Developing a resilience assessment model for critical infrastructures: The case of port in tackling the impacts posed by the Covid-19 pandemic

Abstract

1 Introduction Covid-19 is a pandemic that started towards the end of 2019 and spread quickly (Ivanov, 2020). To this end, the World Health Organization (WHO) identified the outbreak of Covid-19 as a worldwide pandemic leading to quarantine, social distancing, border closure, and the prolonged closure of vital facilities (Ivanov and Dolgui, 2020). This impacted the global economy, social mobility, and health on a global scale (OECD, 2020). Specifically, the Covid-19 outbreak led to misalignment between supply and demand by affecting supply chain nodes to different extents (Araz et al., 2020). For example, it was reported that restrictions limited ports’ services, which led to port call cancellation, delays, and congestion on both hinterland and maritime sides (UNESCAP, 2020). That being said, interconnected and nested logistics services have remained active through such uncertain events (UNCTAD, 2020a). Decision-makers need to cope with the challenge of keeping the balances between safety, security, sustainability, and performance of their systems considering resources, against a variety of strategic, tactical, and operational risks leading to system failure (John et al., 2014). This exhibits urgent demands for resilience-based decision-making which requires a thorough understanding of situations to plan and prepare for potential threats (Golan et al., 2020). In fact, this is nothing new. Since the beginning of this century, the world has undergone unfolded challenges because of climate change, epidemics, geopolitics, terrorism, economic uncertainties, as well as regional conflicts and rivalries. Such complexities pose threats to the appropriate use of critical infrastructures (CIs) that are crucial for societal well-being (Z. Yang et al., 2018). All these make them a serious concern for planners and operators (Rehak et al., 2019): such systems must be designed to be sufficiently resilient and capable of recovering quickly from disruptions. Here Haimes et al. (2008) and Zolli and Healy (2012) criticized past research's inadequacy to propose effective ways to significantly improve the resilience of the socio-economic systems, where such a view has recently been reiterated by Ivanov and Dolgui (2020). Consequently, research relevant to resilience and risk management has received considerable attention in recent years (Ullah et al., 2019), as it could decrease possible socio-economic losses and allow decision-makers to make better moves in the face of challenges (Mitchell, 2013). In this regard, resilience can be understood as the ability of an entity or system to bounce back to a normal condition after its original state is affected by a disruptive event (Wan et al., 2017). Among the CIs, ports generate and sustain economic activities by offering various logistical services, and their attractiveness is vital to the competitiveness of logistics and supply chains (Ng, 2006). Also, being the focal point of global trade, logistics, and supply chains (Ng and Liu, 2014), they are responsible for more than 80% of the global freight movement (UNCTAD, 2020b). Thus the disruption of even a single element in a port could have a significant cascading effect, causing severe imbalances across the entire delivery service network, causing substantial direct and indirect financial losses. Hence, it is important to investigate port performance in tackling disruption through the lens of resilience. Stemming from human behavior and psychology, resilience is not something new (Chapin et al., 2009). The idea initially appeared in the ecological environmental systems (Holling, 1973) on individuals' ability to face pressure and recover quickly from disruptive incidents (Van Der Vegt et al., 2015). This could be found in its early definitions, notably the continuity of associations within a system and a certain degree of ability to absorb and proceed with absorbing changes (Holling, 1973). In this regard, Labaka et al. (2015) argued that despite extensive research, resilience has various definitions. For example, it has been described as a system's capability for developing foresight, recognition, anticipation, and defense against changing risks before detrimental effects occur (Starbuck and Farjoun, 2005). Some scholars describe resilience as the system's capability to sustain a significant disruption and overcome it within a reasonable time and cost (e.g., Haimes et al. (2008)). Also, it has been referred to as preparing and adapting to changing environments and enduring and recovering quickly from disruptions (House, 2013). Part of such differences in the definition is based on the context in which they are applied (e.g., economic systems, education systems, health care systems, ecosystems, CIs) (Southwick et al., 2014). This explains why some researchers have tried to suggest a multidisciplinary definition for resilience (Clauss et al., 2020). That said, the majority of works in the context of CIs addresses the system's vulnerability, where there is limited attention to capacities and interrelations (Hosseini and Barker, 2016). A resilient infrastructure relies on its ability to absorb, adjust, predict, and quickly overcome a possibly disruptive incident (NIAC, 2009). Here we highlight the fundamental features of a resilient system based on the definition by the US National Research Council (NRC), namely ‘the capability of the