Assessing Port Connectivity from the Perspective of the Supply Chain: A Bayesian Network-Based Integrated Approach

Abstract

Maritime transportation is the backbone of global trade, with ports acting as pivotal nodes for the efficient and resilient movement of goods in international supply chains. However, most existing studies lack a systematic and integrated framework for assessing port connectivity. To address this gap, this study develops an integrated Bayesian Network (BN) modeling approach that, for the first time, simultaneously incorporates international connectivity, port competitiveness, and hinterland connectivity within a unified probabilistic framework. Drawing on empirical data from 26 major coastal countries in Asia, the model quantifies the multi-layered and interdependent determinants of port connectivity. The results demonstrate that port competitiveness and hinterland connectivity are the dominant drivers, while the impact of international shipping links is comparatively limited in the current Asian context. Sensitivity analysis further highlights the critical roles of rail transport development and trade facilitation in enhancing port connectivity. The proposed BN framework supports comprehensive scenario analysis under uncertainty and offers targeted, practical policy recommendations for port authorities and regional planners. By systematically capturing the interactions among maritime, port, and inland factors, this study advances both the theoretical understanding and practical management of port connectivity.

1. Introduction

Maritime transportation is the backbone of global trade, carrying over 80% of worldwide merchandise by volume [1]. Seaports, as critical nodes in this system, play a pivotal role in ensuring efficient, robust, and safe transport of goods to sustain international commerce. However, disruptions to port operations, whether caused by natural hazards, geopolitical tensions, or infrastructural bottlenecks, can propagate throughout the maritime network, undermining trade fluidity and economic stability [2]. In recent years, port connectivity has been recognized as a pivotal indicator of port performance and national competitiveness [3]. In this study, port connectivity is defined as the overall extent to which a port is embedded in both global maritime shipping networks and inland transport systems, enabling the efficient, reliable, and flexible movement of goods across the supply chain [4,5,6]. Enhanced connectivity can reduce transport costs and lead times, increase flexibility in response to disruptions, and facilitate sustainable trade growth [4,7]. Conversely, insufficient connectivity not only heightens vulnerability to shocks but also constrains participation in global value chains. Therefore, the level of port connectivity has a direct impact on the reliability of the maritime supply chain and the flexibility of the shipping industry to manage world shipments, which has stimulated recent academic interest in port connectivity analysis.

Against this backdrop, governments and port authorities worldwide are intensifying investments in infrastructure and digitalization to reinforce port connectivity [8]. For example, by 2019, Chinese enterprises had partially or fully constructed, invested in, or managed more than 100 overseas ports, contributing to the global integration of maritime logistics networks [9]. A prominent example is COSCO Shipping’s involvement in the Port of Piraeus, which propelled the port’s global throughput ranking from 93rd to 38th [10]. Similarly, international financial mechanisms such as the International Development Finance Corporation have been established to provide loans to developing countries for port infrastructure development [11]. Additionally, the United States, in collaboration with Japan and Australia, has launched the “Blue Dot Network” initiative to further promote high-standard port infrastructure investments worldwide [12]. These coordinated efforts reflect a growing recognition of the strategic importance of port connectivity for sustainable global trade and economic development.

Despite these advancements, there remains a lack of consensus on how to comprehensively define and measure port connectivity within the broader supply chain context. Existing studies often isolate either international shipping accessibility or hinterland linkages, resulting in partial and potentially biased assessments [4,7]. Recent studies increasingly recognize that port connectivity is a multidimensional concept encompassing three key dimensions: international connectivity, port competitiveness, and hinterland connectivity. International connectivity refers to the degree to which a port is linked to global maritime liner networks, typically measured by indices such as the Liner Shipping Connectivity Index (LSCI), reflecting shipping service diversity, frequency, and quality [1,2]. Port competitiveness encompasses a port’s ability to attract and retain cargo through superior infrastructure, efficient operations, and adaptability to evolving market and sustainability requirements [13]. Hinterland connectivity describes the effectiveness and quality of a port’s linkages with its inland regions, including road and rail networks, which are essential for integrating the port into domestic and regional logistics systems [3,5]. Furthermore, empirical research employing advanced network analysis and probabilistic modeling to reveal the interdependencies among these factors is limited [14,15]. As a result, the combined effects of international shipping, port operations, and hinterland logistics on overall connectivity and supply chain resilience remain insufficiently understood.

Accordingly, to advance understanding in this field, the present study seeks to address the following research questions:

(1)

How can port connectivity be comprehensively and quantitatively assessed in a way that integrates international connectivity, port competitiveness, and hinterland connectivity?

(2)

What are the relative impacts and interdependencies among these three dimensions in determining the overall connectivity of different ports?

(3)

How can advanced probabilistic modeling (such as the BN model) help identify the key determinants and policy levers for improving port connectivity?

Guided by the above research questions and recent theoretical developments, this study proposes the following hypotheses:

H1: 

Port connectivity is jointly determined by international connectivity, port competitiveness, and hinterland connectivity, with each dimension making a statistically significant and distinct contribution.

H2: 

Improvements in port competitiveness, hinterland connectivity, and international connectivity have different effects on port connectivity in emerging Asian economies.

