Y15,Y16,Y17PPD∗=1,Y14,Y15,Y16,Y17=1-∏j=14171-ρj(48)PCCD∗=1=∑Y1,Y18,Y19PCCD∗=1,Y1,Y18,Y19=1-1-ρ11-ρ181-ρ19(49)PMT∗=1=∑DP∗,CCT∗,PD∗,CCD∗PMT∗=1,DP∗,CCT∗,PD∗,CCD∗=1-1-ρ12∏j=11191-ρjThird, downstream demand and end-consumption links:(50)PRE=1=∑Y1,Y20,Y21,Y22,Y23,Y24PRE=Y1,Y20,Y21,Y22,Y23,Y24=1-1-ρ1∏j=20241-ρj(51)PFDE=1=∑Y1,Y25,Y26,Y27,Y28PFDE=1,Y1,Y25,Y26,Y27,Y28=1-1-ρ1∏j=25281-ρj(52)PDR∗=1=∑RE,FDEPDR∗=1,RE,FDE=1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρjAccording to the conditional probability of the above three types of events, the probability of the long-term vulnerability SC∗ of the top event PD-FAF-SC can be obtained as follows:(53)PSC∗=1=∑UP∗,MT∗,DR∗PSC∗=1,UP∗,MT∗,DR∗=1-1-1-∏j=151-ρj1-1-ρ1∏j=6101-ρj×1-ρ12∏j=11191-ρj×1-1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρj


## 3.4.1. Long-Term Vulnerability Model Construction

In order to distinguish it from the calculation of short-term vulnerability, long-term supply chain vulnerability is represented bySC∗, and similar node links such as upstream planting link are represented by UP∗, etc. As the economic crisis risk factors will have a long-term impact on many aspects of the supply chain, this paper uses the unified Y1. Figures 6–8 show the fault tree structure for long-term vulnerability in the middle and lower reaches of the PD-FAF-SC.Figure 6
Fault tree of long-term vulnerability of PD-FAF-SC upstream planting link.Figure 7
Fault tree of long-term vulnerability of PD-FAF-SC transit links.Figure 8
Fault tree for long-term vulnerability of PD-FAF-SC downstream demand links.


## 3.4.2. Long-Term Vulnerability Calculation Based on Bayesian Networks

In accordance with the above idea of short-term vulnerability calculation, the fault tree of long-term vulnerability is first transformed into Bayesian network and given parameters settings to construct a quantitative analysis method.


## 3.4.3. Transform PD-FAF-SC Fault Tree into Bayesian Network

Through the fault tree structure of PD-FAF-SC shown in Figures6–8, and referring to the corresponding relationship between nodes, the logic gate in the long-term vulnerability fault tree is transformed into the conditional probability of Bayesian network; see formulas (30)-(40):(30)UP∗=LCE∩SCEPUP∗=1∣LCE=1,SCE=1=1PUP∗=1∣else=0(31)LCE=Y1∪Y2∪Y3∪Y4∪Y5PLCE=1∣Y1=0,Y2=0,Y3=0,Y4=0,Y5=0=0PLCE=1∣else=1(32)SCE=Y1∪Y6∪Y7∪Y8∪Y9∪Y10PSCE=1∣Y1=0,Y6=0,Y7=0,Y8=0,Y9=0,Y10=0=0PSCE=1∣else=1(33)MT∗=DP∗∪CCT∗∪PD∗∪CCD∗PMT∗=1∣DP∗=0,CCT∗=0,PD∗=0,CCD∗=0=0PMT∗=1∣else=1(34)DP∗=Y11∪Y12PDP∗=1∣Y11=0,Y12=0=0PDP∗=1∣else=1(35)CCT∗=Y1∪Y13PCCT∗=1∣Y13=0,Y1=0=0PCCT∗=1∣else=1(36)PD∗=Y14∪Y15∪Y16∪Y17PPD∗=1∣Y14=0,Y15=0,Y16=0,Y17=0=0PPD∗=1∣else=1(37)CCD∗=Y1∪Y18∪Y19PCCD∗=1∣Y1=0,Y18=0,Y19=0=0PCCD∗=1∣else=1(38)DR∗=RE∩FDEPDR∗=1∣RE=1,FDE=1=1PDR∗=1∣else=0(39)RE=Y1∪Y20∪Y21∪Y22∪Y23∪Y24PRE=1∣Y1=0,Y20=0,Y21=0,Y22=0,Y23=0,Y24=0=0PRE=1∣else=1(40)FDE=Y1∪Y25∪Y26∪Y27∪Y28PFDE=1∣Y1=0,Y25=0,Y26=0,Y27=0,Y28=0=0PFDE=1∣else=1The relationship between “OR” and “AND” gates indicates that the long-term vulnerability fault tree of PD-FAF-SC is expressed as formula (41):(41)SC∗=UP∗∪MT∗∪DR∗PSC∗=1∣UP∗=0,MT∗=0,DR∗=0=0PSC∗=1∣else=1


