Vulnerability Assessment for Port Logistics System Based on DEMATEL-ISM-BWM

: In order to identify and assess the vulnerability of the port logistics system itself, this paper further improves the methodology on the basis of previous studies by using the Deterministic Experimentation and Evaluation Laboratory (DEMATEL) and Interpretive Structural Modeling (ISM) methods to study the correlation between the vulnerability factors of the port logistics system, and the best-worst method (BWM) to identify the key vulnerability points of the system. The results of the study showed that in terms of the correlation between the factors, port consolidation capacity and average arrival time are the most direct factors affecting the vulnerability of the port logistics system, and the strength of government regulation and coordination and the level of port management are important indirect factors affecting the vulnerability of the port logistics system. This paper also found that port loading and unloading facilities and natural disasters are the main vulnerabilities affecting the port logistics system itself. Port enterprises should focus on reducing the vulnerability of the system by strengthening the above aspects. The model constructed in this paper can also be applied to future research on the resilience and sustainability of port logistics.


Introduction
The vulnerability of the port logistics system itself has rarely been studied in depth by scholars.Most of the existing research on the stability of logistics systems focuses on robustness, resilience, vulnerability, etc., but it is crucial to unearth the vulnerabilities that exist in the system because all system breakdowns start from the most vulnerable places, which in turn undermine the overall stability of the system.Ports are the most important and significant gathering and distributing point of global goods are important nodes for trade between countries, and their impact on the development of global trade is significant [1,2].Ports are also important nodes in the global supply chain [3].However, for their own reasons, ports are susceptible to a number of threats to port efficiency, the effects of which are transmitted to the various nodes of the supply chain [4,5].At the same time, as a key transportation node connecting water and land, port logistics is susceptible to a variety of factors from both the seaside and the land side [6].Any interruption of the seaport will have a direct impact on the supply chain to which the seaport belongs and will be transmitted to the supply chain network to have an indirect impact on the whole industry [7].Therefore, with the deepening of international trade and cooperation, the healthy and sustainable development of port logistics, especially the vulnerability study of the port logistics system, has received more and more attention.
The occurrence of various port accidents has also prompted research on the vulnerability of port logistics.Natural disaster risks [8], security risks [9], trade risks [10], environmental risks [11], and operational risks [12] faced by ports can be the trigger for the port logistics system's own vulnerability [13,14], which can lead to a decrease in the efficiency of port operation.However, less research has been completed on mining the vulnerabilities of the port logistics system itself.Most of the current vulnerability studies focus on the specific threats faced by the port logistics sector, neglecting the excavation of the potential vulnerability of the port logistics system under normal conditions, while the concept of the vulnerability of the port logistics system is not yet clear.Therefore, this paper starts from the inside of port logistics and explores the influence of factors such as natural geography, port infrastructure, port information systems, and port support systems.Moreover, it explores the influence of port logistics operations and reveals its physical vulnerability.Also, from the perspective of the entire port logistics efficiency (economic vulnerability), the vulnerabilities that restrict efficiency improvement are identified.
The mainstream methods for studying vulnerability include hierarchical analysis (AHP) [15], data envelopment analysis (DEA) [2,16], analytic network process (ANP) [17], (Technique for Order Preference by Similarity to an Ideal Solution) TOPSIS [18] model, ISM [15,19], DEMATEL [15,19], BWM [20] methods and so on.However, previous studies were unable to analyze in depth the relationship between various factors affecting vulnerability, and the process of determining the "vulnerability point" was too complicated.Therefore, we use DEMATEL, ISM, and BWM methods to identify the correlation of vulnerability factors of the port logistics system, determine their mutual influence (physical vulnerability), and identify key vulnerability factors (economic vulnerability) that affect its efficiency improvement, which previous research has not been completed.
Most of the previous studies have examined port-exposed vulnerabilities in the context of specific scenarios or threats, and there is a lack of mining and exploring potential vulnerabilities in the context of the normal functioning of port logistics systems.However, the correlation between factors is also often overlooked, as the outbreak of a particular source of vulnerability is often the result of the interaction of factors.In this paper, we focus on the port logistics system itself to find and rank the inherent vulnerability factors implicit in the system.Therefore, this paper builds on previous research [21] and proposes a generic vulnerability assessment framework aimed at comprehensively assessing the vulnerability of port logistics.The assessment of the port logistics system in this paper has two main objectives: first, to explore the relationship between the factors affecting the vulnerability of the port logistics system, and second, to identify the most critical vulnerabilities (i.e., bottlenecks) in the port logistics system, so as to capitalize on these vulnerabilities to improve the operational efficiency of the port logistics system and enhance the overall resilience of the port logistics system.This paper is organized as follows.Section 2 contains a literature review that focuses on the port logistics system, the concept of vulnerability, the influence factors on the port logistics system, and vulnerability identification and research methods.Section 3 introduces the proposed port logistics vulnerability assessment framework.Section 4 presents the case study of a port in China.Results and discussions are shown in Section 5. Finally, Section 6 concludes the paper with its main contributions.