system to plan and prepare for, absorb, overcome with, and fit with real or possible disruptions’ (National Research Council, 2012). The definition has two key components: (1) risks decreasing the system's performance (i.e., actual or possible disruptions), and (2) resilience-building capacities resisting system's performance changes and returning it to a new normal (i.e., absorption, recovery, and adaptation/transformation capacities of the system). Later, it was followed by national directives (e.g., PPD (2021)) and explored by many research (e.g., Ramirez-Marquez (2012), Ayyub (2014), and Linkov et al. (2014)), and widely applied in recent research (e.g., Petersen et al. (2020); Doorn et al. (2019); Pescaroli and Needham-Bennett (2021)). As Ayyub (2014) has discussed, such a definition has certain characteristics that make it suitable for practical applications, including the impacts of the Covid-19 pandemic on port resilience. Understanding such, in this study, we develop a Bayesian Belief Network (BBN) model to quantify the port system's resilience in the face of the Covid-19 pandemic. As a tool frequently used in supporting decision-making, BBN handles complexities and uncertainties by spotting disruptive factors, resilience-building capacities, and their interactions (Djalante et al., 2020). The model is then used to model the resilience of the port of Hong Kong's Kwai Tsing Container Terminals (KTCT). In this case, the key contributions of this study are as follows: • Identify port disruptions during a pandemic outbreak, including their cascading effects. • Investigate port resilience-building capacities in the face of a pandemic outbreak. • Develop an extendable model to quantify and assess the port's resilience considering various disruptions raised by a pandemic and resilience-building capacities based on the BBN. • Analyze the resilience of ports. The rest of the paper is as follows. Section 2 consists of the research background, including the literature reviews. Section 3 discusses the framework to develop the model. Section 4 briefly introduces BBN as the analytical tool implemented to build the model based on the introduced framework. Section 5, 6 explains the research process, including data collection. Finally, the results are represented and concluded in Sections 7 and 8, respectively. 2 Research background The key literatures regarding risk and resilience assessment of pandemic impacts are mainly associated with the effects of a pandemic on seaport transportation and the maritime supply chain. Similarly, the effects of the Covid-19 pandemic have mainly been considered the seaborne trade (e.g., Chua et al., 2022; Xu et al., 2021a), port and sea transport (e.g., Mack et al., 2021; Narasimha et al., 2021), and supply chains (e.g., Lahyani et al., 2021; Lopes et al., 2022; Ozdemir et al., 2022). In this case, ports have experienced significant changes to normal operating environments due to the Covid-19 pandemic (UNCTAD, 2022). Addressing the current and potential future challenges inspired researchers and practitioners to rethink strategic resilience in the ‘port’ context. Different natural and human-made disturbances, local or regional, have been widely discussed in the pieces of literature. However, pandemic disruptions, with their global impact and long-lasting effect, have been neglected. As such, it is pivotal to identify the key factors that affect port CIs during the Covid-19 pandemic (Gui et al., 2022; Xu et al., 2021b) and to build a BBN framework to quantify resilience and examine the impacts of different factors in port performance. Here we explore two key questions: 1) How is resilience developed in the context of the port industry? 2) How is BBN implemented in this context? To answer them, we focus on research conducted after 2010 where the port was the focus. For example, we do not cover those studies that analyze the resilience of maritime transport or maritime supply chain where the port is just one (not key) element. Since CIs are exposed to different natural (e.g., hurricanes, tornados, tsunamis, floods, typhoons, volcanic eruptions, earthquakes) and man-made (e.g., pandemic and terrorist attacks) hazards at an unpredictable frequency, intensity, and scale, such systems should be designed in efficient and resilient ways (Djalante et al., 2020). In the meantime, quantifying the impact of threats on CIs performance is far from straightforward (Shafieezadeh and Burden, 2014). That said, considerable research related on port risk management and resilience has been conducted in the past decades. Unsurprisingly, researchers adopted different approaches to identify and assess resilience (Sun et al., 2020). For example, Mansouri et al. (2010) produced the framework of risk management-based decision analysis to investigate port facility resilience based on common fundamental elements of resilience in port infrastructure systems using Decision Tree Analysis (DTA). This helped decision-makers to develop mitigation strategies, contingency plans, and systems for controlling and overseeing potential threats and risk elements; and evaluate the resilience investment plans and strategies that have been adopted. Galbusera et al. (2018) proposed a robust Boolean network approach to examine the resilience of mutual infrastructure, including alleviation factors, allocation plans, and resource constraints. Therefore, fragility, restoration, recovery urgencies, and buffering abilities of provided seismic scenarios were operated to analyze the resilience