## 3.4.4. Long-Term Vulnerability Calculation of PD-FAF-SC Based on Bayesian Networks

The long-term vulnerability assessment of PD-FAF-SC uses the priori probabilityρN=PYN=1, 1≤N≤28, which can be observed at the occurrence of each root event in Bayesian network, and the probability relations between each node to calculate the probability of long-term vulnerability step by step.First, upstream planting links:(42)PLCE=1=∑Y1,Y2,Y3,Y4,Y5PLCE=1,Y1,Y2,Y3,Y4,Y5=1-∏j=151-ρj(43)PSCE=1=∑Y1,Y6,Y7,Y8,Y9,Y10PSCE=1,Y1,Y6,Y7,Y8,Y9,Y10=1-1-ρ1∏j=6101-ρj(44)PUP∗=1=∑LCE,SCEPUP∗=1,LCE,SCE=1-∏j=151-ρj1-1-ρ1∏j=6101-ρjSecond, the midstream circulation links:(45)PDP∗=1=∑Y11,Y12PDP∗=1,Y11,Y12=1-1-ρ111-ρ12(46)PCCT∗=1=∑Y1,Y13PCCT∗=1,Y1,Y13=1-1-ρ11-ρ13(47)PPD∗=1=∑Y14,Y15,Y16,Y17PPD∗=1,Y14,Y15,Y16,Y17=1-∏j=14171-ρj(48)PCCD∗=1=∑Y1,Y18,Y19PCCD∗=1,Y1,Y18,Y19=1-1-ρ11-ρ181-ρ19(49)PMT∗=1=∑DP∗,CCT∗,PD∗,CCD∗PMT∗=1,DP∗,CCT∗,PD∗,CCD∗=1-1-ρ12∏j=11191-ρjThird, downstream demand and end-consumption links:(50)PRE=1=∑Y1,Y20,Y21,Y22,Y23,Y24PRE=Y1,Y20,Y21,Y22,Y23,Y24=1-1-ρ1∏j=20241-ρj(51)PFDE=1=∑Y1,Y25,Y26,Y27,Y28PFDE=1,Y1,Y25,Y26,Y27,Y28=1-1-ρ1∏j=25281-ρj(52)PDR∗=1=∑RE,FDEPDR∗=1,RE,FDE=1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρjAccording to the conditional probability of the above three types of events, the probability of the long-term vulnerability SC∗ of the top event PD-FAF-SC can be obtained as follows:(53)PSC∗=1=∑UP∗,MT∗,DR∗PSC∗=1,UP∗,MT∗,DR∗=1-1-1-∏j=151-ρj1-1-ρ1∏j=6101-ρj×1-ρ12∏j=11191-ρj×1-1-1-ρ1∏j=20241-ρj1-1-ρ1∏j=25281-ρj


## 4. Empirical Analysis

This paper takes the fresh agricultural products trading center in North China as an example. The trading center was established in 2010. It is a typical PD-FAF-SC, whose vulnerability is affected by the environment of logistics, capital flow, and information flow, and it mainly acts on three links in the upper, middle, and lower reaches of the supply chain. Based on the statistical data of trading center over the years, field visits, and expert interviews, the empirical analysis of short-term and long-term vulnerability based on PD-FAF-SC vulnerability is carried out by using the above theoretical results to clarify the risk transfer model of fresh agricultural products trading center supply chain, establishing a dynamic monitoring model for vulnerability.


### 4.1. The Calculation of FAF-SC Short-Term Vulnerability

#### 4.1.1. Short-Term Vulnerability Calculation

After the data statistics, the priori probabilityθi of each root node Xi of Bayesian network where the short-term vulnerability of the PD-FAF-SC occurs can be given. The posteriori probability of Bayesian network is realized by java programming, and then the probability of short-term vulnerability SC and other intermediate events of the parent node in Bayesian networks can be obtained by using the sum (17)-(29) of Figures 3–5 as shown in Table 3.Table 3
Priori probability of the root nodes of the Bayesian network of the short-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−3).
Number Priori probability Node occurrence probability Number Priori probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event X1 θ 1 0.815 0.815 UP1.327 SC1.645 X17 θ 17 12.58 8.245×10−11 0.115 X2 θ 2 0.702 FPS1.301×10−7 X18 θ 18 0.827 X3 θ 3 0.339 X19 θ 19 8.383 PD3.076×10−7 X4 θ 4 0.547 X20 θ 20 0.249 X5 θ 5 0.677 PM0.532×10−7 X21 θ 21 0.147 X6 θ 6 0.874 X22 θ 22 0.366 CCD6.784×10−7 X7 θ 7 0.089 X23 θ 23 0.258 X8 θ 8 0.504 PPE1.663×10−4 X24 θ 24 7.174 X9 θ 9 0.33 X25 θ 25 0.203 DS5.151×10−5 DR0.203 X10 θ 10 0.513 0.513 X26 θ 26 0.303 X11 θ 11 0.314 CP2.765×10−9 MT X27 θ 27 0.169 X12 θ 12 0.109 X28 θ 28 0.779 TC1.020×10−12 X13 θ 13 0.074 X29 θ 29 0.865 X14 θ 14 0.115 CCT X30 θ 30 0.108 X15 θ 15 6.17 X31 θ 31 83.47 X16 θ 16 0.128 X32 θ 32 0.167 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