H3: 

The application of BN modeling reveals both direct and indirect influences among key factors in port connectivity systems and provides distinct accuracy characteristics for port connectivity assessment under uncertainty.

Responding to this challenge, this study develops a novel integrative BN model to systematically assess port connectivity from a holistic maritime supply chain perspective. Specifically, this research contributes to the existing literature by:

(1)

Introducing a comprehensive analytical framework that integrates international connectivity, port competitiveness, and hinterland connectivity simultaneously within a unified probabilistic model.

(2)

Employing Bayesian Network methodology to capture uncertainties and interdependencies among multiple dimensions of port connectivity, thus providing robust and insightful analyses beyond traditional deterministic approaches.

(3)

Demonstrating the effectiveness and practicality of the proposed model through an empirical case study of key coastal ports in Asia, supplemented by sensitivity analyses that identify critical factors influencing connectivity.

By developing and validating this integrative model, the present study not only advances theoretical understanding but also provides actionable insights for policymakers and industry stakeholders to effectively prioritize investments and strategies, ultimately enhancing sustainable maritime trade resilience and efficiency.

The remainder of this paper is organized as follows: Section 1 introduces the background and focus areas; Section 2 reviews the relevant literature; Section 3 details the methodological framework and presents the model construction process; Section 4 offers a case study application and discusses the results; and Section 5 concludes with key findings and directions for future research.

2. Literature Review

2.1. Ports in Maritime Supply Chains

Ports serve as crucial interchange hubs where cargo is transferred between sea transport and other modes (truck, rail, barge), making them indispensable logistics platforms in modern supply chains [6]. By facilitating the dynamic movement of products and information across modes, ports enable timely deliveries to end customers and create value-added services for traders (e.g., warehousing, consolidation) [16]. Recognizing this essential role, a significant strand of research has examined ports from a supply chain perspective. For instance, Notteboom et al. (2013) analyzed 267 port studies of Maritime Policy & Management since 1973, where 27 studies fell into the category of ports in transport and supply chains [17]. The role of ports in the logistical strategies of shipping lines, value-added maritime supply chains, access to the hinterland, and terminal operators has been discussed under this theme.

Building on this foundation, various methodologies have been applied to strengthen port contributions to supply chain efficiency. For example, Lam and Bai (2016) developed a quality function deployment technique to improve the robustness of ports’ maritime supply chains by implementing targeted resilience measures [18]; Liu et al. (2018) analyzed vulnerabilities in the maritime supply chain to identify vulnerable nodes in case of different hazards, thereby informing risk management decisions [19]; and Tovar and Wall (2022) described the relationships between maritime connectivity and port efficiency using port-level connectivity indices [20]. Collectively, these studies underscore that ports are not isolated entities but are embedded within broader supply chain networks. Enhancements in port attributes, such as capacity, reliability, and connectivity, can generate cascading effects that improve end-to-end logistics performance across the entire supply chain.

At the same time, the literature highlights the need for more comprehensive models to quantify port connectivity and its impacts on the supply chain. Although previous studies have provided valuable insights into specific aspects, such as resilience, network positioning, and risk assessment, a unified framework that captures all critical dimensions of port connectivity remains lacking. This gap underscores the necessity for an integrated analytical model, as proposed in this study, to facilitate a more holistic understanding and evaluation of the pivotal role ports play within maritime supply chains.

2.2. Port Connectivity

The concept of maritime connectivity was first formally emphasized by UNCTAD’s introduction of the Liner Shipping Connectivity Index (LSCI) in 2004. The LSCI provided a country-level metric of integration into global liner networks, and it was soon complemented by the Liner Shipping Bilateral Connectivity Index (LSBCI) in 2006 to measure direct shipping connectivity between pairs of countries. These indices underscored the importance of liner network linkages for trade, effectively laying a foundation for quantifying connectivity.

Since then, evolving logistics strategies and the shifting role of ports have kept port connectivity in the spotlight. For example, Jiang et al. (2015) presented a framework to evaluate port connectivity by integrating models of transit time and capacity for every port pair, thus identifying how each link contributes to overall network performance [21]. Martínez-Moya and Feo-Valero (2020) introduced a Foreland Port Connectivity Index to measure a port’s connectivity to overseas markets, accounting for the diversity of destination countries and shipping services [8]. Cheung et al. (2020) took an optimization approach, using a max–min integer programming model to enhance connections between OD pairs and thereby improve the measurement of network connectivity for container shipping [7]. These contributions have advanced our understanding of port connectivity from the network perspective.

However, a common limitation of the above studies is that they focus solely on maritime connectivity, providing an incomplete view. Recent literature highlights that true port connectivity is inherently multi-dimensional, also shaped by a port’s operational competitiveness (including infrastructure quality, service level, and digitalization) and the strength of its hinterland connections [22,23]. For instance, carriers and shippers increasingly optimize entire supply chain routes rather than just individual port calls, meaning that the efficiency of inland transport links and the seamless integration of port-hinterland systems are now critical determinants of a port’s attractiveness [24,25]. Moreover, recent studies show that not all inland connections are equally valuable: ports benefit most from robust links to major logistics hubs, rather than a large number of weak or peripheral links [26]. At the same time, port competitiveness itself is multi-faceted. Shipping lines may prioritize service quality and turnaround times, while port operators focus on physical infrastructure and strategic location [13]. These insights confirm that effective assessment of port connectivity requires an integrated approach, simultaneously considering international maritime linkages, operational competitiveness, and hinterland accessibility.

