Modeling the Resilience of Multimodal Freight Corridors under Disruptions: A Systematic Review

doi:10.21203/rs.3.rs-4831910/v1

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Research Article

Modeling the Resilience of Multimodal Freight Corridors under Disruptions: A Systematic Review

https://doi.org/10.21203/rs.3.rs-4831910/v1

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Objectives

The main objective of this paper is to review the resilience of multimodal freight networks under various disruptions, both natural and manmade. We seek to achieve this through a series of interconnected objectives: 1) Establishing a clear understanding of multimodal freight transportation network resilience by synthesizing diverse definitions from the literature; 2) exploring models employed in simulating multimodal freight network resilience, including emerging trends and best practices; 3) identifying indexes and metrics used for assessing resilience; and 4) categorizing and analyzing the types of disruptions studied in relation to multimodal freight transportation networks, from natural disasters to human-made acts.

Methods

A systematic review was conducted using the preferred reporting items for systematic reviews and meta-analyses (PRISMA) guidelines to rapidly review definitions, models, metrics, and indexes regarding the resilience of multimodal freight transport networks.

Results

We identified a total of 23 studies examining freight transportation network resilience. Among these, seven studies utilized topology-based models to analyze network resilience. One study employed a finite element simulation-based model to assess network behavior under various conditions, while eight studies performed mathematical optimization models to optimize network performance and resource allocation. Additionally, two studies conducted probabilistic models to evaluate the likelihood and impact of disruptions on freight networks, and another two studies implemented real-time analysis models to monitor and respond to changing network conditions in real time. Only one study has used an image-based model to analyze disruption impact on network infrastructure. Although there were few investigations based on advanced high-fidelity models, or real-time analysis models, these approaches were less common among the reviewed studies. Most of the studies found in the literature have been verified using real-world case studies, providing practical perceptions into network resilience. However, a limited number of studies have been validated or calibrated based on actual disruption scenarios, which highlights an important area for potential improvement and further research in future studies.

Conclusion

Freight transportation network resilience is a multifaceted concept encompassing characteristics such as redundancy, functionality, robustness, and vulnerability. The interactions between different modes within multimodal freight corridors enhance network efficiency and resilience, while advanced modeling techniques, such as image-based network flow, agent-based, and finite element simulation models, offer understandings into freight network behavior following a disruption. Optimization models help minimize efficiency losses, delays, and costs during disruptions. These approaches collectively enable freight networks to adapt and recover from unforeseen events, supporting global trade and economic development.

What is the definition of freight transportation network resilience?
How to model resilience, and what are the types of models in the literature?
What are the indexes or metrics used to assess resilience?
What are the types of disruptions applied to freight transportation networks studied in the literature?

Multimodal freight networks play a critical role in supporting economic development, trade, and the seamless flow of goods across local, national, and international markets. As the essential backbone of industrial activities and economic growth, freight transportation networks facilitate the movement of goods and resources necessary for maintaining robust supply chains and promoting global commerce. Multimodal transport refers to the use of more than one mode in a transport chain, such as road and water (Monios and Bergqvist, 2017).

A multimodal freight transportation network specifically involves the integration of at least two or more different transportation modes linked end-to-end to move freight (Misra and Padgett, 2022a). This type of network emphasizes efficient transitions between modes, often using standardized containers and transfer facilities. The U.S. has the largest freight transportation network globally, measured by traffic volume and transports at over $14 billion worth of goods annually (BTS, US DOT 2017). Within this expansive network, highways, railways, port facilities and airports play key roles in intermodal freight transport. Rail-truck intermodal transport represents about 75 percent by ton-miles of the total intermodal freight volume (BTS, US DOT 2017), highlighting its dominance in the industry. Intermodal freight transport provides flexible and cost-effective alternatives to single-mode transport, such as trucking alone, offering improved logistics efficiency. In recent years, freight shippers have increasingly embraced intermodal transport due to its numerous benefits, including cost savings, reduced congestion, and lower environmental impact.

The European hinterland freight transport sector has aimed to shift towards multimodal transport—such as railway, inland waterway, and sea transport—to alleviate road system saturation and promote sustainability (Zhang and Pel, 2016). Multimodal freight transport enables seamless switching between different modes of transport, optimizing the use of available transport facilities and improving overall network efficiency.

In the United States, the American Society of Civil Engineers (ASCE) evaluates the nation’s transportation infrastructure every four years. Its most recent report in 2021 rated the nation’s roads, bridges, railways, and ports at D, C, B, and B-, respectively, indicating areas in need of significant improvement (“ASCE’s 2021 American Infrastructure Report Card | GPA,” 2017). This poor infrastructure condition, combined with potential natural hazards, exacerbates the risks of mobility losses, and further underscores the importance of resilient, efficient, and well-maintained multimodal freight networks.

Figure 1 highlights the condition of bridges according to the U.S. Department of Transportation’s Federal Highway Administration, showcasing the number of bridges in good and fair conditions (Performance History—LTBP InfoBridge). These findings emphasize the necessity for ongoing investment and innovation in multimodal freight networks to ensure their continued efficacy and sustainability in supporting economic growth and development.