#### 4.1.2. Short-Term Vulnerability Analysis

Analysis of Table3 data: the short-term vulnerability of PD-FAF-SC in trading center is P (SC = 1) = 1.645 × 10−3, which has higher risk and is still basically controllable throughout the country. Among them, through the calculation of conditional probability of each node, the main reason for the short-term vulnerability of PD-FAF-SC is concentrated in the upstream planting links: P (UP = 1) = 1.327 × 10−3 which accords with the domestic setting that the upstream production supply link of PD-FAF-SC is the short-term supply chain node and the main bottleneck link at the present stage.The cause of short-term vulnerability of FAF-SC in trading center also exists in the midstream circulation links: P (MT = 1) = 0.115 × 10−3. In China, the production of fresh agricultural products is obviously regional and seasonal, while fresh agricultural products are essential for daily life. The fluctuation of consumption demand is relatively less fluctuating under normal conditions which will result in the deviation of the supply of fresh agricultural products P(X19 = 1) = 8.383 × 10−3, mainly due to factors such as technical error in platform and delays or errors in information transmission. When the upstream supply exceeds the demand in the peak season and the supply is far less than the demand in the off-season, the probability of the imbalance between the upstream and downstream supply and demand is large, which increases the vulnerability of FAF-SC. In recent years, although the investment in cold chain infrastructure in China has been heating up, the overall infrastructure is relatively weak. The infrastructure, technical strength, and integrity of the management of the cold chain of circulation enterprises are not up to the current demand for the circulation of fresh agricultural products in China. The probability of lack of integrity in cold chain management reaches P(X24 = 1) = 7.174 × 10−3, and the probability of insufficient factor of cold chain equipment is P(X15 = 1) = 6.172 × 10−3, which is the primary risk factor of cold chain transportation and cold chain distribution, which affects the smooth operation of domestic PD-FAF-SC.For the supply chain of fresh agricultural products, the probability of short-term vulnerability of downstream consumer retail is P(DR = 1) = 0.203 × 10−3 and the freshness of fresh agricultural products is the decisive factor to determine the sales volume, P (X31 = 1) = 83.47 × 10−3. With the improvement of people’s living standards, the general public’s awareness of food safety has gradually increased. However, the influence of food safety rumors is becoming more and more serious and even causes panic P(X29 = 1) = 0.865 × 10-3, causing downstream retailers to cut off their sales, leading to a large backlog of products produced by upstream agricultural growers or farmers, and even rotten in the ground, which is also one of the factors that influence the vulnerability of trading center PD-FAF-SC.


### 4.2. FAF-SC Long-Term Vulnerability Calculation

#### 4.2.1. Long-Term Vulnerability Calculation

Consistent with the idea of short-term supply chain vulnerability assessment, the priori probabilityρj is given for each root node Yj of the Bayesian network where PD-FAF-SC long-term vulnerability occurs, and then the probability of short-term vulnerability SC and other intermediate events of parent nodes in Bayesian network can be obtained by using Figures 5–7 sum formula (42)-(53), as shown in Table 4.Table 4
Priori probability of the root nodes of the Bayesian network of the long-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−5).
Number Prior probability Node occurrence probability Number Prior probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event Y1 ρ 1 5 LCE1.65 UP※0.0126 SC※6.73 Y16 ρ 16 0.308 Y2 ρ 2 1.23 Y17 ρ 17 31.68 Y3 ρ 3 3.23 Y1 ρ 1 5 CCD※1.153 Y4 ρ 4 1.47 Y18 ρ 18 2.78 Y5 ρ 5 5.54 Y19 ρ 19 3.75 Y1 ρ 1 5 SCE6.84 Y1 ρ 1 5 RE3.894 DR※0.0089 Y6 ρ 6 1.54 Y20 ρ 20 4.12 Y7 ρ 7 42.3 Y21 ρ 21 6.33 Y8 ρ 8 3.79 Y22 ρ 22 4.60 Y9 ρ 9 8.97 Y23 ρ 23 8.52 Y10 ρ 10 6.78 Y24 ρ 24 10.4 Y11 ρ 11 7.91 DP※0.978 MT※6.35 Y1 ρ 1 5 FDE2.287 Y12 ρ 12 1.87 Y25 ρ 25 6.54 Y1 ρ 1 5 CCT※0.774 Y26 ρ 26 2.60 Y13 ρ 13 2.74 Y27 ρ 27 3.74 Y14 ρ 14 2.55 PD※3.821 Y28 ρ 28 5.01 Y15 ρ 15 3.67 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


#### 4.2.2. Long-Term Vulnerability Analysis

According to the calculation results in Table3, the long-term vulnerability of PD-FAF-SC in trading center is shown as P (SC∗ = 1) = 6.73 × 10−5, which is higher than the risk caused by the sudden factors in the short-term supply chain. Most of the factors are long-term cumulative effects that are nonbursty, so the probability of long-term vulnerability is much lower than the short-term vulnerability. Judging from the occurrence probability of each intermediate node, there is no doubt that the transfer link is the first factor of forming the long-term vulnerability of the supply chain: P (MT∗ = 1) = 6.35 × 10−5, which is the main bottleneck of the operation and development of PD-FAF-SC in trading center. It is also the core factor to improve the supply chain resilience efficiency. The main factor restricting the circulation of the middle reaches lies in the low level of information integration of the platform in the platform’s leading operation: P (MT∗ = 1) = 6.35 × 10−5 which may result in a delay in the transmission of information flow, the lack of transportation capacity (Y13) of cold chain transportation and professional auxiliary facilities, and the cold chain transport organization are not in place (X18), causing the short-term fragility of trading center. In addition, the low strategic awareness of high value added in circulation processing (Y11) and the low carbon constraints of green logistics (Y18) are also the main factors contributing to the vulnerability of the middle reaches. This also accords with the characteristics and present situation of the lack of circulation and transportation capacity of China’s fresh agricultural products and the shift to the development of low carbonization. The long term vulnerability of PD-FAF-SC in trading center is also partly caused by P (UP∗=1)= 0.0126 × 10−5. The long-term vulnerability that occurred in the upstream planting links is characterized by the vulnerability of small- and medium-sized fresh agricultural products production enterprises P(SCE = 1) = 6.84 × 10−5. At present, the “company + farmer” supply chain mode of agricultural products has occupied about 45% of China’s agricultural industrialization management mode [16]. The influence of insufficient information communication, climate change, and other natural disasters is higher than that of the large fresh agricultural production enterprises’ vulnerability P (LCE = 1) of 1.65 × 10−5. Orders or trade defaults occur from time to time, which to some extent affects the healthy development of PD-FAF-SC. However, the bullwhip effect caused by incomplete information and the inaccurate demand prediction (Y3P7) and poor information communication (Y4P8) are common in Chinese large-, medium-, and small-scale enterprises producing fresh agricultural products, resulting in the fact that the supply cannot well match the downstream demand for fresh agricultural products. The uncertainty of demand prediction includes not only the mismatch of product quantity, but also the variety richness of fresh agricultural products supplied upstream, and the product quality and nutritional value cannot meet the diversified demand of downstream consumers. In order to prevent maliciously lowering the price of fresh agricultural products, reduce the high loss rate of agricultural products, and further aggravate the agricultural environmental pollution, China has been perfecting various agricultural cooperation ways in recent years, and improving the integration and concentration of agricultural industries.Although, in the long run, the development of deep processing enterprises for agricultural products offsets the obvious seasonal effects of some short-term fresh agricultural products retailers, making the long-term vulnerability of downstream demand and retail consumption links smaller (P∗DR∗=1) = 0.00891× 10−5, however the open import environment, such as imported fresh agricultural products, has a great impact on China’s fresh agricultural products industry, P (Y24 = 1) = 10.4 × 10−5, where it is expected that the supply and demand of domestic fresh agricultural products will be impacted for a long time in a certain period.