Literature Review
In order to have a more in-depth understanding of what vulnerability is, this section will cover the components of port logistics systems and their characteristics, the connotation of port logistics system vulnerability, and clarify the research methodology of this paper.In this section, the current research will be reviewed and summarized from four aspects: port logistics system, vulnerability, the concept of port logistics system vulnerability, and vulnerability research method.

Port Logistics System
Port logistics refers to the comprehensive logistics system centered on the combination of various kinds of transportation and the advantageous conditions of the environment, using the port's own geographical conditions and its proximity to the sea [22,23].
Fluid, carrier, and flow direction are its three main components [24].Through the mobility function of the port, the port undergoes logistics activities shortening the distance between the spatial locations of goods and sending them to where they are needed is the goal of port logistics [25].The carrier is the infrastructure equipment through which the circulation takes place [26].Flow direction is on behalf of the goods in the process of logistics operation, and finally to the distribution of the link, the goods from a comprehensive series of activities, and finally sent to the hands of consumers in a special form of delivery, to complete the final link of logistics [27].The port realizes the function of a modern logistics center with composite advantage, the port's multiple identities have strategic status in international logistics, and the port provides value-added services through the logistics system [28].
The port logistics system is a highly integrated and complex system.The port performs the transformation task of multiple modes of transport, and the internal functional modules of the port are also diverse.Therefore, the factors influencing the development of port logistics are also diverse.

Vulnerability
Vulnerability is a property of the system itself.The inadequacy of the system when exposed to a threat is an important manifestation of this.Although vulnerability is proposed on the basis of risk analysis, they have different emphases.Risk analysis often focuses on human, environmental, and property losses or impacts caused by events [29].When analyzing the vulnerability of the system, research should focus on "the extended set of threats and consequences", "reducing the risk of the system and restoring the system to a new stable state", and "the chain-breaking time before the system establishes a new stability".
Based on the development of vulnerability theory in other fields such as ecology, many experts have offered insights into vulnerability in port studies.Zhang Weixi et al. [30] pointed out that the vulnerability of the logistics system is the basic characteristic of the port.Any change in port-dependent logistics activities will cause changes in the whole system, including transportation, industrial trade, finance, and multimodal transport.Not only is port logistics a relatively complex system, but it is also closely linked to the external environment, which makes it difficult to study the vulnerability of port logistics.At the same time, the port itself is a highly integrated system with multiple components.Assessing the vulnerability of a port is very challenging, as can be seen from the following aspects: first, there are multidimensional definitions of port vulnerability [31] and different experts focus on different latitudes; second, there are no statistics on the critical threshold for the occurrence of major disasters in ports [32]; and third, how to construct vulnerability indicators [33].
The definition of vulnerability of port logistics systems is not yet completely clear, but some experts have provided their own insights.For example, under the disturbance and interference of internal and external factors, the port logistics system loses all or part of its operational capacity due to the instability and sensitivity of its own system, resulting in the decline or stagnation of the efficiency of the logistics system [21].