Freight transportation networks are vulnerable to various types of disruptions that can significantly impact their efficiency and resilience. Natural disasters such as earthquakes, hurricanes, floods, and storms can cause severe damage to infrastructure, leading to network interruptions and delays. Man-made events, including accidents, intentional sabotage, or infrastructure failure, can also disrupt the smooth flow of goods and hinder network operations.

A recent example of a significant disruption is the collapse of the Francis Scott Key Bridge in Baltimore, Maryland (Key Traffic Impacts (updated April 20, 2024) | FMCSA). This event had far-reaching impacts on the local and regional transportation network. The I-95 experienced the greatest increase in all traffic as a result of the bridge collapse, while the I‑695 West saw a slight decrease (less than 1%) in all traffic but a 7% increase in truck traffic. The closure of the bridge necessitated the use of an alternative route, which was the only option for hazardous materials transport. Consequently, diversion routes now take two to four times longer for all traffic and trucks, leading to increased delays and congestion. Moreover, collisions on some alternative routes have increased, intensifying traffic congestion and posing additional safety risks. This event underscores the importance of maintaining resilient transportation networks and planning for potential disruptions to minimize their impact on freight transport and overall mobility. By understanding and preparing for these different types of disruptions, freight networks can enhance their adaptability and ability to recover efficiently from such events.

The methodology employed in this systematic review uses the PRISMA guidelines (Moher et al., 2015), ensuring transparency and consistency in the review process. The rationale for the study was to rapidly review evidence of modeling the ability of multimodal freight transportation networks to sustain its operations and quickness to recover following a significant disruption, indexes, and metrics developed for resilience assessment, drawing from published research.

Search strategy

Our search strategy was designed to be as inclusive as possible of all studies that provide evidence of models, indexes, and metrics regarding the resilience of multimodal freight transport network.

For this systematic review, a comprehensive approach to database selection has been adopted to ensure a broad and diverse scope of literature coverage. Five major databases were systematically searched: Web of Science, Science Direct, The Transportation Research Board (TRB), ProQuest’s, and Business Source Premier. Web of Science offers a multidisciplinary platform including a wide array of scholarly journals and conference papers, facilitating a comprehensive exploration of academic literature across various fields. Science Direct, renowned for its extensive collection of peer-reviewed journals, provides in-depth coverage of scientific and technical literature, offering valuable resources into transportation-related research. The TRB database serves as a focal point for transportation-related research, housing an array of reports, papers, and publications endorsed by the TRB. ProQuest’s expansive collection includes a diverse range of academic disciplines, offering access to dissertations, theses, scholarly articles, and other publications. Additionally, the inclusion of Business Source Premier supports this review with a focus on transportation economics, management, and policy perspectives.

Specific keywords have been chosen to target the title field, aiming to capture studies with high relevance to the research focus. Four categories of search terms were identified: freight transportation modes, disruptive events, network characteristics, and the impacts of disruptions. These keywords include roadway, railway, waterway, and airway, reflecting the diverse modes of freight transportation under review. Additionally, terms such as disruption, delay, natural disasters, hurricanes, earthquakes, landslides, and manmade disasters have been included to cover a wide range of disruptive events that freight transportation networks may face. Moreover, keywords such as recovery, mobility, survivability, sustainability, vulnerability, resourcefulness, and connectivity were chosen to cover multiple aspects associated with freight transportation networks characteristics and resilience. Also, terms like economy, supply chain, rural, multimodal, agriculture, fishing, manufacturing, industry, trucks, freight network, stakeholders, and freight transportation were selected to cover various levels of transportation networks, their stakeholders, and the impacts of infrastructure disruptions on freight network operation. Furthermore, the search criteria were refined to target papers including terms like resilience, resiliency, resilient, redundancy, robustness, rapidity, and freight in the title or abstract. All English language publications from January 2019 through December 2023 were included in the review.

Screening strategy

The search strategy produced a total of 119 papers across the five selected databases: 39 from Web of Science, 5 from Science Direct, 10 from ProQuest’s, 14 from Business Source Premier, and 51 from the TRB database. Following the initial retrieval, 27 duplicate papers were identified and subsequently discarded. This process resulted in a total of 92 unique papers remaining for screening.

Studies identified through the initial database search underwent a two-stage screening process. In the first stage, titles and abstracts were screened to assess their relevance to the research questions and inclusion criteria. To be included in this systematic review, studies must meet several predefined inclusion criteria. Firstly, eligible studies included scholarly peer-reviewed work, State and Federal Department of Transportation (DOT) reports or published commercial research studies. Secondly, work shall be related to the investigation of resilience modeling specifically related to multimodal freight transportation corridors, interpret a specific metric or index for assessing resilience within the context of freight transportation networks, and apply the resilience modeling and assessment to either international or domestic freight transportation networks. On the other hand, articles were excluded if they fall under the categories of editorials, commentaries, preprint articles, news reports, or opinion pieces. These criteria were established to ensure the inclusion of relevant research while excluding nonpeer-reviewed articles. In the second stage, full-text articles of potentially relevant studies were assessed for eligibility based on the predefined inclusion and exclusion criteria. After screening the titles and abstracts, 44 articles were considered potentially relevant and underwent full-text screening to determine if they met all inclusion criteria. Following the full-text screening, 24 studies were identified that met all the inclusion criteria. Figure 2 shows the PRISMA diagram adopted for this review.