### 4.3. Model Calculation

According to the statistical results of the survey, among the 378 typical supply chain risk management accidents causing social impact, 67 supply chain disruptions occurred, accounting for 17.8% of the total number. As we see, supply chain disruption is a key issue to be concerned in PD-FAP-SC of trading centre. Taking a supply chain disruption scenario as an example, this paper sets up a vulnerability dynamic monitoring model. During the eight-year operation of fresh agricultural products trading center, the “Precursor Incident” data of supply chain vulnerability are shown in Tables3 and 4, and the Beta distribution parameters of short-term and long-term supply chain vulnerability are shown in Table 5.Table 5
Parameters of Beta distribution.
Beta distribution Mean value variance a b Short-term supply chain 0.018 0.00003 8 214 Long-term supply chain 0.0025 0.00007 3 126Based on the information mentioned in Table5, the posterior probability of supply chain vulnerability can be calculated, as shown in Table 6.Table 6
Posterior probability of supply chain vulnerability.
Time The 0th year The 1st year The 2nd year The 3rd year The 4th year Short-term supply chain 0.018 0.022 0.025 0.032 0.048 Long-term supply chain 0.0025 0.0016 0.0011 0.0008 0.0004It follows that, with the increase of various uncertain factors and disturbances in the short-term supply chain, the posterior probability of supply chain vulnerability increases year by year to 0.048, an increase of nearly three times. The probability of occurrence of long-term supply chain vulnerability drops to 0.0004, which is nearly 6 times lower, which benefits from the fact that the degree of information internalization of the platform-led supply chain is greatly enhanced, and the change rule conforms to the elastic property of the supply chain.The calculation results prove that the BN model included “Precursor Incident” and dynamic variation rule of supply chain vulnerability can be reflected, to provide guidance for the formulation of prevention and controlling strategies of supply chain vulnerability. With the continuous growth of each transaction subject in the platform-dominated supply chain, it is necessary to appropriately increase the investment in information system, improve the level of platform information integration, and reinforce the detection to key nodes, to reduce the occurrence of “Precursor Incident”. Meanwhile, after the occurrence of “Precursor Incident,” supply chain managers should pay full attention and conduct a thorough risk investigation and focus on improving the weak links in vulnerability exposed in the event, so as to control the vulnerability in an acceptable range, to improve the flexibility of the supply chain and avoid risks that may cause harm or loss to the sustainable development of people’s lives and industries. The model can be further developed. For example, new data sources, such as monitoring data and expertise from different supply chain actors, could be included in the model to improve the accuracy of the larger range and future models.


## 4.1. The Calculation of FAF-SC Short-Term Vulnerability

### 4.1.1. Short-Term Vulnerability Calculation

After the data statistics, the priori probabilityθi of each root node Xi of Bayesian network where the short-term vulnerability of the PD-FAF-SC occurs can be given. The posteriori probability of Bayesian network is realized by java programming, and then the probability of short-term vulnerability SC and other intermediate events of the parent node in Bayesian networks can be obtained by using the sum (17)-(29) of Figures 3–5 as shown in Table 3.Table 3
Priori probability of the root nodes of the Bayesian network of the short-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−3).
Number Priori probability Node occurrence probability Number Priori probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event X1 θ 1 0.815 0.815 UP1.327 SC1.645 X17 θ 17 12.58 8.245×10−11 0.115 X2 θ 2 0.702 FPS1.301×10−7 X18 θ 18 0.827 X3 θ 3 0.339 X19 θ 19 8.383 PD3.076×10−7 X4 θ 4 0.547 X20 θ 20 0.249 X5 θ 5 0.677 PM0.532×10−7 X21 θ 21 0.147 X6 θ 6 0.874 X22 θ 22 0.366 CCD6.784×10−7 X7 θ 7 0.089 X23 θ 23 0.258 X8 θ 8 0.504 PPE1.663×10−4 X24 θ 24 7.174 X9 θ 9 0.33 X25 θ 25 0.203 DS5.151×10−5 DR0.203 X10 θ 10 0.513 0.513 X26 θ 26 0.303 X11 θ 11 0.314 CP2.765×10−9 MT X27 θ 27 0.169 X12 θ 12 0.109 X28 θ 28 0.779 TC1.020×10−12 X13 θ 13 0.074 X29 θ 29 0.865 X14 θ 14 0.115 CCT X30 θ 30 0.108 X15 θ 15 6.17 X31 θ 31 83.47 X16 θ 16 0.128 X32 θ 32 0.167 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