of CIs in the port of Thessaloniki, Greece. Pitilakis et al. (2019) employed a risk-based method with four pre-assessment, assessment, decision, and report phases for stress assessing critical infrastructures exposed to seismic, geotechnical, and tsunami hazards. Argyroudis et al. (2020) established a resilient CI framework that revealed risks by considering the assets' vulnerability to hazards, the pace of damage recovery, and the hazards’ temporal volatility. The proposed framework that consisted of a an asset resilience index for the complete, incomplete, or no revamp of asset damage between the succeeding hazard conditions was applied to a highway bridge revealing the significant influence of the existence time of the second hazard on the resilience index and a substantial mistake by adopting easy imposition of resilience indices from various types of perils. In addition, considering uncertainty in assessing the resilience of infrastructure systems is crucial. Shafieezadeh and Burden (2014) developed a framework for scenario-based resilience assessment of CIs that reflected the uncertainties of the process, the interrelationship of fragility evaluation of structural elements, the degree of earthquake intensity, the repair process, specifications, and service demands against seismic events. Hseih et al. (2014) evaluated port vulnerability from an interdependency viewpoint through orderly approaches containing sensitivity models and fuzzy cognitive maps to foster practitioner's comprehension of the interrelationship of various subsystems of port infrastructure and the cascading impact of the port vulnerability. Trepte and Rice (2014) investigated the US port system to forecast its capability to tackle cargo concentration disruptions. The study was undertaken by addressing the total volume and product categories that ports take in as a starting point and, following that, assess the required capacity to compete with neighboring ports for different types of products. These stated studies have set a concrete baseline to construct a framework for examining the resilience of ports in face of a pandemic. However, more specific research on this area is required. 3 Resilience assessment framework Fig. 1 demonstrates the performance of a system and how resilience-building capacities and disruption interact over time. Although performance is affected by different factors (e.g., aging of port infrastructure), such elements are not included in the pre-disruption period. The trough in the performance curve reflects part of the system's resilience in face of disruptions. Within the time interval of [ t 0 , t e ] the system operates normally, then with disruption occurrence, the performance reduces until t d . Absorptive capacity refers to the degree that the system can absorb the impact of shocks caused by disruptions and minimize consequences. This is the robustness and reliability to mitigate adverse effects of the disturbance (Golan et al., 2020; Rehak et al., 2018; Setola et al., 2016). Fig. 1 Schematic demonstration of resilience phases (modified based on Henry and Ramirez-Marquez (2012) and Linkov et al. (2014)). Fig. 1 Recovery capacity enhances the serviceability during the disruption gradually until t f . This is the system's capability to recover its major functions effectively to the original state or a new (steady) performance level. Successful recovery includes actions that are dictated by available resources. The process usually takes longer than what it experiences in absorption (Linkov et al., 2014; Rehak et al., 2018; Vugrin et al., 2011). It might reach its original state, improve its service, or reach a lower steady-state performance level. Over this long period, the Adaptive/Transformative capacity could support performance stability and enhancement. This indicates the system's ability to learn from disruptive events and adapt to the possible recurrence of disruptions in the aftermath. By predicting and recognizing disruptive events, the infrastructure gains long-lasting preparedness for future disruptions by strengthening its resilience (Rehak et al., 2018; Setola et al., 2016). The hatched area around t f in Fig. 1 emphasizes the importance of considering adaptive/transformative capacities while devising recovery capacities and allocating resources. This could critically determine the final state of the system's performance. That said, the lost performance (LP) of a port is the reduction in performance of the port due to an unexpected event (e.g., disruption, which depends on its absorptive capacity). In other words, the system's absorptive capacity responds to the shock and determines to what extent it might lose performance. Recovered performance (RP) (i.e., the increase in the system's performance after its reduction) depends on the recovery and adaptive/transformative capacities in response to the LP. Fig. 2 shows the developed resilience assessment framework based on these definitions and used in similar research (e.g., Francis and Bekera (2014); Shen and Tang (2015)). Among various metrics used to assess port infrastructure's resilience, the metric used in this study measures the resilience as the ratio of RP to LP (Henry and Ramirez-Marquez, 2012). Fig. 2 Schematic view of the resilience assessment framework (Source: Authors). Fig. 2 4 Bayesian Belief Network (BBN) The BBN has a wide range of applications in the fields of risk assessment for decision-making under uncertainty and risk, and resilience engineering. This is due to its analytical