Despite these advances, comprehensive quantitative models that explicitly capture the interdependencies among these dimensions remain scarce. Most existing assessments either treat the three aspects in isolation or lack a robust way to handle the uncertainty and complex interactions present in real-world port systems. Addressing this gap, the present study introduces an integrated BN framework to jointly evaluate international connectivity, port competitiveness, and hinterland connections within a single probabilistic model. This approach allows for a more nuanced understanding of how these factors collectively shape port connectivity and provides decision-makers with actionable insights for sustainable supply chain development.

2.3. Bayesian Network Applications in Maritime Logistics

Evaluating port connectivity requires the simultaneous consideration of multiple, interdependent criteria, such as competitiveness, infrastructure quality, and service performance [27,28]. Multi-criteria analysis (MCA) has become a core framework in port and logistics management, with established methods including AHP, TOPSIS, and ELECTRE frequently applied for port selection and infrastructure assessment. However, these approaches typically assume independence among criteria and rely on deterministic data, limiting their ability to reflect the complexity and uncertainty inherent in real-world port systems [29,30]. To address these limitations, recent research increasingly adopts probabilistic modeling techniques, particularly BNs, which extend the multi-criteria decision-making paradigm by accommodating uncertainty, variable dependencies, and scenario analysis [31,32,33,34]. The BN framework proposed in this study builds upon the foundations of MCA, serving as a probabilistic extension and complement that enables more robust and flexible decision support for port connectivity evaluation under uncertainty.

Methodologically, BNs have been used as a valuable tool for modeling complex, uncertain systems in the maritime and transport domains [35]. A BN is a probabilistic graphical model that represents variables (nodes) and their conditional dependencies (edges), enabling inference under uncertainty [36]. In the maritime sector, BNs have been extensively applied to risk assessment, reliability evaluation, and decision support [37]. For instance, Jiang et al. (2021a, 2021b) applied BNs to systematically evaluate port safety and vulnerability, offering operational insights to stakeholders and facilitating more informed resource allocation strategies [31,32]. Similarly, John et al. (2016) developed a BN-based model integrating factors such as infrastructure, hinterland access, and management policies, providing a comprehensive framework for enhancing supply chain resilience at seaports [38]. Complementarily, Alyami et al. (2019) further combined BN with an evidential reasoning approach to conduct advanced risk analysis for container ports, illustrating the BN’s utility in complex safety and reliability management scenarios [39]. These studies demonstrate the capacity of BNs to capture intricate interdependencies among risk factors in port operations, yielding probabilistic insights that deterministic models often overlook [40].

Beyond this, BNs have proven valuable in broader transport and logistics contexts with comparable network characteristics. For example, Tang and Huang (2019) applied BN methods to assess urban road network vulnerabilities under disruption scenarios, and Wang et al. (2021) explored influential factors within global aviation networks using similar BN approaches [40,41]. In maritime logistics, specifically, Hossain et al. (2020) employed BNs to model interdependencies between inland waterway ports and surrounding supply chains [16]. Likewise, Jiang and Lu (2020) leveraged Dynamic BNs to estimate accident risks along strategic sea lanes, effectively demonstrating BN’s capacity to handle complex, interconnected transportation networks [32].

Overall, the above literature indicates that BN enables visualization and analytical exploration of how changes or uncertainties in specific variables influence outcome probabilities. This feature significantly enhances decision-making processes by facilitating scenario analysis and identifying critical points within a network [42]. However, few studies have applied BNs to the specific problem of port connectivity. Indeed, to our knowledge, the existing literature has yet to integrate both international shipping connectivity and hinterland connectivity within a unified BN analytical framework. To fill this gap, this study develops a BN-based model to analyze port connectivity under uncertainty. Specifically, the proposed model explicitly combines critical factors across maritime networks, port operational attributes, and inland transport connections, thereby capturing the multidimensional and interdependent nature of port connectivity. Furthermore, this research enhances the diagnostic and inferential capabilities of the BN approach through systematic sensitivity analysis, enabling precise identification of influential connectivity determinants under uncertainty.

3. A Bayesian-Based Framework for Port Connectivity Assessment

To systematically evaluate port connectivity under uncertainty, this study establishes a comprehensive analytical framework grounded in BN theory. As illustrated in Figure 1, the proposed framework comprises four main steps: (1) identification of influencing factors, (2) variable framework and data processing, (3) port connectivity modeling based on BN, and (4) sensitivity analysis. By integrating these procedures, the framework enables the quantification of port connectivity through a probabilistic lens, capturing both direct and indirect effects of international connectivity, port competitiveness, and hinterland integration.