Vulnerability on Port Logistics System
Although there are various research results on port risk or vulnerability analysis, there are more articles on the vulnerability of ports due to the number of port accidents in recent years.It is generally believed that the factors affecting the vulnerability of port logistics can be broadly divided into two aspects.First, natural environmental factors, which mainly include some natural disasters such as earthquakes, tsunamis, sea level rise, lightning, natural fires, climate change, extreme weather, etc.
Joan Pau Sierra et al. [34] assessed the vulnerability of the Catalan port group in the northwestern Mediterranean to sea level rise using linear wave theory and emphasized the need to integrate climate change into long-term port planning and management.Melissa Nursey Bray et al. [35] argued that climate change will have an impact on the port's envi-ronment, infrastructure, staff safety, and supply chain, and made suggestions on the port's appropriate response to climate change from the perspective of adaptability and social elasticity.Nathan J. Wood et al. [36] used Geographic Information System (GIS) technology to assess the impact of earthquakes and tsunamis on port vulnerability.However, this method also has certain limitations.For example, the results of the GIS assessment are too objective, and the weight of specific issues needs to be measured manually.
On the other hand, human environmental factors mainly include operational accidents, man-made fires, improper management, terrorist attacks, sabotage, explosions, etc. Patterson et al. [37] used the (Time-varying Coefficients) TVC model under the Critical Asset Protection Risk Analysis and Management Framework (RAMCAP) to analyze the potential vulnerability of the port infrastructure, personnel, and transportation system of the Santiago United Port in the event of terrorist attacks.Lin Zhou et al. [38] analyzed the "8.12" fire and explosion accident in Tianjin port by using Hfacs-Hc and human factors and classification of hazardous chemicals system and determined the impact of human factors at different levels on port vulnerability.At present, most academic research on vulnerability is based on the context of climate change, natural disasters, and human causes.
There are fewer studies on potential vulnerability threats under normal operation of port logistics systems.

Vulnerability Identification and Research Methods
M. Jiang et al. [39] assessed the vulnerability of ports from the perspective of the supply chain, considering robustness, importance, efficiency, and elasticity as factors affecting vulnerability, and proposed to complete the construction of a vulnerability assessment system by fuzzy logic method and (Entity-relationship) ER method.Hsieh and C.-H. [40] used GIS technology to evaluate the vulnerability of the port in terms of natural disasters faced by the port.It can be seen that the port vulnerability study needs to consider the application of different knowledge.S. Raicu et al. [41] believed that the factors affecting the vulnerability of port logistics can be divided into two main aspects.One is the risk in port logistics operation, such as delayed delivery, excess inventory, poor forecasting, financial risk, port machinery failure, human error, information technology system failure, etc.Second, the external risks of port logistics, such as politics, economic policies, natural disasters, price fluctuations, wars, etc. Cao et al. [42] revealed that there are two major difficulties in using traditional vulnerability assessment methods: one is that the uncertainty of port data is difficult to overcome, and the other is that the correlation between different data is difficult to explore in vulnerability reasoning.Furthermore, they proposed a rapid response port vulnerability assessment framework based on fuzzy evidence reasoning (ER) [43,44] and fuzzy similar ideal solution ranking method (TOPSIS) [18], taking Tianjin Port under the background of the 2015 explosion as a case.However, this method is applied to post-vulnerability and does not consider the combination with pre-vulnerability for research.Vulnerability factors usually have strong concealment and fuzziness, and there are relatively great difficulties and challenges in collecting vulnerability factors.From the research literature at home and abroad, vulnerability identification methods in the field of transportation usually refer to risk identification methods.Later, researchers slowly began to explore the vulnerability of the system measured by quantitative methods.Quantitative vulnerability methods were first developed in the field of ecology.Me.Bar et al. [45] believed that vulnerability is the level of critical value of disasters.Shieh integrated three systems analysis methods of DEMATEL, ISM, and ANP (Analytic Network Process) [17,19] to identify the vulnerability factors affecting the transport system, effectively integrating the characteristics of the vulnerability factors and the interaction between the vulnerability factors.Similarly, Chen et al. [15] integrated DEMATEL, ISM, and AHP to overcome the challenges of vulnerability factor identification.Wang et al. [16] used the DEA and complex network method to study the attractiveness of hub ports.Ozmen [20] applied the BWM-ABAC (alternative by alternative comparison) methodology for vulnerability assessment of seismic hazard management, confirming the validity of the evaluation methodology.1, this paper summarizes typical approaches to studying risk and vulnerability.In previous studies, experts usually combine DEMATEL and ISM models to analyze the correlations between factors and use the AHP/ANP method to identify the key crisp points of the system.The interrelationships between vulnerability factors in port logistics systems are often very complex, and clarifying the influence relationships between them is crucial to determining the key vulnerability points of the system.Through the combination of DEMATEL and ISM methods, the relationship between vulnerability influencing factors can be well identified, presented in the form of a correlation diagram, and quantitatively expressed their importance in the entire system.This is the application of this article.However, there is a disadvantage in applying the AHP/ANP method as follows: firstly, it is computationally large, and n(n − 1)/2 comparisons (n is the number of indicators) are required when making comparisons between indicators.Second, a large number of judgment matrices need to be constructed, which makes the process quite cumbersome.Third, the consistency of the calculation results is poor.Therefore, in order to overcome the above problems, this paper introduces the BWM method, which has relatively fewer calculations and a relatively simple process when performing the identification of vulnerability points, has better consistency, and improves the reliability of the assessment.