During the screening process, one research article was identified that was derived from a prior technical report performed by the same authors. Upon review, it was determined that the information in the research article was a subset of the information presented in the technical report. Additionally, the technical report had a broader scope, providing a more comprehensive understanding of the work. Consequently, the technical report was included in the review due to its generalized scope and more extensive information. However, the research article was excluded from the review as it only offered a partial understanding of the work presented in the technical report. This approach ensured that the review focused on the most complete and relevant information available. The remaining 23 studies formed the final dataset for subsequent data extraction and analysis, contributing to the synthesis of evidence relevant to the research questions and objectives of the review. Any discrepancies between reviewers were resolved through discussion and consensus.

Data extraction

For the remaining 23 studies, we extracted the title, authors, article source, publication year, publication type, country the study was conducted, resilience definition by the authors when available, the type of resilience model used, the specific indexes or metrics calculated, whether they conducted case studies or not, the type of disruption applied to the model, and the assumptions made in the models.

Resilience Definitions and Metrics

Freight transportation network resilience has been examined through multiple aspects, including redundancy, functionality, robustness, criticality, adaptive capacity, sustainability, connectivity, vulnerability, and many other characteristics. Redundancy assesses the resilience of freight networks by examining the existence of multiple means, whether identical or substitutable, for accomplishing a given function. This concept measures route diversity and spare capacity, providing alternative options for maintaining operations during disruptions. Functionality evaluates network performance at a specific point in time during recovery, focusing on network throughput before and after disruptions, particularly in probabilistic hazards like seismic events. Robustness aims to avoid direct and indirect economic losses by measuring how well the network functions amid capacity disruptions on transport elements. Criticality examines the increased cost or delay caused when specific elements or regions of the network are disrupted, highlighting the efficiency of rerouting traffic over the remaining network. Lastly, vulnerability measures the susceptibility of the network to disruptions that could significantly reduce its serviceability, assessed through metrics like cost, delay, emissions, or throughput degradation. Figure 3 describes the system performance with time facing a disruptive event and the different measures of network resilience by Henry and Darayi.

These diverse characteristics offer different perspectives on evaluating the resilience of freight transportation networks, considering disruption types, user dependencies, modes of transportation, and topological features. Despite variations, they share a common goal of assessing resilience under disruptions. Patnala's understanding of the properties of individual characteristics of infrastructure resilience, shown in Fig. 4, can be useful in this study, as freight network resilience is closely linked to the resilience of its infrastructural components.

Table 1 provides a summary of the identified metrics used to assess resilience in freight transportation networks, along with their definitions as clearly stated by the respective authors in the reviewed studies. These metrics reflect different aspects of resilience. The definitions offered by the authors serve to standardize these metrics and establish a clear framework for evaluating the resilience of freight transportation networks. By presenting these metrics and definitions in Table 1, the study aims to facilitate a comprehensive understanding of how resilience is measured across various contexts and methodologies in the reviewed literature.

Table 1

*Existing definitions of resilience metrics for freight transportation networks.*
Definition	Resilience metric	Reference
Definition 1: “A resilient freight transportation system can coordinate the physical infrastructure, user, and organizational dimensions of freight movements in such a way that the effective interactions between them can withstand the negative externalities of disruptive events, maintain an acceptable level of service, and reconfigure to normal operations at minimum cost and time.” Definition 2: “Ability of infrastructure to be less degradable to disruptive events through available routes for moving goods, quickly adapt to the situation, and return to normal operations in less time. It can be improved through increased robustness, redundancy, and flexibility of transportation networks.” Definition 3: “Ability of users to prepare for unforeseen network disruptions in such a way that they continue moving goods through alternative routes or modes, maintain profitability by adapting variations in supply, and bounce back quickly from operational losses. It can be improved through increased efficiency, accessibility, interdependency, and redundancy of users in the advent of disruptive events.” Definition 4: “Ability to anticipate internal or external threats, disseminate information to users, prepare in advance for adverse situations, identify suitable recovery strategies, respond quickly with adequate resources, and adapt to operational changes in time to strive for continuing freight movements under the effect of network disruptions. It can be improved through dedication to continuous improvement, reluctance to simplify interpretations, diligent commitment, and effective communication with users and infrastructure.”	Resilience	(Patnala et al., 2023)
“The post-disruption throughput over pre-event throughput for both a single port (RES_P), and the port system (RES_S), respectively.”	Resilience	(Li et al., 2022)
“The ability of a system to return to its normal state after a change in its state has occurred.”	Resilience	(Wang et al., 2023a)
“The ability of the transport network to withstand the impacts of extreme weather, to operate in the face of such weather and to recover promptly from its effects.”	Resilience	(Woodburn, 2019)
“The ability of a given system to reduce the consequences of disruptions and to maintain the mobility of goods.”	Resilience	(Kharrat et al., 2023)
“An object’s ability to adapt to unfavorable situations.”	Resilience	(Piña-Barcenas et al., 2023)
“The avoidance of direct and indirect economic losses of a transport network, which is defined as the degree to which the transportation network can function in the presence of various capacity disruptions on transport elements.”	Resilience	(He et al., 2021), (Sullivan et al., 2010)
“The maximum potential drop in system performance and the estimated performance drop.”	Resilience	(Darayi et al., 2019b)
“Susceptibility to disruptions that could cause considerable reductions in road network serviceability.”	Vulnerability	(Bababeik et al., 2019)
“Exposure to disorders and perturbations, which mainly emphasizes both the magnitude element and the perturbations’ probability.”	Vulnerability	(Ahmady and Eftekhari Yeghaneh, 2022)
“The network functionality is considered as a measure of network performance at a specific instant of time during the duration of recovery.”	Functionality	(Misra and Padgett, 2022b)
“The criticality of intermodal infrastructure is evaluated by estimating the increased cost (delay) when a particular element or a group of elements meaning a specific region of the entire network, are disrupted by efficiently rerouting the traffic over the residual network.”	Criticality	(Hosseini and Al Khaled, 2021)
“The minimum number of nodes and links that must be removed to disconnect the network.”	Connectivity	(Hamed et al., 2022)
“Formulated as a demand-weighted average of reciprocal shortest path lengths, network efficiency is used as an indicator of overall connectivity for origin-destination (OD) pairs having freight demand.”	Efficiency	(Wu et al., 2022)