3.1. Identification of Influencing Factors

3.1.1. International Connectivity

An analysis of the literature reveals that either the LSCI or LSBCI, which is a subsequent expansion, are effective indicators for reflecting international connectivity because liner shipping is responsible for about 70% of the value of world seaborne trade [8,20]. The LSCI, which measures the degree to which countries are connected to the global maritime shipping network, has lately emerged as the most popular choice. Oliveira and Cariou (2015) proposed a two-stage process featuring bootstrapped truncated regression to explain efficiency scores for 200 container ports in 2007 and 2010 [43]. The LSCI was used as an explanatory variable positively related to container port efficiency. Serebrisky et al. (2016) included the LSCI of country-level connectivity as a control variable in an analysis of the performance of 63 container ports in Latin America and the Caribbean by using a stochastic frontier-based approach [44]. The connectivity index was included as a control variable in a deterministic frontier, and was found to be positively related to throughput. In another study, LSCI connectivity was also included as a control variable in the deterministic frontier by Suárez-Alemá et al. (2016) [45]. Compared with the LSCI, the LSBCI indicates the bilateral connectivity between a coastal country and every other coastal country. Fugazza and Hoffmann (2017) presented an empirical assessment of the relationship between the bilateral maritime connectivity of liner shipping and exports in containerized goods [46].

3.1.2. Port Competitiveness

Hard and soft strengths are the two main components of port competitiveness. Hard strength is defined as an identifiable aspect that includes the infrastructure and scale of operation of the port, while soft strength can be described by the trade convenience of a port. The port infrastructure is the basic guarantee of the high-quality development of ports and the driving force for the economic development of port cities. The scale of port operation is a direct expression of the effect of the application of the port infrastructure, reflecting the comprehensive operational capacity and trade competitiveness of the port. To some extent, it is difficult to directly identify the soft strength of ports. We use the index of convenience of trade, as it directly determines the contribution of a port to international trade, to mark the soft power of a port.

Bastug et al. (2022) claimed that the service level, port tariffs, and convenience of port trade are the most significant criteria for port competitiveness, in addition to location [13]. Peng et al. (2018) incorporated the port infrastructure into a system to assess the competitiveness of coastal ports with continued investment in the infrastructure of international ports along the 21st Century Maritime Silk Road [47]. Sousa et al. (2021) claimed that tariffs and the economic situation of ports play an important role in port competitiveness, and demonstrated this by using a qualitative approach based on secondary data from government departments [48].

3.1.3. Hinterland Connectivity

In the realm of global trade, ports are more than mere maritime junctions; they are central trading hubs that are vital to the efficiency of global supply chains. Their connectivity with the hinterland, the areas where traded goods are consumed or processed, is paramount. The quality of hinterland connectivity is not just an aspect of port operations but a key determinant of their competitive stance. It influences operational efficiency and shapes a port’s ability to compete within shared or overlapping hinterland markets. Thus, enhancing hinterland connectivity emerges as a pivotal strategy for ports aiming to strengthen their position in the global trade network [26].

The hinterland can be defined as a landward area associated with the port. Because the import and export of goods in a given region are mainly carried out through the port, the overall economic development of the hinterland, as well as levels of consolidation and distribution, have an important influence on the development of the port.

Hinterland connectivity indicates the degree of physical interconnection between the port and the hinterland as well as the level of economic development, reflecting the economic benefits of international cargo transportation relying on the infrastructure of hinterland transportation.

Chen et al. (2016) developed a qualitative approach to analyze the connectivity of seaports from the perspective of the hinterland, which provided some strategies to improve the quality of hinterland connectivity [49]. Li et al. (2020) studied the effects of shipper subsidies on port profits to highlight the importance of the hinterland for seaports [50].

3.2. Variable Framework and Data Processing

3.2.1. Variable Description

To facilitate a structured understanding of the subsequent BN modeling, the key variables identified in this study are systematically categorized into three primary dimensions:

International connectivity includes variables that reflect a port’s integration with global shipping networks, such as shipping connectivity indices [2].

Port competitiveness covers factors representing the operational efficiency and service quality of the port, including infrastructure standards, operational scale, and trade convenience [6,13].

Hinterland connectivity considers both transport conditions and economic development, including rail and road accessibility, as well as regional economic indicators [3,4].

These groupings follow mainstream approaches in the recent literature and ensure that both theoretical breadth and empirical measurability are considered. The detailed definitions, classification criteria, and data sources for each variable are summarized in

Table 1. The variable description and discretization results of the proposed BN model.

Influencing Factors	Status	Methods	Data Sources
Trade Tariffs	Low: [0, 5)	Quartile	The Global Competitiveness Report
	Lower Middle: [5, 6)
	Upper Middle: [6, 10)
	High: [10, +∞)
Border clearance efficiency	Poor: [1, 1.7]	Equal-width method	The Global Competitiveness Report
	Normal: (1.7, 3.3]
	Good: (3.3,5]
The efficiency of seaport services	Poor: [1, 3]	Equal-width method	The Global Competitiveness Report
	Normal: (3, 5]
	Good: (5, 7]
Container port throughput	Low: [0, 1,000,000)	Quartile	UNCTAD
	Lower Middle: [1,000,000, 3,000,000)
	Upper Middle: [3,000,000, 10,000,000)
	High: [10,000,000, +∞)
Road mileage	Short: [0, 5000)	Quartile	DRCNET Statistical Database System
	Lower Middle: [5000, 100,000)
	Upper Middle: [100,000, 500,000)
	Long: [500,000, +∞)
Quality of road infrastructure	Poor: [1, 3]	Equal-width method	The Global Competitiveness Report
	Normal: (3, 5]
	Good: (5, 7]
Rail mileage	Short: [0, 1000)	Quartile	DRCNET Statistical Database System
	Lower Middle: [1000, 4000)
	Upper Middle: [4000, 10,000)
	Long: [10,000, +∞)
Efficiency of train services	Poor: [1, 3]	Equal-width method	The Global Competitiveness Report
	Normal: (3, 5]
	Good: (5, 7]
GNI per capita	Low	National Income Classification Standard	Word Bank
	Lower Middle
	Upper Middle
	High
Liner shipping bilateral connectivity	Poor: [0–0.33]	Equal-width method	UNCTAD
	Normal: (0.33–0.66]
	Good: (0.66–1]
Port connectivity	Low	K-Means clustering method elbow rule, contour coefficient	DRCNET Statistical Database System
	Medium
	High

