Review on Energy Resilience

Computers & Industrial Engineering 93 (2016) 252–266

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Computers & Industrial Engineering

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Modeling infrastructure resilience using Bayesian networks: A case study of inland waterway ports

http://dx.doi.org/10.1016/j.cie.2016.01.007 0360-8352/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd St., Rm. 124, Norman, OK 73019, United States. Tel.: +1 405 325 3721; fax: +1 405 325 7555.

E-mail address: [email protected] (K. Barker).

Seyedmohsen Hosseini, Kash Barker ⇑ School of Industrial and Systems Engineering, University of Oklahoma, United States

a r t i c l e i n f o

Article history: Received 14 September 2015 Received in revised form 5 January 2016 Accepted 10 January 2016 Available online 13 January 2016

Keywords: Resilience Bayesian network Transportation

a b s t r a c t

Infrastructure systems, including transportation, telecommunications, water supply, and electric power networks, are faced with growing number of disruptions such as natural disasters, malevolent attacks, human-made accidents, and common failures, due to their age, condition, and interdependence with other infrastructures. Risk planners, previously concerned with protection and prevention, are now more interested in the ability of such infrastructures to withstand and recover from disruptions in the form of resilience building strategies. This paper offers a means to quantify resilience as a function of absorptive, adaptive, and restorative capacities with Bayesian networks. A popular tool to structure relationships among several variables, the Bayesian network model allows for the analysis of different resilience build- ing strategies through forward and backward propagation. The use of Bayesian networks to quantify resi- lience is demonstrated with the example of an inland waterway port, an important component in the intermodal transportation network.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction Activities that account for response and recovery are commonly

Infrastructure systems are faced with growing number of dis- ruptions due to their age, condition, and interdependence with other infrastructures. These systems are subject to common cause failure, but also natural disasters that are becoming more frequent and more impactful (e.g., Hurricane Sandy in 2012, the Japanese earthquake and tsunami of 2011, the Haiti earthquake in 2010, Hurricane Katrina in 2005).

The resilience of infrastructure systems in the face of the variety of disruptive events and resulting consequence has become an increasingly important topic among planners. Infrastructure sys- tems must be designed in a way so that they are resistant enough to withstand and recover quickly from disruptions. Previously, the emphasis of preparedness planning dealt with protection and pre- vention of disruptive events. Such strategies may not be sufficient to withstand disruptive events, particularly for uncharacteristically devastating events, because it is almost impossible in practice to harden infrastructure systems against all types of disruptive events. Accordingly, the concept of resilience emerged to supple- ment a mitigation-focused philosophy, recognizing the significance and need for timely response and recovery from disruptions.

referred to as post-disruption or contingency strategies. A suitable resilience strategy for a critical infrastructure might be different from one to another. For example, rerouting alternative is a suit- able resilience strategy for transportation and communication net- works when the connectivity and redundancy degree of networks are high, however having a high degree of connectivity is not suit- able for power grid systems where the cascading failures are common.

In this paper, we propose the novel quantification of resilience with Bayesian networks, a technique that has found popularity in such fields as reliability engineering but with little application in resilience modeling. Bayesian networks can model the causal rela- tionships among various aspects of resilience and are especially useful when varying levels of data describing those relationships are known (e.g., data sets describing commodity flows through a port, expert elicitation of the effects of a natural hazard on the con- dition of dock-specific equipment). Different disruptive scenarios, as well as different resilience building strategies, can be simulated, and a sensitivity analysis of parameters can be performed for a robust analysis.

To illustrate the proposed quantification approach, we use an inland waterway port case study. Inland ports play a vital role in intermodal transportation networks by maintaining the flow of commodities among industries and regions. The disruption of ports can have significant adverse impacts on supply and demand, ulti- mately affecting productivity. U.S. inland waterway infrastructure

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was recently given the grade of D- (American Society of Civil Engineers, 2013), with locks and dams increasingly vulnerable to common cause failure and natural disasters that could exploit their state of repair. Port closures could result in cargo congestion at the gates, vessel queuing, backlogs at warehousing transloading facili- ties, and manufacturing production stoppages (National Cooperative Freight Research Program (NCFRP), 2014). For exam- ple, the impact of a 10-day shutdown of West Coast port could be approximately $2.1 billion per day on the overall economy (West coast port congestion could cost retailers $ 36.9 billion in the next 24 months, 2015). Closures to inland waterway ports can have significant regional impacts (Pant, Barker, & Landers, 2015; Pant, Barker, Ramirez-Marquez, & Rocco, 2014).