Port Logistics System Vulnerability Assessment Model
This paper first adopts the qualitative analysis method and establishes the method resume evaluation index system based on expert interviews as well as a literature review.The DEMATEL method is used to construct the overall impact matrix of the vulnerability factors of the port logistics system, reflecting the comprehensive impact relationship among the factors, and the multilevel structural model is established by combining with the ISM model to describe the hierarchical relationship of the vulnerability factors intuitively.The BWM method is used to identify the important factors affecting the vulnerability of the port logistics system.Through the above steps, the key vulnerability factors of the port logistics system are identified, and their mutual influence relationship is clarified through the correlation analysis of the vulnerability factors.

Port Logistics System Vulnerability Indicator System Construction
Considering that the port logistics system is a complex system, it is difficult to collect data and analyze data using the quantitative indicator method, this paper uses quantitative indicators in establishing the indicator system, and is based on interviews with several experts in the port field and previous relevant studies.The Delphi method is used to collect relevant data and establish a vulnerability assessment system for the port logistics system [21] (Table 2).[48] ship access management level C 12 [49] customer relationship management level C 13 [30] port logistics support system and policy B 4 [30] port peripheral facilities C 14 [

DEMATEL Method
DEMATEL is a method for systematic factor analysis using graph theory and matrix tools.The specific steps are as follows: Step 1: The Delphi method, brainstorming method, or expert interviews were used to determine each factor (Table 2).
Step 2: Determine the degree of direct influence among the elements.First, the direct influence matrix of vulnerability impact factors was determined using the expert scoring method.The relationship between factors is divided into five levels.Level 0 means no influence relationship, 1 means weak influence, 2 means relatively weak influence, 3 means moderate influence and 4 means strong influence.Thus, direct influence matrix A is created.a ij denotes the effect of i on j, the elements in column ∑ n j=1 a ij denotes the sum of the rows in the matrix.
Step 3: Normalized direct influence matrix.Use Equation (1) to calculate the normalized direct influence matrix G.
where max 1<i<n n ∑ j=1 a j denotes the largest row and value in the direct impact matrix.
Step 4: Determine the integrated impact matrix.The normalized direct impact matrix is calculated by Equation (2).
where E is the unit matrix.
Step 5: Calculate the degree of influence and the degree of being influenced.The degree of interaction and influence among risk factors is calculated according to Equation (3).
The influence value of the corresponding vulnerability factor in each row that is influenced by other factors is called the degree of influence.
where f i is the sum of the row elements in the integrated influence matrix T, indicating the degree of risk factor i the degree of direct or indirect influence on risk factor j; e i is the sum of the column elements in the integrated influence matrix T.
Step 6: Determine the centrality and causality of factors.
where R i indicates the centrality of the vulnerability factor and C i indicates the causality of the vulnerability factor.
The causality was plotted using the degree of cause C i and the degree of center D i + R i as the vertical and horizontal axes.Let the intersection of the horizontal and vertical coordinates be (x,0) and x be the average of the corresponding centrality of each factor.

ISM Method
The basic idea of the ISM model is to screen the main factors that constitute the vulnerability of the port logistics system through expert discussions and questionnaires, and then use the vulnerability factor matrix and the adjacency matrix of the directed graph to identify the relationships between the main vulnerabilities and their impacts.Based on the basis of DEMATEL analysis, the adjacency matrix F of the vulnerability factors of the port logistics system is obtained by using Equation (8) (given β = 0.01).
As shown in Equation ( 9), the adjacency matrix F is added to the unit matrix E to obtain the multiplication matrix B. Then, the multiplication matrix B is successively multiplied until the matrix no longer varies to obtain the reachable matrix R.
Based on the reachable matrix, the factor levels are divided and the skeleton matrix is obtained, and finally, a multi-order directed graph is drawn based on the skeleton matrix.