FREIGHT TRANSPORTATION MODES

Interactions between different modes of transportation within multimodal freight corridors play a pivotal role in enhancing the overall efficiency and resilience of the freight network. By utilizing a combination of roadway, railway, waterway, and airway, freight networks can optimize the movement of goods based on factors such as cost, speed, and capacity, depending on the demands of each shipment. This strategic integration of different transport modes allows the network to adapt to changing conditions, disruptions, and logistical requirements.

In Europe, efforts have been made to shift freight transport toward multimodal options like railway, inland waterway, and sea transport to reduce the burden on road systems, alleviate congestion, and enhance overall sustainability. Two promising solutions in this shift are intermodal transport and synchromodal transport (Mes and Iacob, 2016). Intermodal transport involves the consecutive use of various transportation modes to move goods, often leveraging standardized containers to facilitate seamless transitions between modes. This approach offers shippers greater flexibility, allowing them to select the most efficient and cost-effective route for each leg of the journey. Additionally, intermodal transport can reduce reliance on a single mode, increasing resilience by providing alternative options during disruptions. Synchromodal transport builds upon intermodal transport by aiming for real-time and flexible switching among different modes based on the latest logistics information (van Riessen et al., 2015). This dynamic approach enables freight to be rerouted efficiently to avoid disruptions or optimize transport options according to changing circumstances. By incorporating real-time data, synchromodal transport maximizes the utilization of all available transport facilities, further boosting the resilience and adaptability of the freight network. Both intermodal and synchromodal transport offer significant benefits for freight networks, including enhanced operational efficiency, improved resource utilization, and increased resilience against disruptions.

Table 2 presents the identified freight transportation network resilience models and their associated metrics found in the reviewed literature. The results and conclusions drawn from these findings will be discussed in the upcoming sections, providing a comprehensive overview of the state of research in this area.