power that can be used for decision-making under uncertainty and model both qualitative and quantitative variables (Hossain et al., 2019a; Patriarca et al., 2018). It is often adopted as a decision support tool for different types of risk assessment and resilience strategy development as it builds a cause and effect diagram simply (Lee et al., 2009), such as risk analysis (Goerlandt and Montewka, 2015; Lawrence et al., 2020; Montewka et al., 2014; Panahi et al., 2020; Song et al., 2013; Trucco et al., 2008; Xue and Xiang, 2020; Yang et al., 2008; Zhang et al., 2013), reliability engineering (Cai et al., 2019; Hänninen, 2014; Mahdi et al., 2018; Norrington et al., 2008; Yang et al., 2008, 2013, 2018; Zhisen Yang et al., 2018; Zhang and Thai, 2016), safety modeling (Convertino and Valverde, 2018; Hänninen et al., 2014; Mahdi et al., 2018), sustainability analysis (Awad-Núñez et al., 2016, 2015), resilience assessment (Alyami et al., 2014; Hossain et al., 2019a; 2020; Hosseini and Barker, 2016; John et al., 2016), to name but a few. An overview of utilizing BN for risk and resilience assessment of CIs, like ports, is presented here: Hosseini and Barker (2016) implemented a BBN model infrastructure resilience of an inland waterway port and quantified resilience as a task of restorative, absorptive, and flexible abilities. Also, Hossain et al. (2019b) proposed a metric for port performance to evaluate inland port efficiency based on six parameters, namely 1) facility, 2) availability, 3) economy, 4) service, 5) connectivity, and 6) environment. They captured both quantitative and qualitative factors to rank the impact of the criteria based on a port performance index. Later, Hossain et al. (2020) proposed a model for assessing geographical, service provision interdependencies between an inland port infrastructure and its neighboring supply chain to demonstrate the negative impacts of disruptions on the whole infrastructure's performance. The studies suggest that BBN is a highly useful tool for dealing with uncertain situations and inferring knowledge to support timely decisions. 4.1 The BBN theory Constructed on the Bayes theorem, BBN is a probabilistic structure of Directed Acyclic Graphs (DAG), in which nodes represent the variables of the structure, and connections – pointing from parent to child nodes – represent the dependency or causal relationship between such nodes. Here, root nodes – those without a parent node – are quantified with a prior probability. The conditional probability is then used for child nodes, represented as Conditional Probability Tables (CPTs). Conditional probabilities reflect causal relationships among variables of a BBN. Then, the joint probability is written based on the probability of event Y occurring (child node) when event X (parent node) occurs. For a random number of variables X 1 , X 2 , … , X n , and a DAG with n nodes, for which node j ( 1 ≤ j ≤ n ) is associated with the variable X j , the following represents the fundamental mathematical expression of the BBN: (1) P ( X 1 , X 2 , … , X n ) = ∏ j = 1 n P ( X j | p a r e n t ( X j ) ) To elaborate Eq. (1), a sample DAG with six nodes is represented in Fig. 3 . Here, the joint probability distribution of the BBN is given by: (2) P ( X 1 , X 2 , … , X 6 ) = P ( X 1 ) P ( X 2 ) P ( X 3 | X 1 , X 2 ) P ( X 4 | X 2 ) ( X 5 | X 3 , X 4 ) P ( X 6 ∨ X 5 ) Fig. 3 An example of Bayesian Belief Network (BBN) with six nodes (Source: Authors). Fig. 3 4.2 BBN quantification For such a network, variables (nodes) should be quantified according to their type. For Boolean variables (e.g., True/False), the False state describes as the negative result while the True state identifies as the positive result (Fenton and Neil, 2013). For all those up to three parent nodes (i.e., zero, one, two, or three) experts were asked to directly determine the probability of each scenario, i.e., 23 scenarios assuming two states (e.g., True and False) for each node. Here we benefited from the weighting technique for those with more than three parent nodes, considering the level of complexity, i.e., more than 16 scenarios assuming two states (e.g., True and False) for each node. To determine the weight of features incorporated into a parent node, expert judgment was used by applying the Fuzzy Analytical Hierarchy Process (FAHP) based on pair-wise comparisons of such features (Tseng and Cullinane, 2018). To achieve this, we asked participants to determine the relative weight of parent nodes, and later we combined them with their probability to determine the probability of each scenario for the child node. NoisyOR functions were used to determine Boolean variables as we preferred to quantify the effect of each causal factor on its parent node independently of considering all possible combinations of states of the other parents. The NoisyOR function simplifies the elicitation of complex conditional probability tables and soothes the presumption that a factor can be reported as a "True" state only when a parent is also in the "True" status (Kyburg and Pearl, 1991; Perreault et al., 2016). This is demonstrated by introducing the 'leak' factor which suggests that there are other unknown parent variables (nodes). By doing so, the assessment would become more realistic. To comprehend the operational concept of NoisyOR, we assume that there is a set of n causal factors, X 1 , X 2 , ... , X n of a condition, Y. Likelihood of Y is being True once only one causal factor, X 1 is true, and all other reasons other than X 