The remainder of the paper is as follows. Section 2 provides background literature on resilience modeling and on the construc- tion of Bayesian networks. Section 3 describes the contributors of port resilience used in this paper, and Section 4 provides the devel- opment and analysis of the Bayesian network for port resilience. Concluding remarks are given in Section 5.

2. Literature review

This section offers some background on the study of resilience, as well as the use of Bayesian networks, which will be used to quantify resilience in this paper.

2.1. Quantifying resilience

Despite the extensive research recently on the subject of resili- ence, most work in infrastructure systems deal with system vul- nerability (withstanding a disruption) rather than system resilience (withstanding then recovering) (Eusgeld, Kroger, Sansavini, Schlapfer, & Zio, 2009; Johansson & Hassel, 2010; Johansson, Hassel, & Zio, 2013; Wang, Hong, & Chen, 2010). Various general metrics have been defined to measure the resilience that is applicable to the infrastructure systems (Carvalho, Barroso, Machado, Azevedo, & Cruz-Machado, 2012; Chang & Shinozuka, 2004; Hashimoto, 1982; Jain & Bhunya, 2010; Losada, Scaparra, & O’Hanley, 2012; Muller, 2012; Vugrin, Baca, Mitchell, & Stamber, 2014). Hosseini, Barker, and Ramirez-Marquez (2016) classified the literature related to the resilience measurement approaches into two groups: qualitative based approaches and quantitative based approaches. Qualitative approaches were further divided into conceptual frameworks and semi-qualitative indices, while quanti- tative approaches were further divided into general probabilistic and deterministic measures and structural-based models (e.g., optimization, simulation, fuzzy logic models).

Several works have focused on transportation and logistics sys- tems, in particular. Omer, Mostashari, and Lindemann (2014) introduced a metric for infrastructure system resilience, measuring the closeness centrality of network before and after a disruptive event. Soni, Jain, and Kumar (2014) proposed a deterministic mod- eling approach based on graph theory to measure supply chain resilience. Their proposed approach is able to capture dynamic nat- ure of environment for handling disruptive events in supply chains. Carvalho et al. (2012) applied discrete event simulation technique to assess alternative supply chain scenarios for improving supply chain resilience. The authors considered two performance mea- sures including lead time ration and total cost for comparing the merit of alternatives. Rajesh and Ravi (2015) addressed the enablers of supply chain risk mitigation and then proposed Grey theory and DEMATEL approaches to explore cause/effect among the enablers of supply chain risk mitigation. Faturechi, Levenberg, and Miller-Hooks (2014) proposed a mathematical model to evaluate and optimize airport resilience, focusing on

the quick restoration of post-event take-off and landing capacities to the level of pre-disruption capacities. Vugrin, Turnquist, and Brown (2014) proposed a multi-objective optimization model for transportation network recovery, designed as a lower-level prob- lem that involves solving a regular network flow problem and an upper-level problem that explores the optimal recovery sequences and modes. The objective of the optimization model presented by Vugrin et al. (2014) is to maximize the resilience of disrupted transportation networks. Their proposed model was applied to two networks: a maximum flow network and a complex congested traffic flow network for recovery task sequencing. Khaled, Jin, Clarke, and Hoque (2015) proposed a mixed integer nonlinear pro- gramming problem and heuristic solution approach for evaluating critical railroad infrastructures to maximize rail network resili- ence. Youn, Hu, and Wang (2011) proposed a metric for measuring the resilience of engineered systems, calculating the degree of pas- sive survival rate (i.e., reliability) plus proactive survival rate (i.e., restoration), as represented by Eq. (1)

Resilience ðWÞ , Reliability ðRÞ þ Restoration ðqÞ ð1Þ Restoration in Eq. (1) is defined as the ability of an engineered

system to restore by detecting, predicting, and mitigating the effects of disruptive events. Restoration is modeled as the joint probability (1 � R) of system failure, the probability (KD) of cor- rectly diagnosing the failure event, probability (KP) of correctly predicting the failure event, and the probability (k) of successfully mitigating the event. By considering restoration elements, the resi- lience formula in Eq. (1) can be rewritten with Eq. (2).