BWM Method
Step 1: In a set of evaluation indicators C = {C 1 , C 2 , • • • , C n }, the best indicator C B and the worst indicator C W are selected.
Step 2: Compare the optimal indicator C B with all other indicators within this evaluation indicator set two by two with each other, so as to construct a comparison set A B = {a B1 , a B2 , • • • , a Bn } based on the optimality criterion, where a Bn denotes the relative degree of preference between C B and the C n , which is scored on a scale from 1 to 9.
Step 3: Similar to step 2, the worst indicator C W is compared with all other indicators within this evaluation indicator set two by two with each other to construct a comparison set based on the worst-case criterion A W = {a 1W , a 2W , • • • a nW } T , where a nW denotes the degree of preference of the C n over C W .
Step 4: Solve the best weights using Equation (10).Solving the following nonlinear programming problem yields the optimal weights W j for each evaluation metric and an indication δ * of the result of solving for the weights.The closer δ * is to 0, the smaller the error in the result of solving for the weights, and the more plausible it is.
where δ = max{| w B w i − a Bj |, | w j w w − a jw |}, W B is the weight of the best indicators and W W is the weight of the worst indicators.

Vulnerability Assessment Model
By introducing the unit matrix to transform the comprehensive impact matrix into the overall impact matrix, and utilizing certain calculation methods to transform the overall impact matrix into the reachable matrix, the integration of the two methods can not only quantitatively calculate the importance of the vulnerability factors of the port logistics system to the accidents, but also clarify the interrelated relationship between the impact factors through the delineation of the hierarchy.Finally, the key vulnerability factors are identified by combining the BWM method.The vulnerability assessment model of the port logistics system in this paper is shown in Figure 1.
all impact matrix into the reachable matrix, the integration of the two methods can not only quantitatively calculate the importance of the vulnerability factors of the port logistics system to the accidents, but also clarify the interrelated relationship between the impact factors through the delineation of the hierarchy.Finally, the key vulnerability factors are identified by combining the BWM method.The vulnerability assessment model of the port logistics system in this paper is shown in Figure 1.