1 are False. The NoisyOR purpose is characterized by Eq. (3) where for each i, v i = P ( Y = T r u e | a s X i = T r u e , X j = F a l s e , f o r e a c h j ≠ i ) is the chances of the condition being True if and only if that causal factor is True (Fenton and Neil, 2013). (3) N o i s y O r ( X 1 , v 1 , X 2 , v 2 , … , X n , v n , l ) Leak factor, l, is a non-zero possibility of the effects that would be created, even though all causes are false. l represents the probability that Y will be True even if all its causal variables are false. So, the provisional likelihood of Y gained by the NoisyOR function is presented below: (4) P ( Y = T r u e | X 1 , X 2 , ... , X n ) = 1 − ∏ i = 1 n To further clarify, we specified a value (between 0 and 1) for each causal factor to use the NoisyOR function. This value captured the probability that the consequence would be true in case of this cause is true. For example, if there is a 24% chance of port closure would cause a delay effect on the landside, the value associated with the cause of port closure would be 0.24. Then, the study identified all the values (one for each of the causes). Also, it is required to indicate an additional value, called the ‘leak value’ to, for example, 0.1, which would be the probability of a landside delay if all risk factors were absent. In other words, the leak factor represents causes of landside delay that are excluded in the model. The posterior probability distribution of disruption and resilience-building capacity nodes are specified by their parent nodes’ weighted sum of probabilities. The weight of each factor shows its importance. In the following equation, the weighted mean (WMEAN) function is represented, where i is the number of variables immediately associated with o the weighted average node (capacity node), and w i indicates the weight of i th variable: (5) W M E A N = ∑ i w i X i = 1,2 , … , n , ∀ i = 1 ; 0 < w i < 1 ; ∑ i w i = 1 For continuous variables, historical data usually determines all the past allocations of the continuous variable. Through the adoption of a truncated normal distribution (TNORM), continuous variables are modelled accordingly (Fenton and Neil, 2013). Equation nodes can consider continuous values rather than a provisional probability distribution table. As such, it explains the key relationship of a discrete node with its parents (Bayes Fusion, 2020). 4.3 End nodes: resilience and performance Disruptions lead to LP, which is highly dependent on absorptive capacity. Thus, the LP is set to zero when a port does not lose its performance, and the disruptions are absorbed. As per Table 1 , the Node Probability Table (NPT) for lost performance is adopted on three main variables, namely the probability of disruption occurrence (LDO), absorption, and actual performance (AP). The LP is calculated as a product of the probability of disruption occurrence (PDO) and AP if absorptive capacity fails to take in the shock caused by disruptions. AP is the product of the rate of capacity deployment and expected performance. A port's utilization rate (UR) during regular operation is obtained from historical data that vary between 0.8 and 1.0. Table 1 Node probability table (NPT) for lost performance (LP)( Source: Authors). Table 1 Absorptive Capacity False True Expression P D O × A P 0 In this case, RP is a function of three variables, namely recovery and adaptive/transformative capacities, and LP. Here we assume that, if recovery and adaptive/transformative capacities perform successfully, a port's CIs would improve the UR of its LP (i.e., zero). Table 2 illustrates the NPT for RP. Table 2 Node probability table (NPT) for recovered performance (RP)( Source: Authors). Table 2 Recovery and Adaptive/Transformative Capacities False True Expression 0 U R × L P 5 Research process The research process can be found in Fig. 4 . Fig. 4 The research process (Source: Authors). Fig. 4 It is divided into four main phases (I, II, III, and IV), as follows: I. Identification of resilience elements: We gathered a comprehensive list of the risks (disruptive factors) (i.e., factors adversely affecting port performance in the face of the pandemic) and resilience-building capacities (i.e., absorption, recovery, and adaptation/transformation capacities). This was performed concerning the literatures, the latest news and reports by international organizations, and experts' input extracted through semi-structured interviews (see Section 6). II. Building the resilience assessment model: We extracted the relationships between disruptive factors and those of identified capacities to build the system's model, based on the resilience assessment framework (see Section 3). In doing so, literature and inputs from the first phase were implemented. Later, the network was verified by circulating the outcome among experts who attended the first phase. III. Model quantification: We determined the (conditional) probability of the model nodes. In doing so, we investigated the port of Hong Kong, China and benefited from its historical data. IV. Resilience assessment: The total resilience of the studied port was measured based on the model outcome. Also, different techniques were used to shed light on the most important resilience-building capacities. 