Resilience ðWÞ , R þ k � KP � KD � ð1 � RÞ ð2Þ Youn et al. Youn et al. (2011) also proposed an optimization

model to minimize system lifecycle cost, subject to system’s resili- ence constraint. Both lifecycle cost and system resilience are mod- eled as functions of target component reliability, target component redundancy, and target component prognostics and health man- agement (PHM) efficiency.

Hosseini, Yodo, and Wang, (2014) proposed a generic Bayesian network approach for quantifying the resilience of an electric motor supply chain, where the resilience of supply chain is mea- sured by the metric proposed by Youn et al. (2011). Reyes Levalle and Nof (2015a), Reyes Levalle and Nof (2015b) proposed an approach based on fault tolerance by teaming principle of collabo- rative control theory for design and operation of resilient supply networks. Their proposed approach is capable of achieving higher fault tolerance with fewer resources in the case of disruptions.

Note that many of the previous approaches to quantifying resi- lience focus solely on modeling system reliability, whereas more recent methods also account for system recovery. Such a trend aligns with the comprehensive definition of infrastructure resili- ence presented by the National Infrastructure Advisory Council (NIAC), (2009), which defines the resilience as the ability to pre- dict, adapt and/or quickly recover from a disruptive event. Given this definition, we are primarily motivated by the time- dependent resilience measure proposed by Henry and Ramirez- Marquez (2012) which represents resilience metric at time t, ZðtÞ, as ratio of recovery to loss at time t. The performance of a system over time, uðtÞ, is generally represented in Fig. 1. Three transition states have been defined in which a system can operate: (i) S0, the baseline or steady state when system operates under nor- mal conditions until disruptive event ej occurs at time te, (ii) Sd, the disrupted state at time td due to disruptive event ej disrupting the performance of system, and (iii) Sf , the recovered state at time tf , resulting from recovery activities triggered at time ts.

Depicted in Fig. 1, the system operates normally with service function of uðt0Þ (e.g., inventory rate, capacity level) within time

Fig. 1. System performance and state transition to describe resilience (adapted from Henry and Ramirez-Marquez (2012).

Fig. 2. An example of BN with seven variables.

254 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

interval ½t0; te�. With presence of disruption event ej at time te the system service function reduces from uðt0Þ to uðtdÞ at time td. The system service function remains constant from time td to time ts until the resilience action takes place in time ts, then the system service function gradually increases and reaches a new steady state at time tf . Based on description, system resilience given in Eq. (3) read the resilience of system at a given disruptive event ej at time t, t 2 ½ts; tf� describes the ratio of recovery to loss at such point in time.

ZðtjejÞ ¼ uðtje jÞ � uðtdjejÞ

uðt0Þ � uðtdjejÞ ð3Þ

Barker, Ramirez-Marquez, and Rocco (2013) proposed a resilience-based component importance measures for infrastruc- ture networks which quantify the (i) potential adverse impact on system resilience from a disruption affecting link i, and (ii) poten- tial positive impact on system resilience when link i cannot be dis- rupted. Pant, Barker, Ramirez-Marquez, and Rocco (2014) proposed a stochastic resilience measure based on proposed metric in Eq. (1) to evaluate the system resilience under uncertainty by including time to total system restoration, time to full system service resili- ence, and time to a%-resilience, applied to quantify resilience of inland waterway ports. Baroud, Ramirez-Marquez, Barker, and Rocco (2014) extended these stochastic resilience measures to study the resilience of links and nodes along an inland waterway. We consider an inland waterway port case study in this work, dis- cussed subsequently.

2.2. Bayesian networks

Bayesian networks (BNs) are structured based on Bayes’ theo- rem, capable of updating the prior probability of some unknown variable when some evidence describing that variable exists. In real world applications of risk analysis, there are frequently many unknown variables and many distinct pieces of evidence, some of which may be linked. BNs can graphically represent such problems where uncertain variables are represented as vertices (nodes), with an edge representing the causal relationship between two vertices, forming a directed graph in which cycles are not allowed. BNs are an excellent tool for computing the posterior probability distribu- tion of unobserved variables conditioned on some variables that have been observed, encoding both quantitative and qualitative information in a conditional probability format (e.g., variables could be Boolean (yes/no), qualitative (low/medium/high), or con- tinuous, among others). The ability to model variables of several types is the main property of BN that motivates us to employ it for quantifying of system resilience. Consider a large intercon- nected network like power grids where the failure of a component