Table 2

*Freight transportation network resilience models and their metrics.*
Study	Setting	Transportation modes	Resilience measure	Model types	Resilience index	Type of disruption	Case study
(He et al., 2021)	Netherlands	Roadway, railway, and inland waterway	Network robustness	All-or-nothing (AoN) Modal-split logit model (MS) User equilibrium (UE) System optimum (SO)	The robustness indicator $\:{\eta\:}_{G}$	Structural disruption of individual network element (e.g., node or link) Capacity degradation	The Dutch freight transport
(Darayi et al., 2019b)	United States	Roadway, railway, and inland waterway	Static economic resilience	The Inoperability Input-Output Model (IIM), using optimization software LINGO, version 15	Inoperability $\:{q}_{k}$. Final consumption perturbation $\:{c}_{k}^{*}$	Removal of individual network components (interdiction)	Oklahoma freight network
(Hrušovský et al., 2021)	Europe	Roadway, railway, and inland waterway	Costs, time, and CO₂ emissions	Mixed Integer Linear Programming	Number of affected services Number of affected orders	Link(s) disruption	The intermodal transportation network in Germany, Austria, Czech Republic, Slovakia, and Hungary
(Hosseini and Al Khaled, 2021)	United States	Roadway, railway, and waterway	OD-specific traffic flow with optimum cost	Mixed Integer Programming (MIP) Linear programming (LP)	The criticality level	Congestion, capacity degradation	The transportation network spans five U.S. states: Alabama, Arkansas, Louisiana, Mississippi, and Tennessee
(Jansuwan et al., 2021a)	United States	Roadway and railway	Network redundancy	(Dial, 1971)‘s SCOTH algorithm, which is a logit-type stochastic assignment, was used to compute the efficient or reasonable path Polynomial-time complexity to count the number of efficient routes between an OD pair Bi-level programming to compute the network-wide reserve capacity and, Bi-level multi-modal network spare capacity model, using the nonlinear solver in LINGO	Two network-based measures: • Route diversity • Network spare capacity: • Reserve capacity • Multi-modal network spare capacity	Congestion	Utah’s bi-modal freight network for transporting coal.
(Misra and Padgett, 2022b)	United States	Roadway and railway	The network time-evolving functionality, based on network throughput	Monte Carlo simulation (MCS) for estimating intermodal network resilience The intermodal network is modeled using an integrated adjacency matrix	Network functionality $\:Q\left(t\right)$ Resilience index $\:R\left({t}_{r}\right)$	Seismic hazard and can be applied to any probabilistic hazards	Seismic disruption of Memphis intermodal network
(Ahmady and Eftekhari Yeghaneh, 2022)	Iran	Roadway and railway	Vulnerability. Disturbance response preparation	MIP The ε-constraint method called AUGMECON2, developed by (Mavrotas, 2009)	Index of the cargo type Index of the nodes Index of an OD matrix Index of the start node of an O.D. matrix Index of the end node of an O.D. matrix	Link failure	The Iranian intermodal transport network
(Okuda et al., 2023)	Simulated	Railway and roadway	The effect of disaster countermeasure	Mathematical optimization	Volume of freight transportation (DV) Sum of costs borne by freight operators during restoration (TC) (restoration costs (DC), and investment costs (IC))	Natural disasters	Simulated
(Cetiner et al., 2019)	United States	Intermodal port and truck transportation	Network functionality.	An image-based structure-specific modeling. An external HDT (Heavy Duty Truck) model.	Network resilience (R) Network functionality indicators: • Total travel time traveled (TTT) • Total travel distance covered and delay (TTD)	Earthquake	The intermodal freight network in the ports of Los Angeles and Long Beach
(Arabi et al., 2021)	United States	Roadway and waterway	Proactive and reactive responses of port truck operations during disruptions	A metric-based GPS dataset collected by Streetlight	Temporal duration, $\:t$, of each disruption phase Depth of impact, $\:{D}_{s}$ Total impact, $\:I$ Staging and overloading (extended impact) periods, $\:{I}_{es}$, Gradient method to capture the performance stability, $\:{g}_{t}$	Natural and human-made disasters Hurricane Harvey, and two holiday events as case studies	The port of Huston, Texas
(Wang et al., 2023)	China	Roadway and waterway	Time and cost	A nonlinear mathematical programming model, which can be discretized to a 0–1 Knapsack problem by the finite element method and calculated with branch-and-bound algorithm	The port congestion time improvement rate (TIR) The total transportation cost improvement rate (CIR)	COVID-19 pandemic	The Yangtze River economic belt
(Chandra et al., 2020)	United States	Roadway only	Travel time	Probabilistic topology-based model.	The resiliency indicator $\:{(r}_{n}).$	Congestion following a disruption	The multimodal freight transportation network in Southern California
(Fu et al., 2022a)	China	Roadway	Efficiency, capacity, activity, connectivity, and negotiability	A combination of the entropy weighting method EWM and "VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian" VIKOR model.	Efficiency index Capacity index Activity index Connectivity index Negotiability index	COVID-19 pandemic	Wuhan freight network
(Piña-Barcenas et al., 2023)	Mexico	Roadway	The operational robustness of freight transportation corridors	A dual graph theory-based logistics approach	Betweenness centrality index Bonacich power index Clustering coefficient Articulation nodes Degree index	Simulated disruption	Mexican freight transportation corridors
(Hamed et al., 2022)	United States	Railway	Network connectedness efficiency	Topological analysis model, with its adjacency matrix	Network connectedness efficiency $\:\stackrel{-}{E}\left(c\right)$	The decrease in freight flow and the increase in the physical length of links	Aggregate U.S. freight rail network
(Bababeik et al., 2019)	Iran	Railway	The vulnerability The increased cost or delay	A bi-level MIP	Routing cost (RC) Scheduling cost (SC) Total cost (TC)	Single link failure Multiple links failure	The railway network of Iran
(Wu et al., 2022)	Simulated	Railway only	Network efficiency	Optimization model using Genetic Algorithm (GA)	The minimized cumulative loss of efficiency	Link(s) failure	A simulated rail freight network.
(Mao et al., 2023)	United States	Railway only	Connectedness efficiency of freight rail networks Criticality of Nodes and Links	Weighted topological analysis	The network connectedness efficiency $\:\stackrel{-}{E}\left(c\right)$	Disabling nodes and links by natural or human-made disasters	US freight rail network
(Woodburn, 2019)	United Kingdom	Railway only	Delays caused by Network Rail	Empirical analysis using a mix of quantitative and qualitative methods	The freight delivery metric (FDM)	Storm Frank	Closure of Lamington Viaduct
(Li et al., 2022)	Global	Waterway	Overall port sharing capacities	Stackelberg equilibrium Nash equilibrium MIP	Resilience $\:\left(RES\right)$ for both a single port ($\:RE{S}_{p}$), and the port system ($\:RE{S}_{s}$) Demand fulfilment rates $\:\left(DFR\right)$ for both single port ($\:DF{R}_{p}$), and system ($\:DF{R}_{s}$) Return on investment ($\:ROI$) for both single port ($\:RO{I}_{p}$), and system ($\:RO{I}_{s}$)	Earthquake, flooding, tsunami, hurricane	Ports of Singapore, Port Klang, Jakarta, and Belawan
(Choudhary et al., 2021)	India	Generally multimodal	Sustainability-related risks	An interval 2-tuple linguistic (ITL) model and a digraph matrix approach (DMA)	Sustainability risk index (SRI)	Fleet management risks (FM) Financial risks (FI) Informational risks (IN) Ecological and social risks (E&S) Market risks (MR) Operational risks (OP) Organizational and governmental risks (O&G)	The Indian freight transportation network