### 4.1.2. Short-Term Vulnerability Analysis

Analysis of Table3 data: the short-term vulnerability of PD-FAF-SC in trading center is P (SC = 1) = 1.645 × 10−3, which has higher risk and is still basically controllable throughout the country. Among them, through the calculation of conditional probability of each node, the main reason for the short-term vulnerability of PD-FAF-SC is concentrated in the upstream planting links: P (UP = 1) = 1.327 × 10−3 which accords with the domestic setting that the upstream production supply link of PD-FAF-SC is the short-term supply chain node and the main bottleneck link at the present stage.The cause of short-term vulnerability of FAF-SC in trading center also exists in the midstream circulation links: P (MT = 1) = 0.115 × 10−3. In China, the production of fresh agricultural products is obviously regional and seasonal, while fresh agricultural products are essential for daily life. The fluctuation of consumption demand is relatively less fluctuating under normal conditions which will result in the deviation of the supply of fresh agricultural products P(X19 = 1) = 8.383 × 10−3, mainly due to factors such as technical error in platform and delays or errors in information transmission. When the upstream supply exceeds the demand in the peak season and the supply is far less than the demand in the off-season, the probability of the imbalance between the upstream and downstream supply and demand is large, which increases the vulnerability of FAF-SC. In recent years, although the investment in cold chain infrastructure in China has been heating up, the overall infrastructure is relatively weak. The infrastructure, technical strength, and integrity of the management of the cold chain of circulation enterprises are not up to the current demand for the circulation of fresh agricultural products in China. The probability of lack of integrity in cold chain management reaches P(X24 = 1) = 7.174 × 10−3, and the probability of insufficient factor of cold chain equipment is P(X15 = 1) = 6.172 × 10−3, which is the primary risk factor of cold chain transportation and cold chain distribution, which affects the smooth operation of domestic PD-FAF-SC.For the supply chain of fresh agricultural products, the probability of short-term vulnerability of downstream consumer retail is P(DR = 1) = 0.203 × 10−3 and the freshness of fresh agricultural products is the decisive factor to determine the sales volume, P (X31 = 1) = 83.47 × 10−3. With the improvement of people’s living standards, the general public’s awareness of food safety has gradually increased. However, the influence of food safety rumors is becoming more and more serious and even causes panic P(X29 = 1) = 0.865 × 10-3, causing downstream retailers to cut off their sales, leading to a large backlog of products produced by upstream agricultural growers or farmers, and even rotten in the ground, which is also one of the factors that influence the vulnerability of trading center PD-FAF-SC.


## 4.1.1. Short-Term Vulnerability Calculation

After the data statistics, the priori probabilityθi of each root node Xi of Bayesian network where the short-term vulnerability of the PD-FAF-SC occurs can be given. The posteriori probability of Bayesian network is realized by java programming, and then the probability of short-term vulnerability SC and other intermediate events of the parent node in Bayesian networks can be obtained by using the sum (17)-(29) of Figures 3–5 as shown in Table 3.Table 3
Priori probability of the root nodes of the Bayesian network of the short-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−3).
Number Priori probability Node occurrence probability Number Priori probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event X1 θ 1 0.815 0.815 UP1.327 SC1.645 X17 θ 17 12.58 8.245×10−11 0.115 X2 θ 2 0.702 FPS1.301×10−7 X18 θ 18 0.827 X3 θ 3 0.339 X19 θ 19 8.383 PD3.076×10−7 X4 θ 4 0.547 X20 θ 20 0.249 X5 θ 5 0.677 PM0.532×10−7 X21 θ 21 0.147 X6 θ 6 0.874 X22 θ 22 0.366 CCD6.784×10−7 X7 θ 7 0.089 X23 θ 23 0.258 X8 θ 8 0.504 PPE1.663×10−4 X24 θ 24 7.174 X9 θ 9 0.33 X25 θ 25 0.203 DS5.151×10−5 DR0.203 X10 θ 10 0.513 0.513 X26 θ 26 0.303 X11 θ 11 0.314 CP2.765×10−9 MT X27 θ 27 0.169 X12 θ 12 0.109 X28 θ 28 0.779 TC1.020×10−12 X13 θ 13 0.074 X29 θ 29 0.865 X14 θ 14 0.115 CCT X30 θ 30 0.108 X15 θ 15 6.17 X31 θ 31 83.47 X16 θ 16 0.128 X32 θ 32 0.167 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