below.

3.2.2. Sample Selection

Asia is globally recognized as the leading engine of economic growth and international trade, representing over 60% of global container port throughput and serving as a pivotal hub for maritime logistics and supply chain connectivity [51].

To ensure both scientific rigor and empirical representativeness, this study covers 26 major coastal countries in Asia, as shown in Figure 2, including China, the Republic of Korea, Japan, the Philippines, Cambodia, Thailand, Malaysia, Brunei, Singapore, Indonesia, Bangladesh, India, Pakistan, Sri Lanka, Iran, Jordan, Israel, Saudi Arabia, Bahrain, Qatar, Kuwait, the United Arab Emirates, Oman, Yemen, Georgia, and Cyprus. This selection represents virtually all economically significant and logistically active maritime nations in the region, and is consistent with the sample selection practices of recent international studies [1,2].

3.2.3. Data Sources and Preprocessing

As shown in Table 1, all variable data for this study were obtained from internationally recognized and authoritative sources, including the Global Competitiveness Report, UNCTAD (unctadstat.unctad.org), the DRCNET Statistical Database System (data.drcnet.com.cn), and the World Bank (data.worldbank.org).

(1)

Missing data treatment

To ensure the integrity and reliability of the dataset, all variables were thoroughly checked for missing values prior to modeling. For continuous variables with a small proportion of missing data (less than 5% of total observations), mean imputation was applied. For categorical variables, missing values were filled using the mode. These imputation methods are widely endorsed in recent maritime logistics and transportation literature for datasets with low missingness, as they are simple, computationally efficient, and minimize the risk of introducing bias when missing data are limited and randomly distributed [52]. Samples with extensive missing values across multiple key variables were excluded to maintain analytical consistency and prevent the propagation of uncertainty in the model.

(2)

Variable discretization

Although the BN framework is capable of handling both continuous and discrete data, data discretization is often preferred in empirical applications, especially in complex supply chain and logistics environments, due to several key advantages. Discretizing continuous variables can significantly improve model interpretability, enhance parameter stability, and reduce the risk of overfitting, particularly when dealing with limited sample sizes or non-normal distributions. Furthermore, effective discretization lowers computational complexity and increases robustness to outliers and measurement noise, which is especially beneficial for transport and port connectivity modeling [53]. For these reasons, this study adopts discrete node modeling in the BN framework, in line with recent best practices in the field [31,32].

Specifically, bilateral cargo trade, used as a proxy for inter-country port connectivity, was discretized using K-means clustering, with the optimal number of clusters determined by the elbow method and the silhouette coefficient [54]. Trade tariffs, border clearance efficiency, road infrastructure quality, port service efficiency, and train service efficiency, sourced from the Global Competitiveness Report, were discretized using the equal-width binning method, consistent with best practices for handling ordinal logistics data [55]. For port container throughput, road mileage, and rail mileage, the quadratic method was applied to minimize the impact of extreme values and ensure representativeness of the underlying distribution. Gross national income (GNI) was categorized according to the World Bank’s National Income Classification Standard.

These discretization procedures are widely recognized for their ability to balance model robustness, computational efficiency, and interpretability, and are strongly supported by current practice in recent BN models and maritime logistics research [31,32,33,34]. The detailed discretization criteria and coding schemes for all variables are provided in Table 1.

Nevertheless, it should be acknowledged that variable discretization inevitably introduces certain limitations. The selection of discretization thresholds may affect the sensitivity and granularity of the results, and inappropriate binning could mask subtle relationships or create artificial boundaries. To mitigate these risks, all discretization criteria in this study are determined based on authoritative standards, empirical distribution, and cross-validation against the existing literature.

3.3. Port Connectivity Modeling Based on BN

3.3.1. Model Structure and Principles

BN is a widely used probabilistic graphical model that encodes the conditional dependencies among a set of variables in the form of a directed acyclic graph. Each node in the BN corresponds to a system variable, while directed edges represent probabilistic relationships and potential causal influences. This graphical structure enables efficient reasoning under uncertainty, integration of diverse data sources, and robust analysis of both direct and indirect effects in complex systems such as port connectivity [33,34,56,57].