6 Study area and data collection To develop the model and analyze ports in face of a pandemic (phases I and II), we obtained experts' inputs through conducting 28 semi-structured interviews with appropriate professionals who worked as container terminal operators and port authorities for at least ten years in Canada, China, the Netherlands, and the United Arab Emirates (UAE). In addition to the availability of appropriate interviewees, by the time when this study took place, these countries also hosted many of the world's largest ports and terminals. In this case, information extracted from the latest news and reports by international organizations (see Section 5) was helpful in helping us to raise the right questions and obtained highly useful information. Specifically, we asked them questions that were closely related to the identification of resilience factors (Phase I) and their connections (Phase II). Table 3 provides detailed information on the interviewees' profiles. Table 3 The profiles of interviewees (Source: Authors). Table 3 Characteristic Range Frequency Job title/Position President/Director 5 Senior deputy director 6 Division director 7 Supervisor 4 Senior engineer 6 Age range Under 40 5 40–50 8 51–60 13 Above 60 2 Education background Bachelor 13 Master 12 Doctoral 3 Years of experience in the industry 10–15 4 16–20 6 21–25 3 Above 25 5 Location Canada 4 China 14 Netherlands 5 United Arab Emirate 5 After developing the model with a table representing all the definitions, we circulated the outcomes among interviewees, benefiting from the Delphi technique. After three rounds of circulations, we have reached a full consensus among the study participants on resilience factors and their interrelations. For details, see Appendix A. To conduct Phases III and IV, we applied the developed model on Kwai Chung and Tsing Yi Container Terminals (KTCT) in the port of Hong Kong, China. Located in southern China and renowned for its high efficiency, KTCT contributes an annual container-handling capacity of more than 20 million Twenty-Foot Equivalent Units (TEUs) by nine container terminals operated by five different operators, namely Modern Terminals Ltd. (MTL), Hongkong International Terminals Ltd (HIT), COSCO-HIT Terminals (Hong Kong) Ltd. (CHT), Goodman DP World Hong Kong Ltd., and Asia Container Terminals Ltd (ACT). As confirmed by several interviewees, keeping the port and its terminals open was extremely important even during the difficult periods (e.g., a pandemic), understanding its pivotal roles in sustaining the daily lives of all the city of Hong Kong's residents, bringing in vital commodities, not least food, medical supplies, and other basic necessities. To quantify the model, we reached out to 13 senior managers, all with more than at least ten years of experience in KTCT's operation. Among them, three attended the first series of the stated interviews (see above). During the meetings, we explained the whole process and represented the developed model to the rest of the team. To simplify the process, we assumed only two states for all the nodes, namely "True" and "False". That said, we asked them to determine the probability of each state or scenario for all the nodes with up to three parent nodes (i.e., zero, one, two, and three). For those with more than three parent nodes, we asked them to determine the relative weight of each parent node (i.e., the contribution of the parent node to the child node, see Section 4.2). 7 Results and discussion 7.1 Model and quantification After Phases I and II have been completed, we obtained a general model to measure the resilience of the port. It includes 30, 13, ten, and eight nodes under disruption, absorption, recovery, and adaptation/transformation elements, respectively. Besides, the interplay among such nodes is simulated through 93 connections. After gathering the data (Phase III),1 we quantified the model, measured its resilience, and identified critical factors (Phase IV). With the assistance of the GeNIe software, the resilience assessment model for KTCT can be found in Fig. 5 . Fig. 5 The resilience assessment model of Kwai Chung and Tsing Yi Container Terminals (KTCT) (Remarks: (pink): disruptions, (yellow): absorption capacity, (blue): recovery capacity, (green): adaptation/transformation capacity) (Source: Authors). Fig. 5 The disruption node with two main states (i.e., True = 53% and False = 47%) suggests a 53% chance that KTCT's disruption would occur and adversely affect its resilience. On the other hand, there is a 47% possibility that the disruption would not happen. Considering the states for the absorption node, the system is 69% successful in absorbing shocks of disruptions based on its absorption capacity. This is 67% and 63% for recovery adaptation/transformation capacities, respectively. The overall resilience of KTCT is 83%. In this case, it is important to understand the contribution of variables in building the system's resilience, so that port and terminal decision-makers can effectively plan for the future by prioritizing their current actions. This can be done through sensitivity analysis (SA) and scenario analyses. 