could possibly trigger the failure of successive components. BNs can be used to quantify the resilience of such systems due to their interconnected structure among their components. BNs have been deployed in several applications of infrastructure system reliability (Asriana Sutrisnowati, Bae, & Song, 2014; Kabir, Tesfamariam, Francisque, & Sadiq, 2015; Khakzad, 2015; Morris, Vine, & Buys, 2015), but their use in modeling resilience is underdeveloped in the literature. For example, Asriana Sutrisnowati et al. (2014) pro- posed a novel BN model from event log for analyzing the lateness probability in port logistics. The proposed BN model is constructed by decomposition of a dependency graph that generated from event log in port management systems. The proposed BN model can provide valid inference for activity lateness probabilities and also beneficial recommendations to port managers for improving existing activities.

Let V ¼ fX1; X2; . . . ; Xng be the set of variables in a BN whose structure specifies conditional independence. An outgoing edge from Xi to Xj indicates a relationship that value of variable Xj is dependent of the value of Xi variable. If there is outgoing edge from Xi to Xj then Xi is the parent node of Xj and Xj is a child node of Xi. Three classes of nodes exist in BN: (i) nodes without a child node are called leaf nodes, (ii) nodes without a parent node are called root nodes, and (iii) nodes with parent and child nodes are called intermediate nodes. For example, in Fig. 2, nodes X1 and X2, called as root node, in which are parents of nodes X3, X4, and X5 (interme- diate nodes). Finally, nodes X6 and X7 are called as leaf nodes.

The causal relationships among variables of a BN are measured by conditional probability distributions. The full joint probability

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distribution of a BN consisting of n variables X1; X2; . . . ; Xn is found in Eq. (4).

PðX1;X2;...;XnÞ ¼ PðX1jX2;X3;...;XnÞPðX2jX3;...;XnÞ���PðXn�1jXnÞPðXnÞ

¼ Yn i¼1

PðXijXiþ1;...;XnÞ

ð4Þ However, Eq. (4) can be further simplified with knowledge of

what the parents of each node are. For example, if we know that node X1 has exactly two parents, X2 and X4, then the part of joint probability distribution PðX1jX2; . . . ; XnÞ can be replaced with PðX1jX2; X4Þ, as only X2 and X4 affect the occurrence of X1. As such, the joint probability of distribution of a BN can be written using parent nodes of each node. Suppose that ParentsðXiÞ denote the set of parent nodes of node Xi, then the joint probability distribu- tion of the BN can be simplified in Eq. (5).

PðX1; X2; . . . ; XnÞ ¼ Yn i¼1

PðXijParentsðXiÞÞ ð5Þ

A BN can consist of continuous, discrete, or mixed variables. Conditional distributions are commonly referred to as conditional probability tables (CPT). The causal relationship between variables and corresponding CPT are determined based on expert knowledge.

An illustrative example of BN with seven variables as depicted in Fig. 2. The corresponding decomposition of the joint distribution of variables is given by Eq. (6).

PðX1;X2;...;X7Þ ¼ PðX1ÞPðX2ÞPðX3jX1ÞPðX4jX1;X2ÞPðX5jX2ÞPðX6jX3;X4Þ ¼ PðX7jX3;X4;X5Þ

ð6Þ It is clear that to calculate the joint distribution,

PðX1; X2; . . . ; X7Þ, the unconditional probabilities of PðX1Þ and PðX2Þ, as well as the conditional probabilities of PðX3jX1Þ; PðX4jX1; X2Þ, PðX5jX2Þ, PðX6jX3; X4Þ, and PðX7jX3; X4; X5Þ, must be determined.

An important property of BN is the ability to update belief prop- agation or forward propagation, or the ability to update marginal probabilities, PðXiÞ, after observing other variables. For example, the conditional probability for variable X3 given evidence e, ðe ¼ fX1; X2; X4; X5; X6; X7gÞ can be calculated with Eq. (7).

PðX3jeÞ ¼ PðX1; X2; X3; X4; X5; X6; X7Þ PðX1; X2; X4; X5; X6; X7Þ

¼ PðX1; X2; X3; X4; X5; X6; X7ÞP X3 PðX1; X2; X4; X5; X6; X7Þ

ð7Þ

The calculation represented by Eq. (7) is not computationally efficient and can be simplified with Eq. (8).