As illustrated in Figure 2, the BN model used in this study is organized in a hierarchical, multi-layer structure. The bottom layer (e.g., X₁, X₂) consists of observable input variables, such as infrastructure quality and regional GDP, which represent the fundamental attributes of ports and their surrounding environments. The intermediate node (X₃) aggregates these inputs into a multidimensional latent factor, corresponding to key constructs like international connectivity, port competitiveness, or hinterland integration. The top node (X₄) then captures the overall port connectivity, serving as the final system outcome and integrating the effects of all upstream variables.

As shown in Figure 3, the structure of the BN explicitly encodes the conditional dependencies among variables. Based on this structure, the joint probability distribution of all variables in the network can be factorized as follows:

$$P(X_1,X_2,\dots ,X_n)={\displaystyle \prod _1^{n}P(X_i/Parten(X_i))} (i=1,2,\dots ,n)$$

(1)

where $Parten(X_i)$ denotes the parent nodes of $X_i$.

3.3.2. Topological Structure Determination

Determining the topological structure is a critical step in BN modeling, as it defines the conditional dependencies and potential causal relationships among variables. Generally, there are three main approaches to BN construction. The first is a data-driven approach, in which algorithms utilize large volumes of historical data to learn the network structure and parameters, offering advantages in objectivity and methodological rigor. However, this approach often faces significant limitations in practice, such as (1) high demands on data quality and quantity, and (2) potential inconsistencies between the learned structure and established domain knowledge. The second approach relies entirely on expert knowledge to define the network, with strengths and limitations that are complementary to those of the data-driven method. Consequently, a third, hybrid approach is often adopted, integrating both data-driven techniques and expert input to leverage the benefits of each and mitigate their respective shortcomings [40].

As illustrated in Figure 4, the BN model constructed in this study features a hierarchical, multi-layer structure, with observable input variables at the bottom layer, multidimensional latent factors in the middle layer, and overall port connectivity as the final outcome at the top layer. The selection and definition of each variable are detailed in Table 1 and Section 3.2.1.

Recognizing the potential subjectivity associated with expert input in BN structure determination, this study adopted a widely recommended strategy in the literature: cross-validation among multiple experts, transparent documentation of decision processes, and structural sensitivity analysis to evaluate robustness [58]. In this research, expert opinions were elicited in several rounds and compared against empirical data and prior studies. Any major disagreements were resolved through consensus, and alternative network structures were assessed to ensure model stability.

3.3.3. Conditional Probability Parameter Learning

The conditional probability parameters in the BN model quantify the causal relationships among nodes and are estimated using the Expectation-Maximization (EM) algorithm. The EM algorithm is widely recognized for its effectiveness in parameter estimation with incomplete or latent data.

In this study, all conditional probability tables (CPTs) were learned iteratively using the EM algorithm, which alternates between the Expectation (E-step) and Maximization (M-step) to maximize the likelihood function. Specifically, Equation (2) constructs the joint probability of observed and hidden variables, while Equation (3) defines the objective function for parameter updates.

$$Q_i(z^{(j)})=p(x_i,z^{(j)};\theta )$$

(2)

$$\theta =\max \theta {\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{Q}_i(z^{(j)})\ln \frac{p(x_i,z^{(j)};\theta )}{Q_i(z^{(j)})}}}$$

(3)

where $x_i$ denotes the observed data related to factors influencing the port connectivity of a certain group of countries, and $z^{(j)}$ is the hidden variable associated with $x_i$. $p(x_i,z^{(j)};\theta )$ represents the joint probability distribution of $x_i$ and $z^{(j)}$ given the parameter set θ. The function $Q_i(z^{(j)})$ describes the probability distribution of the hidden variable $z^{(j)}$ with respect to the observed data $x_i$ under the current parameter estimate θ.

This approach enables robust and efficient parameter learning even in the presence of missing data, ensuring the reliability of the BN model.

3.3.4. Deductive Inference

Once the BN is established, deductive inference, also called forward analysis, can be used to assess the target node ($T$) under different configurations of input variables ($X_1,X_2,\dots X_n$). The joint probability distribution of T, described by $P(T=t)$, can be calculated as follows:

$$P(T=t)={\displaystyle \sum _1^N[}P(T=t|X_1=x_1,\dots ,X_n=x_n)\times P(|X_1=x_1,\dots ,X_n=x_n)]$$

(4)

where N is the number of states of the node $X_i(i=1,2,\dots ,n)$, $P(|X_1=x_1,\dots ,X_n=x_n)$ describes the joint probability distribution of $X_i$, and $P(T=t|X_1=x_1,\dots ,X_n=x_n)$ represents the conditional probability distribution of $T$.

3.4. Sensitivity Analysis

Sensitivity analysis is essential for identifying and quantifying the most influential variables within a BN model. This process enables decision-makers to pinpoint critical variables, prioritize management interventions, and enhance the overall effectiveness of port connectivity improvement strategies. In this study, we adopt mutual information as the main metric for sensitivity analysis, due to its proven effectiveness in capturing both direct and indirect dependencies in probabilistic graphical models [59].

Mutual information measures the degree of dependence between each input variable and the target node (port connectivity), allowing for robust ranking of variable influence even under uncertainty.