7.2 Sensitivity analysis (SA) SA is a useful technique to validate the structure of the BN model (Hossain et al., 2019b; Lawrence et al., 2020) by examining the impact of the contributors in the target node within the same model. Indeed, it is a widely accepted method to identify which node has a further influence on its associated node. As such, SA examines the relative value of the independent variable(s) for a specific set of conditions on a particular dependent variable (Borgonovo and Plischke, 2016). This possesses certain advantages over other techniques, such as an in-depth study of all the variables allowing decision-makers to identify what and where they can make improvements, whether the origin of the inference is rational, and what an incremental effect might impact the modelled results. Here we used GeNIe to acquire more insight into the model and better understand how the parent nodes influence the child nodes of the underlying BBN structure. The impact of the absorption capacity's causal factors is analyzed by setting absorption as a target node. As an illustrative example, Fig. 6 shows the sensitivity analysis for absorption. The range of the bars related to every sensitivity node demonstrates a measure of the influence on the corresponding node's absorption capacity. Fig. 6(a) shows the impact of the parent nodes of absorption capacity on it when this capacity exists as “False”, while Fig. 6(b) illustrates the influences of those variables once the capacity acts as “True”. We did both analyses to check the impact of variables when absorption was “True” or “False”. By doing so, we found that port connectivity performed the maximum impact while electronic exchange platforms exhibited the minimum impact on absorptive capacity. Despite the wide impactful range of port connectivity from 0.637 to 0.703, the electronic exchange platform's impact was bounded to a restricted range between 0.663 and 0.694. This suggests that the enhancement of connectivity within the port system would create the largest effect of increasing the port's absorptive capacity. In contrast, improvement in the electronic exchange platforms would not have a significant impact on the port infrastructure's absorption capacity. Fig. 6 Sensitivity analysis for absorption (Source: Authors). Fig. 6 Fig. 7 provides the SA of the recovery capacity. Fig. 7 Sensitivity analysis for recovery (Source: Authors). Fig. 7 Based on this, training exhibited the maximum effect, while operational adjustment had the minimal effect on enhancing the recovery process of port infrastructure. The probability of recovery presented the results of training shifts from 0.538 (on the condition that it is “False”) to 0.715 (providing that it is “True = On”); furthermore, the influence of operational adjustment is bounded to a restricted range, between 0.595 and 0.693. The SA of adaptation/transformation can be found in Fig. 8 . Fig. 8 Sensitivity analysis for adaptation/transformation (Source: Authors). Fig. 8 Fig. 8 depicts that both service improvement and technology have a considerable influence on improving adaptation to new conditions. According to Fig. 8(b), the chance of adaptation generated by the outcomes of service improvement shifts from 0.475 (on the condition that it is “False”) to 0.718 (in case that it is “True”); the result of technology moves from 0.489 to 0.714. Hence, we found that improving service improvement and technology would lead to better adaptation to new circumstances. Based on the SA, port connectivity, training, and service improvement are considered the main factors playing a part in enhancing the port infrastructure's resilience. These results are consistent with the real-world scenarios, as port hinterland and maritime connectivity are among the top priorities for the port managers. During its early stage, Covid-19 has severely affected port calls and liner shipping connectivity levels. The lockdowns in major ports have had heavily impacted liner shipping connectivity (UNCTAD, 2020c). Also, the hinterland connectivity impact on ports' resilience was highlighted by the Covid-19 pandemic. Health policies and robust measures are required to prevent virus transmission in the recovery phase, whether on ships or ports of call worldwide. It is crucial to respond in a quick and determined way to keep the port operational, emphasizing the port community's health and safety. In the absence of urgent actions, the post-pandemic recovery would be severely affected, potentially weakening long-term sustainability. Indeed, the Covid-19 pandemic can be a significant driver for adopting emerging industrial 4.0 technologies, such as drones, AI-based surveillance, blockchain, digital twins, autonomous freight, Internet of Things (IoT), and real-time dashboards. Strengthening digitalization and eliminating paperwork in the maritime industry have simplified operational flows, enhance operational resilience, reduce costs, decrease risk, deliver efficiencies, and introduce transparency. Implementing a digitalization strategy can prepare the port infrastructure for the future and establish sustainability by risk analysis and resilience assessment based on different potential scenarios. 7.3 Belief propagation The capability of propagating the influence of verification via the network, indicated as propagation analysis, is a valuable feature of the BBN. Types of analysis can be performed during propagation analysis. The influence of a recognized variable in the target node is measured by forwarding propagation (Fenton and Neil, 2013). In this study, three observations driven by sensitivity analysis with the highest impact on resilience capacities have been integrated into the underlying BBN model to update all unobserved variables’ conditional probabilities. The results are presented in Table 4 . The decision variables, including port connectivity, training, and service improvement, are chosen from absorptive, recovery, and adaptation/transformation capacities regarding their importance to port resilience. Based on the first scenario, port connectivity is not helpful (“False” state) in the absorption of disruptions, resulting