PðX3jeÞ ¼ PðX1ÞPðX2ÞPðX3jX1ÞPðX4jX1; X2ÞPðX5jX2ÞPðX6jX3; X4ÞPðX7jX3; X4; X5ÞP X3 PðX1ÞPðX2ÞPðX3jX1ÞPðX4jX1; X2ÞPðX5jX2ÞPðX6jX3; X4ÞPðX7jX3; X4; X5Þ

¼ PðX3jX1ÞPðX6jX3; X4ÞPðX7jX3; X4; X5ÞP X3 PðX3jX1ÞPðX6jX3; X4ÞPðX7jX3; X4; X5Þ

ð8Þ

3. Elements of inland waterway resilience

A case study of the Port of Catoosa, an inland waterway port in the Mississippi River Navigation System located near Tulsa, Okla- homa, is used to illustrate the measurement of resilience using Bayesian networks. We choose this case study because inland waterway ports play a crucial role in the U.S. economy. These ports serve as hubs that connect components of intermodal transporta-

tion systems, including barge, train, truck transportation modes (MacKenzie, Barker, & Grant, 2012). According to Waterborne Commerce Statistics Center (2009), approximately one billion tons of cargo or 40% of U.S. waterway commerce traverse through inland port (Waterborne Commerce Statistics Center, 2009). Ninety percent of this cargo consists of coal and petroleum products and crude materials, all of which are important commodities for U.S. manufacturing and production (MacKenzie, Santos, & Barker, 2012; MacKenzie et al., 2012) and are primary commodities at the Port of Catoosa. The impact of disruptive events on inland ports can be devastating and could barricade production at many indus- tries in the U.S.

The Port of Catoosa is the largest port in Oklahoma and is the lar- gest inland waterway port in the U.S. by land area. Over 2.8 million tons of different types of commodities, including fertilizers, chemi- cals, grains, and metal products were shipped imported and exported through the port in 2014. Industries in many states, includ- ing Alabama, Arkansas, Iowa, Illinois, Kentucky, Louisiana, Missis- sippi, Oklahoma, Ohio, and Texas, are served by the Port of Catoosa.

The Port of Catoosa consists of four major docks, each of which deals with a specific commodity type (Pant et al., 2015). The Liquid Bulk dock is used for moving different types of liquids, including asphalt, chemicals, and refined petroleum products. The Grains dock handles agricultural products such as corn, wheat, and soy- beans. The Dry Bulk dock moves a variety of loose commodities such as sands, gravel, and fertilizer that can be handled by con- veyer. The Dry Cargo dock loads and unloads large items, primarily iron, steel, and machinery. This study concentrates on the Dry Cargo dock, whose products are categorized by the North American Industry Classification System (NAICS) economic sectors: Fabri- cated metals, Machinery, Primary metals, and Miscellaneous manufacturing.

3.1. Port disruptions

Natural disasters (e.g., floods, tornados) and hazardous material threats (e.g., fires, explosions, liquid spills) are the primary disrup- tion concerns of decision makers at the Port of Catoosa. As such, natural disasters and hazardous material threats are considered in the BN model as major sources of vulnerability at the port. Hazardous material threats are considered short-term in their dis- ruptive consequences, where natural disasters may have more extended consequences. For example, Hurricane Irene impacted many east coast ports in 2011, causing utility (power/water) sys- tem failures; lack of availability of transportation fuels; damage to port intermodal services, including barge, trucks, rails; dam- age/loss to cargo, vessel, and security systems; loss of dock/port access; and a loss of communication within and outside of ports, among others (The National Impact of a West Coast Port Stoppage, 2014).

3.2. Resilience capacity

Resilience capacity is the resilience enhancement features that could increase the ability of system to absorb, adapt, and restore from disruptions. Biringer, Vugrin, and Warren (2013) proposed the concept of resilience capacity with three categories that each represents temporal attributes before, during, and after a disrup- tive event: absorptive capacity, adaptive capacity, and restorative capacity. These categories are discussed below in the context of the inland waterway port, and they appear in Fig. 3.

3.2.1. Absorptive capacity Absorptive capacity is the capability of the system to absorb or

withstand the impact of disruptive events and minimize the conse- quences, akin to robustness in the resilience triangle literature

Inland waterway port resilience capacity

Absorptive capacity Restorative capacityAdaptive capacity

Backup utility systems

Extra handling equip.