## 4.1.2. Short-Term Vulnerability Analysis

Analysis of Table3 data: the short-term vulnerability of PD-FAF-SC in trading center is P (SC = 1) = 1.645 × 10−3, which has higher risk and is still basically controllable throughout the country. Among them, through the calculation of conditional probability of each node, the main reason for the short-term vulnerability of PD-FAF-SC is concentrated in the upstream planting links: P (UP = 1) = 1.327 × 10−3 which accords with the domestic setting that the upstream production supply link of PD-FAF-SC is the short-term supply chain node and the main bottleneck link at the present stage.The cause of short-term vulnerability of FAF-SC in trading center also exists in the midstream circulation links: P (MT = 1) = 0.115 × 10−3. In China, the production of fresh agricultural products is obviously regional and seasonal, while fresh agricultural products are essential for daily life. The fluctuation of consumption demand is relatively less fluctuating under normal conditions which will result in the deviation of the supply of fresh agricultural products P(X19 = 1) = 8.383 × 10−3, mainly due to factors such as technical error in platform and delays or errors in information transmission. When the upstream supply exceeds the demand in the peak season and the supply is far less than the demand in the off-season, the probability of the imbalance between the upstream and downstream supply and demand is large, which increases the vulnerability of FAF-SC. In recent years, although the investment in cold chain infrastructure in China has been heating up, the overall infrastructure is relatively weak. The infrastructure, technical strength, and integrity of the management of the cold chain of circulation enterprises are not up to the current demand for the circulation of fresh agricultural products in China. The probability of lack of integrity in cold chain management reaches P(X24 = 1) = 7.174 × 10−3, and the probability of insufficient factor of cold chain equipment is P(X15 = 1) = 6.172 × 10−3, which is the primary risk factor of cold chain transportation and cold chain distribution, which affects the smooth operation of domestic PD-FAF-SC.For the supply chain of fresh agricultural products, the probability of short-term vulnerability of downstream consumer retail is P(DR = 1) = 0.203 × 10−3 and the freshness of fresh agricultural products is the decisive factor to determine the sales volume, P (X31 = 1) = 83.47 × 10−3. With the improvement of people’s living standards, the general public’s awareness of food safety has gradually increased. However, the influence of food safety rumors is becoming more and more serious and even causes panic P(X29 = 1) = 0.865 × 10-3, causing downstream retailers to cut off their sales, leading to a large backlog of products produced by upstream agricultural growers or farmers, and even rotten in the ground, which is also one of the factors that influence the vulnerability of trading center PD-FAF-SC.


## 4.2. FAF-SC Long-Term Vulnerability Calculation

### 4.2.1. Long-Term Vulnerability Calculation

Consistent with the idea of short-term supply chain vulnerability assessment, the priori probabilityρj is given for each root node Yj of the Bayesian network where PD-FAF-SC long-term vulnerability occurs, and then the probability of short-term vulnerability SC and other intermediate events of parent nodes in Bayesian network can be obtained by using Figures 5–7 sum formula (42)-(53), as shown in Table 4.Table 4
Priori probability of the root nodes of the Bayesian network of the long-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−5).
Number Prior probability Node occurrence probability Number Prior probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event Y1 ρ 1 5 LCE1.65 UP※0.0126 SC※6.73 Y16 ρ 16 0.308 Y2 ρ 2 1.23 Y17 ρ 17 31.68 Y3 ρ 3 3.23 Y1 ρ 1 5 CCD※1.153 Y4 ρ 4 1.47 Y18 ρ 18 2.78 Y5 ρ 5 5.54 Y19 ρ 19 3.75 Y1 ρ 1 5 SCE6.84 Y1 ρ 1 5 RE3.894 DR※0.0089 Y6 ρ 6 1.54 Y20 ρ 20 4.12 Y7 ρ 7 42.3 Y21 ρ 21 6.33 Y8 ρ 8 3.79 Y22 ρ 22 4.60 Y9 ρ 9 8.97 Y23 ρ 23 8.52 Y10 ρ 10 6.78 Y24 ρ 24 10.4 Y11 ρ 11 7.91 DP※0.978 MT※6.35 Y1 ρ 1 5 FDE2.287 Y12 ρ 12 1.87 Y25 ρ 25 6.54 Y1 ρ 1 5 CCT※0.774 Y26 ρ 26 2.60 Y13 ρ 13 2.74 Y27 ρ 27 3.74 Y14 ρ 14 2.55 PD※3.821 Y28 ρ 28 5.01 Y15 ρ 15 3.67 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