Instance Verification
In this paper, five more experts (two professors from the Maritime Management Department of the school, two logistics operators with 15 years of service from the terminal, and one from a relevant maritime government department) in the port field were invited to analyze various potential threats in the daily operation of the port logistics system and to score the DEMATEL method and the BWM method [26].The combined results (direct influence matrix A) of their opinions are shown in Appendix A (Table A1).The normalized direct influence matrix G is shown in Table A2.The integrated impact matrix T is shown in Table A3.
According to Equations ( 1)-( 5), the row sum (f i ) and column sum (e i ) of the integrated influence matrix, as well as the centrality (R i ) and the cause degree (C i ) of each element were obtained, as shown in Table 3.
As can be seen from Table 3, the top three influencing factors are frequency of natural disasters (C 3 ) (f i = 2.103), personnel management ability and staff quality (C 10 ) (f i = 2.055), and port construction conditions (C 2 ) (f i = 1.666).These three factors are most likely to have an impact on the others.In the analysis of the degree of being influenced, the main factors with higher scores are average ship time in port (C 9 ) (e i = 3.191), port consolidation capacity (C 15 ) (e i = 3.094), and port berth condition (C 6 ) (e i = 2.524), suggests that these three factors are the most influenced by other factors and the most susceptible to perturbation.
The causality-centrality coordinates of the factors influencing port logistics vulnerability are plotted according to Table 2, as shown in Figure 2.  In terms of the centrality of factors, the first three factors include port consolidation capacity (C15), average time of ships in port (C9), and port berth status (C6).Improving these factors is essential to reduce the vulnerability of the port logistics system.
In terms of the causality of the factors, the outcome factor with the highest rank among all the outcome factors is the average time of the ships in port (C9), which indicates that it is vulnerable to other factors.Among all the causal factors, the factor with the higher rank is the frequency of natural disasters (C3), indicating that the occurrence of natural disasters is most likely to affect other factors.
From the subsystem perspective, a high infrastructure centrality value also indicates that the port infrastructure is more important in the overall port logistics system, and its overall causality value is negative, indicating that the overall vulnerability of the port infrastructure is high and the system is more vulnerable to shocks.Collapse under the influence of internal and external factors.Meanwhile, the port operations subsystem has a high utility score and a low centrality score, which means that the system can easily have a significant impact on other systems directly or indirectly and is one of the most sensitive.
According to Equation ( 8), this paper takes β to be 0.1, and the resulting reachability In terms of the centrality of factors, the first three factors include port consolidation capacity (C 15 ), average time of ships in port (C 9 ), and port berth status (C 6 ).Improving these factors is essential to reduce the vulnerability of the port logistics system.
In terms of the causality of the factors, the outcome factor with the highest rank among all the outcome factors is the average time of the ships in port (C 9 ), which indicates that it is vulnerable to other factors.Among all the causal factors, the factor with the higher rank is the frequency of natural disasters (C 3 ), indicating that the occurrence of natural disasters is most likely to affect other factors.
From the subsystem perspective, a high infrastructure centrality value also indicates that the port infrastructure is more important in the overall port logistics system, and its overall causality value is negative, indicating that the overall vulnerability of the port infrastructure is high and the system is more vulnerable to shocks.Collapse under the influence of internal and external factors.Meanwhile, the port operations subsystem has a high utility score and a low centrality score, which means that the system can easily have a significant impact on other systems directly or indirectly and is one of the most sensitive.
According to Equation ( 8), this paper takes β to be 0.1, and the resulting reachability matrix F is shown in Table A4.The reachability matrix was entered directly into the SPSS software and analyzed directly using its internal ISM modeling program.ISM modeling of the vulnerability influences of the port logistics system was conducted, and a directed relationship diagram (Figure 3) was obtained and graded for 18 vulnerability influences affecting the port logistics system (Table 4).Table 4. Hierarchy of factors influencing the vulnerability of port logistics system.

Levels Elements
First floor (top floor) C4(conditions of port handling facilities), C5(port storage conditions), C6(port berthing conditions), C7(transportation conditions in the port), C9(average time of ships in port), C11(level of cargo information management), C12(level of ship entry and exit management), C13(level of customer relationship management), C14(port peripheral facilities), C15(port consolidation and distribution efficiency), C16(level of development of port-side industries) Second layer C1(water depth and channel conditions), C2(port construction conditions), C8(quality supervision and management level) Third layer C3(natural disasters), C10(people management skills and staff quality) Fourth layer C17(administrative level of the port) Fifth layer(ground floor) C18(government supervision and coordination) According to Table 4, among all the 18 factors, C4 (conditions of port handling facilities), C5 (port storage conditions), C6 (port berthing conditions), C7 (transportation conditions in the port), C9 (average time of ships in port), C11 (level of cargo information man-  Applying Equation ( 9), this paper derived the weights for the 18 vulnerability factors (Table 5) and utilized them to determine the primary vulnerability factors impacting the port logistics system.