Repositioning

Skilled labor, mgmt.

Budget restoration

Storm surge protection

Communication

Space utilization

Maintenance

Reliability

Mode flexibility

Quick evacuation

Resource restoration(substitution)

Fig. 3. Resilience capacity characteristics of an inland waterway port.

Fig. 4. Calculating the value of Reliability at the port.

256 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

(Bruneau et al., 2003; Vugrin, Warren, & Ehlen, 2011). Absorptive capacity refers to all activities that need to be taken to absorb shocks of disruptions in advance. We identified five features of absorptive capacity that are effective for our case study (National Cooperative Freight Research Program (NCFRP), 2014; Sturgis, Smythe, & Tucci, 2014).

– Backup utility systems. Having backup power generators can be viewed as an absorptive feature of resilience capacity to main- tain continuity of port operations. Power system failure is a common failure in the observation of port disruptions, as a number of the 17 ports interviewed by the U.S. Government Accounting Office (Government Accountability Office, 2007) reported that the purchase of redundant back-up power gener- ation is critical in the case of emergencies.

– Extra cargo handling equipment. Redundant cargo handling facil- ities, including cranes and reachstackers, can reduce the impact of disruptions to the Dry Cargo dock. Further, extra fuel avail- ability is a related option to improve absorptive capacity.

– Storm surge protection. Physical protection, called as storm surge protection (e.g., barge channel protection) can improve the port’s robustness to flood damage.

– Skilled labor and management. Training operators and managers to react to and control a disruption to maintain continuity is an absorptive measure. In addition, the use of skilled labor reduces the time of loading and unloading tasks by fully utilizing equip- ment such as cranes and reachstackers.

– Communication and coordination. An effective flow of informa- tion and coordination before disruption triggers between National Weather Service, port staff, dock operators, utility operators, vessel operators, shipping agents, regulatory agen- cies, and emergency agencies can reduce the impact of disrup- tions. A report related to the port resilience released by Center for a New American Security (Sturgis et al., 2014) high- lighted that communication and coordination between the members of the port community of New York and New Jersey during Hurricane Sandy was one the most influential recovery efforts that has been made. Hence, through the lessons learned

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from the Port of New York and New Jersey, it is not hard to look at communication and coordination between the members of port community as the backbone of port resilience planning.

– Space utilization. The landscape of ports may be utilized differ- ently depending on the size of operations. The larger operations usually have the potential to more efficiently utilize cargo han- dling capacity because they are less likely to be stuck with small pieces of unused terminal space (National Cooperative Freight Research Program (NCFRP), 2014, http://www.joc.com/port- news/terminal-operators/building-port-resilience_20130827. html). For example, for a port terminal with two berths and four cranes receiving an oversized vessel, the terminal has no alter- native but to allow the unused capacity to remain idle. There- fore, a balance for the usage of berth and cranes can be made by larger facility in contiguous dock space by minimizing capac- ity waste.

– Maintenance and reliability. Port maintenance activities, includ- ing on-time repair scheduling of cargo handling equipment and availability of spare equipment, strengthen a port’s ability to withstand disruptions. The reliability of a port, defined as the probability that port continues its normal operations for a given time interval under normal operating conditions, is a measure of the effectiveness of port maintenance.

3.2.2. Adaptive capacity Adaptive capacity is the capability of system to adapt itself and

attempt to overcome a disruption without any recovery activity (Vugrin et al., 2011). It refers to the ability of a system to be reor- ganized and perform efficiently with some extra effort and cost in response to a disruption. Design for adaptive capacity can enhance the resilience of infrastructure systems. Three features of adaptive capacity are identified as contributors to the resilience of inland waterway ports (National Cooperative Freight Research Program (NCFRP), 2014; Sturgis et al., 2014).

– Repositioning. It is common for containers to be stacked at dock locations, however repositioning containers and large items on the ground in the case of natural disasters can be useful. The impact of repositioning has been recognized in the aftermath of Hurricane Sandy at Port of New York and New Jersey, where a large number of containerized cargo could have been saved if they had been repositioned at the yard. The U.S. Federal Emer- gency Management Agency (FEMA) http://object.cato.org/ sites/cato.org/files/pubs/pdf/pa764_1.pdf emphasized on the role of prepositioned equipment program (PEP) in many of infrastructures to prevent severe damages.