### 4.2.2. Long-Term Vulnerability Analysis

According to the calculation results in Table3, the long-term vulnerability of PD-FAF-SC in trading center is shown as P (SC∗ = 1) = 6.73 × 10−5, which is higher than the risk caused by the sudden factors in the short-term supply chain. Most of the factors are long-term cumulative effects that are nonbursty, so the probability of long-term vulnerability is much lower than the short-term vulnerability. Judging from the occurrence probability of each intermediate node, there is no doubt that the transfer link is the first factor of forming the long-term vulnerability of the supply chain: P (MT∗ = 1) = 6.35 × 10−5, which is the main bottleneck of the operation and development of PD-FAF-SC in trading center. It is also the core factor to improve the supply chain resilience efficiency. The main factor restricting the circulation of the middle reaches lies in the low level of information integration of the platform in the platform’s leading operation: P (MT∗ = 1) = 6.35 × 10−5 which may result in a delay in the transmission of information flow, the lack of transportation capacity (Y13) of cold chain transportation and professional auxiliary facilities, and the cold chain transport organization are not in place (X18), causing the short-term fragility of trading center. In addition, the low strategic awareness of high value added in circulation processing (Y11) and the low carbon constraints of green logistics (Y18) are also the main factors contributing to the vulnerability of the middle reaches. This also accords with the characteristics and present situation of the lack of circulation and transportation capacity of China’s fresh agricultural products and the shift to the development of low carbonization. The long term vulnerability of PD-FAF-SC in trading center is also partly caused by P (UP∗=1)= 0.0126 × 10−5. The long-term vulnerability that occurred in the upstream planting links is characterized by the vulnerability of small- and medium-sized fresh agricultural products production enterprises P(SCE = 1) = 6.84 × 10−5. At present, the “company + farmer” supply chain mode of agricultural products has occupied about 45% of China’s agricultural industrialization management mode [16]. The influence of insufficient information communication, climate change, and other natural disasters is higher than that of the large fresh agricultural production enterprises’ vulnerability P (LCE = 1) of 1.65 × 10−5. Orders or trade defaults occur from time to time, which to some extent affects the healthy development of PD-FAF-SC. However, the bullwhip effect caused by incomplete information and the inaccurate demand prediction (Y3P7) and poor information communication (Y4P8) are common in Chinese large-, medium-, and small-scale enterprises producing fresh agricultural products, resulting in the fact that the supply cannot well match the downstream demand for fresh agricultural products. The uncertainty of demand prediction includes not only the mismatch of product quantity, but also the variety richness of fresh agricultural products supplied upstream, and the product quality and nutritional value cannot meet the diversified demand of downstream consumers. In order to prevent maliciously lowering the price of fresh agricultural products, reduce the high loss rate of agricultural products, and further aggravate the agricultural environmental pollution, China has been perfecting various agricultural cooperation ways in recent years, and improving the integration and concentration of agricultural industries.Although, in the long run, the development of deep processing enterprises for agricultural products offsets the obvious seasonal effects of some short-term fresh agricultural products retailers, making the long-term vulnerability of downstream demand and retail consumption links smaller (P∗DR∗=1) = 0.00891× 10−5, however the open import environment, such as imported fresh agricultural products, has a great impact on China’s fresh agricultural products industry, P (Y24 = 1) = 10.4 × 10−5, where it is expected that the supply and demand of domestic fresh agricultural products will be impacted for a long time in a certain period.


## 4.2.1. Long-Term Vulnerability Calculation

Consistent with the idea of short-term supply chain vulnerability assessment, the priori probabilityρj is given for each root node Yj of the Bayesian network where PD-FAF-SC long-term vulnerability occurs, and then the probability of short-term vulnerability SC and other intermediate events of parent nodes in Bayesian network can be obtained by using Figures 5–7 sum formula (42)-(53), as shown in Table 4.Table 4
Priori probability of the root nodes of the Bayesian network of the long-term vulnerability of the trading center PD-FAF-SC, the probability of the parent node, and the intermediate node (10−5).
Number Prior probability Node occurrence probability Number Prior probability Node occurrence probability Base event Intermediate event Top event Base event Intermediate event Top event Y1 ρ 1 5 LCE1.65 UP※0.0126 SC※6.73 Y16 ρ 16 0.308 Y2 ρ 2 1.23 Y17 ρ 17 31.68 Y3 ρ 3 3.23 Y1 ρ 1 5 CCD※1.153 Y4 ρ 4 1.47 Y18 ρ 18 2.78 Y5 ρ 5 5.54 Y19 ρ 19 3.75 Y1 ρ 1 5 SCE6.84 Y1 ρ 1 5 RE3.894 DR※0.0089 Y6 ρ 6 1.54 Y20 ρ 20 4.12 Y7 ρ 7 42.3 Y21 ρ 21 6.33 Y8 ρ 8 3.79 Y22 ρ 22 4.60 Y9 ρ 9 8.97 Y23 ρ 23 8.52 Y10 ρ 10 6.78 Y24 ρ 24 10.4 Y11 ρ 11 7.91 DP※0.978 MT※6.35 Y1 ρ 1 5 FDE2.287 Y12 ρ 12 1.87 Y25 ρ 25 6.54 Y1 ρ 1 5 CCT※0.774 Y26 ρ 26 2.60 Y13 ρ 13 2.74 Y27 ρ 27 3.74 Y14 ρ 14 2.55 PD※3.821 Y28 ρ 28 5.01 Y15 ρ 15 3.67 Data sources:Compilation of National Agricultural Products Cost-Benefit Data, China Commodity Exchange Market Statistics Yearbook, International Agricultural Products Trade Statistics Yearbook, exchange center platform information database, and expert interview data.