Formally, two discrete random variables X and Y can be defined as follows:

$$H(X:Y)={\displaystyle \sum _{y\in Y}{\displaystyle \sum _{x\in X}P(x,y)\log (\frac{P(x,y)}{p(x)p(y)}}})$$

(5)

where $P(x,y)$ denotes the joint probability distribution function of $X$ and $Y$, and $p(x)$ and $p(y)$ represent the marginal probability distribution functions of $X$ and $Y$, respectively.

This approach, widely validated in the BN and risk assessment literature, enables robust quantification of each input’s contribution to the target node under uncertainty [32,33]. By ranking mutual information values, both direct and indirect key determinants are identified, providing a scientific basis for evidence-based intervention and resource allocation.

4. Case Study

4.1. Forward Analysis

Based on the forward inference procedure described above, port connectivity was evaluated for all sampled ports using the BN model. The aggregated results are presented in Figure 5, with further details provided in Figure 6 and Figure 7.

Figure 5 illustrates that the overall port connectivity among the selected Asian countries is relatively low. Only 8.7% of the countries exhibit a high level of port connectivity, while the probability of low connectivity is nearly ten times higher, reaching 86%. Figure 6 further details the distribution of high, medium, and low connectivity levels among country pairs.

Port connectivity is influenced by factors such as international connectivity, port competitiveness, and hinterland connectivity, all of which affect the infrastructure and service quality of ports. As shown in Figure 6, high port connectivity is predominantly concentrated between China and countries participating in the Belt and Road Initiative. Chinese ports demonstrate strong competitiveness, comprehensive hinterland collection and distribution systems, and high international connectivity, all of which lay a solid foundation for advancing port connectivity in Asia. For example, the Jakarta–Bandung High-Speed Railway, a flagship infrastructure cooperation project between China and Indonesia, will reduce travel time between Jakarta and Bandung from three hours to just 40 min, significantly enhancing Indonesia’s hinterland connectivity [46]. Additionally, a Chinese company secured the contract for the Sabah Container Terminal Expansion Project in Malaysia, which is expected to increase the terminal’s annual throughput from TEU 500,000 to TEU 1.25 million upon completion, thereby facilitating trade flows in the Sabah region and stimulating Malaysia’s economy [47].

Moreover, port connectivity among ASEAN countries (e.g., Malaysia–Thailand) generally remains at a medium level, as shown in Figure 6. This can be attributed to, on the one hand, active economic cooperation and port infrastructure development among ASEAN countries, and on the other hand, ongoing challenges related to the consolidation of domestic hinterland and distribution systems.

To further analyze port connectivity between China and Belt and Road countries, Figure 7 lists the specific factors influencing their connectivity levels. The LSBC values are consistently high between China and each of the Belt and Road countries. However, the comparative efficiency of rail services varies, with only Malaysia demonstrating a relatively favorable situation.

4.2. Sensitivity Analysis Results

A comprehensive sensitivity analysis was undertaken to systematically identify the key determinants of port connectivity and to derive actionable implications for decision-makers. As illustrated in

Table 2. Sensitivity of node–port connectivity.

Node	Mutual Information	Proportion (%)
Port connectivity	0.717	100
Port competitiveness	0.477	66.6
Port trade convenience	0.142	19.9
Port operation scale	0.122	17.0
International connectivity	0.118	16.5
Rail transportation level	0.081	11.3
Port infrastructure	0.054	7.56
Port container throughput	0.043	5.99
Efficiency of seaport service	0.021	2.83
Trade tariffs	0.017	2.32
Road transportation level	0.011	1.5
Border clearance efficiency	0.010	1.37
…	…	…

, mutual information was employed within the BN framework to quantify the degree of sensitivity between variables. The results demonstrate that port competitiveness, trade convenience, operational scale, and international connectivity exert the most substantial influence on port connectivity. However, it is important to emphasize that these indicators are distributed across different hierarchical layers within the BN structure. Notably, port competitiveness and international connectivity function as intermediate nodes, integrating the effects of multiple lower-level variables, such as trade convenience, port operation scale, and port infrastructure.

To clarify these hierarchical dependencies, a multi-layered sensitivity analysis was performed, as detailed in

Table 3. Sensitivity of the node ‘port connectivity’ with its parent nodes.

Node	Mutual Information	Proportion (%)
Hinterland connectivity	0.118	19.8
Port competitiveness	0.477	79.9
International connectivity	0.002	0.30

,

Table 4. Sensitivity of the intermediate nodes.

Intermediate Nodes	Intermediate Nodes	Mutual Information	Proportion (%)
Hinterland connectivity	Road transportation level	0.066	10.4
	Rail transportation level	0.562	89.3
	Economic development level	0.001	0.3
Port competitiveness	Port trade convenience	0.459	59.5
	Port operation scale	0.188	24.2
	Port infrastructure	0.125	16.3

and

Table 5. Sensitivity of intermediate nodes with root nodes.

Intermediate Nodes	Root Nodes	Mutual Information	Proportion (%)
Road transportation level	Road mileage	0.068	76.0
	Quality of road infrastructure	0.021	24.0
Rail transportation level	Efficiency of train service	0.071	48.7
	Rail mileage	0.075	51.3
Port trade convenience	Trade tariffs	0.252	75.3
	Border clearance efficiency	0.083	24.7

. The parent nodes of port connectivity include port competitiveness (79.9%), hinterland connectivity (19.8%), and international connectivity (0.3%), each demonstrating markedly different levels of impact, with port competitiveness emerging as the primary driver. This finding suggests a strategic transition from an emphasis on quantitative expansion to a focus on qualitative, in-depth port development. Among the constituents of port competitiveness, trade convenience was identified as the most influential factor (59.5%), underscoring the centrality of streamlined trade procedures.