in a reduced expected port resilience from 83.23% to 82.26%. The second scenario is referred to as two failed events related to port connectivity and training, which have an adverse impact on absorption and recovery. Scenario 2 drops absorption, recovery, and resilience values, respectively, to 57%, 55%, and 80.42%. Finally, the third scenario shows the impacts of the failure of port connectivity, training, and service improvement, which reduces all resilience capacities and has a more considerable negative impact on resilience, reducing it to 71.60%. The results of the observations on resilience capacities and consequently expected port resilience created by the preceding scenarios are specified and summarized in Table 4. Table 4 Forward propagation scenarios (Source: Authors). Table 4 Scenario Port Connectivity Training Service improvement Absorption (%) Recovery (%) Adaptation/Transformation (%) Expected Resilience (%) Failure Events Base Model 69.00 65.00 63.00 83.23 1 False 57.00 65.00 63.00 82.26 One 2 False False 57.00 55.00 63.00 80.42 Two 3 False False False 57.00 55.00 48.00 71.60 Three Belief propagation analysis represents the advantage of the interrelationship among the variables of the basic BBN model. Based on the forward propagation analysis, all the resilience capabilities are critical for developing resilient port CIs. Propagation analyses enable decision-makers to establish various considerations in the fundamental model with the essential uncertainty to forecast the performance of CIs and obtain a crystal clear understanding for future operations, planning, and management. In addition, policymakers could make effective crucial decisions and build flexible planning to survive any disturbance to the underlying infrastructure according to the forecast. 8 Conclusion The outbreak of Covid-19 pandemic has revealed the weakness of robust and organized coordination of the operations of ports around the world. Indeed, multifaceted precautionary measures for maritime services and against Covid-19 at ports have induced a progressive shortage of shipping service supply and decreased the operational performance of ports. As such, the Covid-19 pandemic has comprehensively reshaped the industry's environment and posed significant challenges and threats to ports' critical infrastructures (CIs). In addition, it has increased the uncertainty in global supply chains due to the changeable shipping market and the low productivity of port services. Indeed, the risk of supply chain disruptions has been sustained at a high level for a prolonged period. In response, how to mitigate such risk arising from typical epidemic control and prevention has eventually been an urgent issue for the sustainability of ports, from the global to local levels. Hence, in this study, we have proposed a resilience assessment model for critical port infrastructure systems to maintain strategic relationships among the key stakeholders, including terminal operators, shipping firms, logistics service providers, port decision-makers, and port authorities. To our best knowledge, the critical infrastructure systems of ports are seriously under-researched. Hence, our study is in line with the latest research hotspots and topic trends of the ocean and coastal management. By the time when this study took place, we were still suffering a high level of uncertainty. Nevertheless, the silver lining is that it offers a valuable, unprecedented opportunity for researchers like us to show our ability to react with a prompt approach to challenges, providing contributions to proceed with the changes in human society. We believe that our study offers pivotal academic and practical contributions, not least identifying and classifying underlying factors about resilience capacities and disruptions, as well as the development of an interactive model to assess and monitor the resilience of port CIs. We can use the research outcomes to develop effective and practical business continuity plans for ports and port facilities. It ensures that the personnel and resources are well-protected after a major disruption, thus allowing them to continue functioning effectively and efficiently. Also, with suitable minor modifications based on feedback from relevant experts/stakeholders, this model can be used to quantify the resilience of any CIs. In addition, BNN can help to plan and evaluate the resilience of a specific port or numerous ports in the region to different disruptive incidents. It offers us a unique opportunity to investigate the results of possible decisions about disruptions. Furthermore, our findings initiate the construction of identical metrics to quantify the maritime transport system's resilience. For further research, our expert interpretation can provide practical knowledge for improving the accuracy of NPTs by using the Delphi technique, swing weights, and classical methods. This sheds light on the possibility of extending, frequent updating, and increasing the resolution of the network. Besides, the development of new resilience model might further encourage interdisciplinary research, such as building resilient vaccine supply chains using cloud-based blockchain. This could provide a breakthrough for ports to improve their capacities and move towards industry 4.0 in the post-pandemic future. Hence, we strongly believe that the study offers the ideal platform for further research and development on resilient port, transport, and urban CIs. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.