(Kharrat et al., 2023) presented a proposal of indicators assessing freight transport sustainability and resilience by reviewing existing studies in the transport field. Applying multi-criteria analysis (MCA) to examine the available indicators, they selected twenty sustainability indicators and six resilience indicators based on predefined selection criteria. These indicators were used to determine the degree of sustainability and resilience of the freight network. The proposed resilience indicators are as follows:

Mobility: The availability of alternative modes of transportation, ensuring flexibility and adaptability in the network.
Expenditure from Freight Transport: The recovery budget allocated for freight transport, which influences the network’s ability to recover quickly and efficiently from disruptions.
Air Quality: Authorized emissions, ensuring compliance with environmental standards and contributing to cleaner, healthier transportation operations.
Efficiency of Resource Use: The efficient exploitation of resources, promoting optimal use of available assets and energy sources.
Commitment and Trust: The readiness of resources and personnel to be mobilized during a disruption, enhancing the network’s ability to respond effectively to emergencies.
Employment: The impact of disruptions on employment, specifically the degree of disruption-generated unemployment that may arise.

Interactions between different modes of transportation within multimodal freight corridors bring both challenges and opportunities that affect the resilience of the freight network. Coordination and integration across modes are key to leveraging the strengths of each mode while minimizing vulnerabilities. However, unexpected events such as accidents, infrastructure failures, or adverse weather conditions can negatively impact transportation operations, leading to reduced serviceability and potentially hindering the network’s performance.

The impact of such events varies depending on their type and duration, as well as the frequency and severity of the disruptions. For example, a minor accident on a local road may have a limited effect, while a tree blocking an important railway corridor can cause significant delays and rerouting (Hrušovský et al., 2021). Therefore, it is crucial to distinguish between different events based on their potential risks to the network and develop targeted strategies for mitigation and recovery.

One challenge in the context of multimodal freight transportation is the relative scarcity of publications focusing on specific solutions for individual transportation orders, as the literature tends to emphasize overall network reliability. This gap in research could limit the development of customized approaches to enhance the resilience and efficiency of intermodal transport.

Moreover, increased collaboration among stakeholders, including shippers, carriers, and infrastructure providers, can lead to more integrated and efficient freight operations. By sharing information and aligning objectives, stakeholders can better manage risks and optimize the use of available resources across modes (Li et al., 2022).

Freight transportation networks can be affected by a variety of disruptions that pose challenges to their efficiency and resilience. These disruptions can vary in nature and impact, ranging from natural disasters to human-induced events. Natural disasters such as earthquakes, flooding, hurricanes, and tsunamis can cause severe damage to infrastructure, leading to capacity degradation and structural disruptions of individual network elements, such as nodes and links. Seismic hazards, in particular, present a probabilistic threat that can impact various regions differently (Misra and Padgett, 2022a).

In addition to natural disasters, freight networks face other types of disruptions, including congestion, which can arise from high traffic volumes or incidents on the road, causing delays and reduced serviceability. The removal of individual network components or interdiction, whether planned or unplanned, can disrupt the flow of goods and necessitate rerouting. Similarly, pandemics can lead to operational challenges, as seen during COVID-19 (Wang et al., 2023b), (Fu et al., 2022b), affecting freight flows, creating unexpected delays or changes in demand.

Capacity degradation, a decrease in freight flow, and an increase in the physical length of links, due to detours or changes in routing, can also hinder the efficiency and reliability of freight networks (Hosseini and Al Khaled, 2021). Additionally, holiday events and seasonal variations in traffic patterns may introduce temporary disruptions and shifts in demand, impacting network performance (Arabi et al., 2021).

The cumulative effect of these disruptions can lead to increased costs, delays, and overall network vulnerability. By understanding and addressing these diverse types of disruptions, freight transportation networks can improve their resilience and adapt more effectively to unforeseen challenges.