Additionally, hinterland connectivity was found to be the second most critical determinant, with rail transportation level exerting the greatest influence (89.3%) among its subcomponents. This highlights the pivotal role of sea–rail intermodal transport in improving port connectivity. At the foundational level, root variables such as road mileage, rail mileage, and trade tariffs exhibited pronounced impacts on their respective intermediate nodes, accounting for 76.0%, 51.3%, and 75.3% of the effects, respectively, as shown in Table 5.

4.3. Discussion

The results of this study, from a supply chain perspective, reveal pronounced disparities in port connectivity across Asia, with only 8.7% of ports achieving high integration. This finding extends recent evidence that Asian ports, despite their strategic role in global supply chains, still lag in end-to-end connectivity and supply chain coordination [1]. Unlike traditional indices such as LSCI that primarily assess maritime liner integration, the proposed Bayesian Network model adopts a systems perspective by capturing both direct and indirect relationships among port operations, hinterland transport, and international networks. This approach enables a comprehensive diagnosis of supply chain bottlenecks and supports scenario-based policy analysis. The analysis further demonstrates that port competitiveness and hinterland connectivity, rather than international shipping links alone, are the primary drivers of overall port connectivity in Asia, which contrasts with patterns observed in established maritime hubs such as Singapore and Rotterdam. Sensitivity analysis demonstrates that improvements in rail infrastructure, trade facilitation, and service efficiency are the most effective levers for enhancing port connectivity in Asia. These results suggest that rather than a “one-size-fits-all” strategy, policymakers and supply chain managers should tailor interventions to address specific local bottlenecks and developmental stages.

Building on these diagnostic capabilities, the practical value of the BN approach becomes clear. First, it provides robust, scenario-based decision support for both public-sector policymakers and port managers. The model can simulate the system-wide impacts of targeted infrastructure investments or management reforms, helping to optimize resource allocation and coordinate policy implementation. Second, by explicitly mapping causal relationships and quantifying the relative importance of each variable, the model enables both policymakers and industry practitioners (e.g., port operators, logistics companies) to prioritize interventions according to each port’s real-world constraints and supply chain role, greatly enhancing the relevance and feasibility of recommendations.

Drawing on the empirical insights of Section 4.1 and Section 4.2, the practical implications of our BN-based sensitivity analysis extend far beyond generic improvement measures. The model highlights that policy and management strategies must be differentiated according to each port’s current connectivity level and dominant bottlenecks. For high-connectivity hubs, incremental gains depend primarily on sustained improvements in service efficiency and management practices to reinforce global leadership. Medium-connectivity ports, particularly those in fast-growing ASEAN economies, are best positioned to benefit from targeted investments in rail infrastructure and operational system upgrades. For most low-connectivity ports, the priority lies in strengthening fundamental hinterland links and trade facilitation, which are essential prerequisites for moving up the supply chain integration ladder.

Several limitations of this study should be acknowledged. While the cross-sectional dataset and reliance on expert-informed BN structure may introduce some subjectivity and limit the capture of dynamic supply chain changes, the core findings are most applicable to ports with similar institutional and infrastructural contexts. Nonetheless, the use of mutual information-based sensitivity analysis and systematic cross-validation enhances the robustness and reliability of the results. Policymakers and practitioners should be aware that the precision and scope of the BN model’s recommendations depend on the availability and granularity of input data, as well as the representativeness of the expert knowledge incorporated. Future applications in other regions or more complex supply chain environments will benefit from longitudinal or real-time data, broader stakeholder engagement, and the adoption of automated structure-learning algorithms to further reduce subjectivity and increase adaptability. Despite these constraints, the BN framework’s ability to integrate multiple data sources and quantify differentiated intervention priorities provides a valuable tool for evidence-based port and supply chain management. As digitalization and data-sharing practices continue to improve, the model’s applicability and policy relevance will be further enhanced.

5. Conclusions

This study developed an integrated Bayesian Network framework to systematically assess port connectivity by combining international connectivity, port competitiveness, and hinterland integration. Empirical results from 26 major Asian coastal countries reveal that most ports exhibit low or medium connectivity, with port competitiveness and hinterland infrastructure emerging as the principal determinants, while international shipping links play a secondary role at the current stage of development.

Compared with traditional single-index approaches, the BN model captures the complex interdependencies shaping port connectivity and enables evidence-based, differentiated policy support. The findings highlight the need to tailor interventions to the specific conditions and constraints of each port, emphasizing investment in service efficiency and hinterland integration for a sustainable supply chain.

While this framework is demonstrated in the Asian context, it offers a methodological reference for broader applications in global port connectivity research. Future work should extend this approach to different regions and incorporate dynamic, real-time data to further enhance its practical role in maritime supply chains and related policy decision-making.

In summary, this research provides both theoretical and practical contributions to the assessment and strategic development of port connectivity, supporting more resilient and efficient maritime supply chains.