Result and Discussion
(1) In terms of the correlation between the factors, it is more likely that the impact will affect vulnerability factors such as port loading and unloading facility conditions, port storage conditions, port consolidation and distribution efficiency, port berth conditions, average ship time in port, and port peripheral supporting facilities are more likely to be influenced by other vulnerability factors.While factors such as government supervision and coordination, the administrative management level of the port, and natural disasters are more likely to have an impact on other factors, which shows the interaction between influencing factors better than previous studies [13].
(2) From a subsystem perspective, the port infrastructure system and the operation management system are the two main aspects that affect the vulnerability of port logistics.
Port infrastructure is the first to be hit in the event of an emergency, so it is critical that port infrastructure is screened for vulnerability, and routine inspection and maintenance of port infrastructure should be strengthened to troubleshoot exposed risks of failure to ensure that it is resilient to risk when it occurs.Operational management systems are critical for port recovery from shocks [35,37] and their influence on the overall vulnerability of the port logistics system to threats is critical.Therefore, enterprises should promote the modernization and reform of operational management systems and constantly improve their ability to deal with and defend against threats, thereby strengthening the resilience of the system [22].Relevant port departments should focus on identifying and controlling risks in these two aspects, actively maintaining and repairing port infrastructure, and improving the efficiency of port operations and management.The relevant port departments should focus on identifying and controlling risks in these two aspects, actively maintaining and repairing port infrastructure, and improving the efficiency of port operations and management.(3) From the viewpoint of the port logistics system as a whole, frequency of natural disasters (C 3 ) and port handling facilities conditions (C 4 ), with weights of 0.2483 and 0.2695, respectively, are the two most critical vulnerability factors.The port should focus on strengthening the detection of natural disasters and early warning, so as to minimize the vulnerability of the port logistics system.The port should focus on strengthening the detection of natural disasters and early warning [13,15,31], and maintain and manage the related handling facilities as much as possible, so as to minimize the vulnerability of the port logistics system.
Port companies should focus on improving the operation and maintenance level of port facilities as well as the professionalism of operators to ensure that the infrastructure is able to maintain a normal level of operation when subjected to internal and external shocks and no interruptions in the supply chain.Government departments responsible for port management should strengthen supervision of the standardized activities of port enterprises and strive to improve the level of coordinated development of ports and inland cities, so as to reduce the vulnerability of the port logistics system and increase overall resilience.

Conclusions
This paper quantified the vulnerability risk of each part and subsystem of the port logistics system using the port logistics vulnerability assessment model constructed by DEMATEL, ISM model, and BWM method.Based on input from mostly port experts, which reveals more about the reasons for the vulnerability of the port logistics system itself than previous studies [22,34,45], the most vulnerable links and main vulnerability factors in the port logistics system are identified.This paper identifies the frequency of natural disasters and port handling facility conditions.These are the two key factors that most affect the vulnerability of the port logistics system, and the port operators concerned should take effective measures to increase the robustness.At the same time, they should pay attention to potential risks in port infrastructure and operations to reduce overall vulnerability.
The contribution of this article is mainly twofold: (1) Vulnerability mining of the system itself is taken as the main research objective, which is lacking in the current research.
(2) The insights on port logistics systems presented in this paper can also provide a reference for research on the overall security of ports and promote research on port resilience, which is conducive to the sustainable and healthy development of port logistics.

Figure 1 .
Figure 1.Flow chart of vulnerability assessment of port logistics system.

Figure 1 .
Figure 1.Flow chart of vulnerability assessment of port logistics system.

Systems 2023 , 18 Figure 3 .
Figure 3. Directional relationships of vulnerability factors in port logistics systems.

Figure 3 .
Figure 3. Directional relationships of vulnerability factors in port logistics systems.According to Table 4, among all the 18 factors, C 4 (conditions of port handling facilities), C 5 (port storage conditions), C 6 (port berthing conditions), C 7 (transportation conditions in the port), C 9 (average time of ships in port), C 11 (level of cargo information management), C 12 (level of ship entry and exit management), C 13 (level of customer relationship management), C 14 (port peripheral facilities), C 15 (port consolidation and distribution efficiency), C 16 (level of development of port-side industries) are at the top level, indicating that these factors are most easily disturbed by other factors and play a more direct role in the vulnerability of the port logistics system.C 18 (government supervision and coordination), C 17 (administrative level of the port), C 10 (people management skills and staff quality), and C 3 (natural disasters) are located at the lower level, which means that these factors are most easily influence other factors and play an indirect role in the vulnerability of the port logistics system.

Table 1 .
Common vulnerability assessment methods.

Table 2 .
Port logistics system vulnerability evaluation index system.

Table 3 .
f i , e i , R i , C i values of vulnerability elements.
Systems 2023, 11, x FOR PEER REVIEW 11 of 18

Table 4 .
Hierarchy of factors influencing the vulnerability of port logistics system.

Table 5 .
Vulnerability factor weights were obtained from the BWM approach.

Conflicts of Interest:
The authors declare no conflict of interest.

Table A1 .
Port Logistics System Vulnerability Impact Factors Direct Impact Matrix A.

Table A2 .
Port Logistics System Vulnerability Normalized Direct Influence Matrix G.

Table A4 .
Port Logistics System Vulnerability Impact Factors Reachability Matrix F.