Disruptions affecting freight transportation networks vary widely in their nature and impact, depending on factors such as predictability, duration, and severity. Each hazard is characterized by its location, intensity or magnitude, frequency, and probability. The duration of the disruption is a significant factor, representing the length of time a hazard persists and the potential effects on network operations. Predictability is a key aspect that influences the severity of a disruption. Some hazards, such as volcanic eruptions and tropical storms, can be forecasted with some degree of accuracy, allowing time for preparation and mitigation measures. However, events like earthquakes are much harder to predict, striking without warning and often causing more severe impacts. The regularity of hazards also plays a role in determining their severity. For example, a series of earthquakes with multiple aftershocks can exacerbate damage and hinder recovery efforts. Similarly, during hurricane seasons, repeated storms can cause cumulative damage, complicating efforts to restore network functionality. Areal extent is another important consideration; hazards that cover large areas, such as widespread flooding or extensive hurricanes, are likely to have a greater impact on the freight network. Additionally, the number of hazards affecting a location can increase severity, especially when multiple events occur simultaneously or in quick succession.

Reviewed Frieght Networks Resilience Models

The reviewed research encompasses a variety of models used to assess freight network resilience, each offering unique insights into different aspects of resilience. Network flow models, agent-based models, and simulation models are commonly utilized to study the behavior of freight networks under different scenarios. For instance, modeling redundancy involves using Dial’s SCOTH algorithm, a logit-type stochastic assignment method to compute efficient or reasonable paths (Jansuwan et al., 2021b). This approach allows for polynomial-time complexity to count the number of efficient routes between an origin-destination (OD) pair, providing insights into route diversity and network spare capacity. Bi-level programming models, including a bi-level multi-modal network spare capacity model using a nonlinear solver in LINGO, help compute network-wide reserve capacity. In estimating functionality, MCS is often employed for assessing intermodal network resilience. An integrated adjacency matrix is used to model the intermodal network, enabling the analysis of interactions between different modes of transport and potential bottlenecks (Misra and Padgett, 2022a). For robustness, a dual graph theory-based logistics approach is used alongside traditional models such as AoN, Modal-split logit model (MS), UE, and SO. These models assess the degree to which a network can function effectively in the presence of various disruptions (He et al., 2021). Models such as MIP and LP are widely used to model the criticality and vulnerability of freight network links. These optimization techniques allow researchers to evaluate the susceptibility of network components to disruptions and prioritize areas for targeted intervention.

Advanced modeling techniques incorporate multiple aspects of resilience assessment, such as image-based structure-specific modeling approaches (Cetiner et al., 2019). This comprehensive method uses extensive data to model impacts on network infrastructure, such as bridges. Finally, optimization models using GA have been applied to calculate the minimized cumulative loss of efficiency, the increase in cost, or delay. These advanced techniques provide innovative solutions for enhancing freight network resilience. Overall, these diverse models contribute to a comprehensive understanding of freight network resilience by addressing various aspects such as redundancy, functionality, robustness, criticality, and vulnerability. By leveraging these models, researchers can develop targeted strategies to improve freight network resilience and ensure the sustainability and efficiency of transportation systems.

Table 3

*Types of models based on their complexity.*
Study	Model types	Resilience index
Topology-based models
(He et al., 2021)	AoN Modal-split logit model (MS) UE SO	The robustness indicator
(Jansuwan et al., 2021b)	(Dial, 1971)’s SCOTH algorithm, which is a logit-type stochastic assignment, is used to compute the efficient or reasonable path Polynomial-time complexity to count the number of efficient routes between an OD pair Bi-level programming to compute the network-wide reserve capacity and, Bi-level multi-modal network spare capacity model, using the nonlinear solver in LINGO	Two network-based measures: • Route diversity • Network spare capacity: • Reserve capacity • Multi-modal network spare capacity
(Piña-Barcenas et al., 2023)	A dual graph theory-based logistics approach	Betweenness centrality index Bonacich power index Clustering coefficient Articulation nodes Degree index
(Hamed et al., 2022)	Topological analysis model, with its adjacency matrix	Network connectedness efficiency $\:\stackrel{-}{E}\left(c\right)$
(Bababeik et al., 2019)	A bi-level MIP	RC SC TC
(Mao et al., 2023)	Weighted topological analysis	Network connectedness efficiency $\:\stackrel{-}{E}\left(c\right)$
(Choudhary et al., 2021)	An interval 2-tuple linguistic (ITL) model and a DMA	SRI
Simulation-based models
(Wang et al., 2023b)	A nonlinear mathematical programming model, which can be discretized to a 0–1 Knapsack problem by the finite element method and calculated with branch-and-bound algorithm	The port congestion TIR The total transportation CIR
Mathematical optimization models
(Darayi et al., 2019a)	The IIM, using optimization software LINGO, version 15	Inoperability $\:{q}_{k}$ Final consumption perturbation $\:{c}_{k}^{*}$
(Hosseini and Al Khaled, 2021)	MIP LP	The criticality level
(Jansuwan et al., 2021b)	(Dial, 1971)‘s SCOTH algorithm, which is a logit-type stochastic assignment, is used to compute the efficient or reasonable path Polynomial-time complexity to count the number of efficient routes between an OD pair Bi-level programming to compute the network-wide reserve capacity and, Bi-level multi-modal network spare capacity model, using the nonlinear solver in LINGO	Two network-based measures: • Route diversity • Network spare capacity: • Reserve capacity Multi-modal network spare capacity
(Ahmady and Eftekhari Yeghaneh, 2022)	MIP The ε-constraint method called AUGMECON2, developed by (Mavrotas, 2009)	Index of the cargo type Index of the nodes Index of an O.D. matrix Index of the start node of an O.D. matrix Index of the end node of an O.D. matrix
(Fu et al., 2022b)	A combination of the entropy weighting method EWM and "VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian" VIKOR model.	Efficiency index Capacity index Activity index Connectivity index Negotiability index
(Bababeik et al., 2019)	A bi-level MIP	RC SC TC
(Wu et al., 2022)	Optimization model using GA	The minimized cumulative loss of efficiency
(Li et al., 2022)	Stackelberg equilibrium Nash equilibrium MIP	Resilience $\:\left(RES\right)$ for both a single port ($\:RE{S}_{p}$), and the port system ($\:RE{S}_{s}$) Demand fulfilment rates $\:\left(DFR\right)$ for both single port ($\:DF{R}_{p}$), and system ($\:DF{R}_{s}$) Return on investment ($\:ROI$) for both single port ($\:RO{I}_{p}$), and system ($\:RO{I}_{s}$)
Real-time models
(Hrušovský et al., 2021)	Mixed Integer LP	Number of affected services Number of affected orders
(Woodburn, 2019)	Empirical analysis using a mix of quantitative and qualitative methods	The FDM
Probabilistic models
(Misra and Padgett, 2022a)	MCS for estimating intermodal network resilience The intermodal network is modeled using an integrated adjacency matrix	Network functionality $\:Q\left(t\right)$ Resilience index $\:R\left({t}_{r}\right)$
(Chandra et al., 2020)	Probabilistic topology-based model	The resiliency indicator $\:\left({\varvec{r}}_{\varvec{n}}\right)$
Image-based models
(Cetiner et al., 2019)	An image-based structure-specific modeling An external HDT model	Network resilience (R) Network functionality indicators: • Total TTT • Total travel distance covered and delay (TTD)