## 4.2.2. Long-Term Vulnerability Analysis

According to the calculation results in Table3, the long-term vulnerability of PD-FAF-SC in trading center is shown as P (SC∗ = 1) = 6.73 × 10−5, which is higher than the risk caused by the sudden factors in the short-term supply chain. Most of the factors are long-term cumulative effects that are nonbursty, so the probability of long-term vulnerability is much lower than the short-term vulnerability. Judging from the occurrence probability of each intermediate node, there is no doubt that the transfer link is the first factor of forming the long-term vulnerability of the supply chain: P (MT∗ = 1) = 6.35 × 10−5, which is the main bottleneck of the operation and development of PD-FAF-SC in trading center. It is also the core factor to improve the supply chain resilience efficiency. The main factor restricting the circulation of the middle reaches lies in the low level of information integration of the platform in the platform’s leading operation: P (MT∗ = 1) = 6.35 × 10−5 which may result in a delay in the transmission of information flow, the lack of transportation capacity (Y13) of cold chain transportation and professional auxiliary facilities, and the cold chain transport organization are not in place (X18), causing the short-term fragility of trading center. In addition, the low strategic awareness of high value added in circulation processing (Y11) and the low carbon constraints of green logistics (Y18) are also the main factors contributing to the vulnerability of the middle reaches. This also accords with the characteristics and present situation of the lack of circulation and transportation capacity of China’s fresh agricultural products and the shift to the development of low carbonization. The long term vulnerability of PD-FAF-SC in trading center is also partly caused by P (UP∗=1)= 0.0126 × 10−5. The long-term vulnerability that occurred in the upstream planting links is characterized by the vulnerability of small- and medium-sized fresh agricultural products production enterprises P(SCE = 1) = 6.84 × 10−5. At present, the “company + farmer” supply chain mode of agricultural products has occupied about 45% of China’s agricultural industrialization management mode [16]. The influence of insufficient information communication, climate change, and other natural disasters is higher than that of the large fresh agricultural production enterprises’ vulnerability P (LCE = 1) of 1.65 × 10−5. Orders or trade defaults occur from time to time, which to some extent affects the healthy development of PD-FAF-SC. However, the bullwhip effect caused by incomplete information and the inaccurate demand prediction (Y3P7) and poor information communication (Y4P8) are common in Chinese large-, medium-, and small-scale enterprises producing fresh agricultural products, resulting in the fact that the supply cannot well match the downstream demand for fresh agricultural products. The uncertainty of demand prediction includes not only the mismatch of product quantity, but also the variety richness of fresh agricultural products supplied upstream, and the product quality and nutritional value cannot meet the diversified demand of downstream consumers. In order to prevent maliciously lowering the price of fresh agricultural products, reduce the high loss rate of agricultural products, and further aggravate the agricultural environmental pollution, China has been perfecting various agricultural cooperation ways in recent years, and improving the integration and concentration of agricultural industries.Although, in the long run, the development of deep processing enterprises for agricultural products offsets the obvious seasonal effects of some short-term fresh agricultural products retailers, making the long-term vulnerability of downstream demand and retail consumption links smaller (P∗DR∗=1) = 0.00891× 10−5, however the open import environment, such as imported fresh agricultural products, has a great impact on China’s fresh agricultural products industry, P (Y24 = 1) = 10.4 × 10−5, where it is expected that the supply and demand of domestic fresh agricultural products will be impacted for a long time in a certain period.


## 4.3. Model Calculation

According to the statistical results of the survey, among the 378 typical supply chain risk management accidents causing social impact, 67 supply chain disruptions occurred, accounting for 17.8% of the total number. As we see, supply chain disruption is a key issue to be concerned in PD-FAP-SC of trading centre. Taking a supply chain disruption scenario as an example, this paper sets up a vulnerability dynamic monitoring model. During the eight-year operation of fresh agricultural products trading center, the “Precursor Incident” data of supply chain vulnerability are shown in Tables3 and 4, and the Beta distribution parameters of short-term and long-term supply chain vulnerability are shown in Table 5.Table 5
Parameters of Beta distribution.
Beta distribution Mean value variance a b Short-term supply chain 0.018 0.00003 8 214 Long-term supply chain 0.0025 0.00007 3 126Based on the information mentioned in Table5, the posterior probability of supply chain vulnerability can be calculated, as shown in Table 6.Table 6
Posterior probability of supply chain vulnerability.
Time The 0th year The 1st year The 2nd year The 3rd year The 4th year Short-term supply chain 0.018 0.022 0.025 0.032 0.048 Long-term supply chain 0.0025 0.0016 0.0011 0.0008 0.0004It follows that, with the increase of various uncertain factors and disturbances in the short-term supply chain, the posterior probability of supply chain vulnerability increases year by year to 0.048, an increase of nearly three times. The probability of occurrence of long-term supply chain vulnerability drops to 0.0004, which is nearly 6 times lower, which benefits from the fact that the degree of information internalization of the platform-led supply chain is greatly enhanced, and the change rule conforms to the elastic property of the supply chain.The calculation results prove that the BN model included “Precursor Incident” and dynamic variation rule of supply chain vulnerability can be reflected, to provide guidance for the formulation of prevention and controlling strategies of supply chain vulnerability. With the continuous growth of each transaction subject in the platform-dominated supply chain, it is necessary to appropriately increase the investment in information system, improve the level of platform information integration, and reinforce the detection to key nodes, to reduce the occurrence of “Precursor Incident”. Meanwhile, after the occurrence of “Precursor Incident,” supply chain managers should pay full attention and conduct a thorough risk investigation and focus on improving the weak links in vulnerability exposed in the event, so as to control the vulnerability in an acceptable range, to improve the flexibility of the supply chain and avoid risks that may cause harm or loss to the sustainable development of people’s lives and industries. The model can be further developed. For example, new data sources, such as monitoring data and expertise from different supply chain actors, could be included in the model to improve the accuracy of the larger range and future models.


## 5. Conclusions

(1) Because the fresh agricultural products supply chain is a complex large scale system, its vulnerability analysis is a problem. Aiming at the dynamic change characteristics of vulnerability in the operation process of platform-oriented fresh agricultural product supply chain, “Precursor Incident” information is extracted, and the quantitative calculation method and idea of dynamic vulnerability based on bow-tie model and Bayesian network model are proposed.(2) The application of Bayesian network model can make full use of the “Precursor Incident” information in the production process for modelling calculation, analyze and predict the risk change trend, overcome the ambiguity of comprehensive risk assessment, and improve the prediction accuracy of supply chain vulnerability assessment, which can provide intuitive reference for the prevention and control of supply chain risk.(3) The calculation results of accidents caused by supply chain vulnerability events show that increasing evidence information “Precursor Incident” will result in remarkable growth of supply chain vulnerability. It is suggested that supply chain managers shall proceed with a complete and thorough accident investigation to “Precursor Incident” and highlight improving weak safety links, reducing the number of “Precursor Incidents” and then control and lower vulnerability and advance the supply chain resilience.



---

*Source: 6874013-2018-12-19.xml*