Quality of available models

While a few investigations explored advanced high-fidelity models or Artificial intelligence (AI)-based models, these techniques were less common among the reviewed studies, potentially due to their complexity and resource requirements. Most studies applied their models to real-world case studies, yielding practical insights into network resilience and providing actionable recommendations for stakeholders. However, a limited number of studies validated or calibrated their models based on actual disruption scenarios, indicating an area for potential improvement and future research to increase the robustness and applicability of these models.

In conclusion, freight transportation network resilience is a complex, multifaceted concept that encompasses various characteristics such as redundancy, functionality, robustness, criticality, adaptive capacity, sustainability, connectivity, and vulnerability. Understanding and addressing these diverse aspects are essential to maintaining a resilient and efficient freight network, particularly in the face of disruptions that vary widely in nature and impact. The interactions between different modes of transportation within multimodal freight corridors play a pivotal role in enhancing the overall efficiency and resilience of the freight network. Seamless coordination and integration across modes enable networks to better absorb and recover from unexpected events, minimizing potential disruptions to the flow of goods.

AI plays a pivotal role in modeling and assessing freight network resilience by leveraging real-time data for remote monitoring of traffic and the structural health of network infrastructure following a disruption. AI applications can significantly enhance emergency management and performance evaluation, providing transportation networks with the ability to adapt quickly and maintain high levels of operational efficiency. AI technologies such as predictive analytics enable freight networks to anticipate potential disruptions and optimize routing decisions in real time. By analyzing vast amounts of data from various sources, AI can identify patterns and forecast traffic flows, helping operators respond proactively to changing conditions. This capacity for predictive insights aids in developing a digital twin environment that mirrors the physical transportation network, offering a virtual platform for testing scenarios and evaluating network performance.

Optimization algorithms driven by AI help determine the most efficient allocation of resources and traffic management strategies during disruptions. This capability supports the creation of robust decision support systems that guide network operators in making informed, timely decisions to mitigate impacts and enhance resilience. AI can also assist in the assessment of network components’ integrity through continuous monitoring and analysis of structural data. By providing real-time alerts and notifications, AI enables transportation networks to notify first responders during critical situations, improving emergency response times and enhancing safety. By seamlessly integrating emergency communication strategies with state-of-the-art AI technology, transportation systems can sustain their responsiveness and enhance adaptability within dynamic environments. The role of AI r in freight network resilience extends beyond immediate emergency response, fostering a more resilient, adaptable, and efficient transportation network that can better withstand and recover from disruptions.

Competing interests

The authors declare no competing interests.

Funding

This project has been funded by the Pacific Northwest Transportation Consortium, University Transportation Center for Federal Region 10, University of Washington.

Author Contribution

A.I and A.A.R received funding, prepared project tasks ans identified the project goals. T.L wrote the main manuscript text. All authors reviewed the manuscript.

Availability of data and materials

No datasets were generated or analysed during the current study..

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Modeling the Resilience of Multimodal Freight Corridors under Disruptions: A Systematic Review

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