– Mode flexibility (substitution). In the case of a port disruption, shipping at ports for a specific transportation mode (e.g., water- way) can be congested and delayed. Under this condition, mode flexibility enables cargo to be shipped through an alternative transportation mode with some extra shipping costs to avoid supply disruptions (MacKenzie et al., 2012).

– Quick evacuation. Time response evacuation of cargo and facili- ties in the case of disruption can enhance the resilience of port operations. For example, thousands of new vehicles stored at the port of New Jersey and New York were flooded and ruined following Hurricane Sandy because their engines burned due to exposure to salt water. In contrast, other East Coast ports responded to Hurricane Sandy with evacuation very quickly and sustained minimal damage (National Cooperative Freight Research Program (NCFRP), 2014).

3.2.3. Restorative capacity Restorative capacity refers to the ability of a system to repair or

restore damages from a disruption (Vugrin et al., 2011). Restorative capacity is different from adaptive capacity in the sense that it is

considered to be a permanent feature of system resilience, while adaptive capacity is a temporary feature (i.e., repairing equipment permanently in place versus ensuring continuity through a non- standard manner that results in an increase in service cost or time). Note that the repair of port facilities during the recovery period may not necessarily restore performance to its pre-damaged state and may exceed prior performance capabilities.

Two components of budget restoration and resource restora- tion, including technical and equipment restoration have been found as major contribution into the restorative capacity of our case study.

– Budget restoration. In the context of port recovery, the damaged equipment (e.g., crane, power generator) can be repaired or restored depending on the severity of disruption but also on budget availability. Budget limitations are the primary driver of resilience enhancing investments (Haimes, 2009).

– Resource restoration. Resource restoration includes the availabil- ity of human-based resources (e.g., skilled labors, technical engineers), and non-human-based resources (e.g., repair equipment).

4. Quantifying resilience capacity with Bayesian networks

In this section, we employ a Bayesian network to quantify sys- tem resilience as a function of the various elements of resilience capacity shown in Fig. 3. We illustrate with the inland waterway port example. The graphical model of proposed BN is depicted in Fig. 5.

4.1. Type of variables

Three types of variables were used to model the various ele- ments of resilience capacity, depending on how each are mea- sured: (i) Boolean variables that measure a dichotomous response (true/false, yes/no, on/fail), (ii) qualitative variables that measure ordinal categories used for weights of factors contributed to the absorptive, adaptive, and restorative capacities, and (iii) con- tinuous variables that measure random variables with a known probability distribution. Much of the works in applying BNs use only Boolean variables (Garvey, Carnovale, & Yeniyurt, 2015; Liu, Liu, Cai, & Zheng, 2015; Trucco, Cagno, Ruggeri, & Grande, 2008; Xu, 2012), though many characteristics of a system require a more sophisticated representation. Also many analyses are hindered by the types of variables allowed by particular BN software (we use AgenaRisk Fenton & Neil, 2013).

The majority of discrete variables or Boolean variables are defined in the form of two states: the True state represents the suc- cess state (or positive outcome), and the False state represents the fail state (or negative outcome). Similarly, Boolean states (Yes and No) of the Resilience improvement variable and states (On and Fail) of the Reliability variable are the counterparts of True and False states. For example, the probability table for Maintenance and inspection variable includes True = 0.7982 and False = 0.2017, sug- gesting that the maintenance and inspection of the port’s facilities are successful 79.82% of the time, while such activities fail 20.17% of the time. Another example is the prior distribution of the storm surge protection variable with two states of True = 0.84 and False = 0.16, which refers to a 84% chance that storm surge protec- tion implemented by port authorities may successfully succeed to hinder the negative impacts of disruptive events according to his- torical data, while there’s a 16% chance that it may fail.

An example of a continuous variable is the one that describes Availability of spare equipment, which is modeled using a truncated normal distribution denoted by TNORM with a mean of 87%, variance of 3%, and lower and upper bounds of 50% and 100%,

Fig. 5. The graphical depiction of the proposed Bayesian network model.

258 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

respectively, as represented in Eq. (9). Note that that the lower and upper bounds show that the availability of spare equipment in the worst and best possible scenario may not be below 50% and beyond 100%, respectively. All prior probability distributions of continuous variables in this work are generated using TNORM.

Availability of spare equipment � TNORM ðl ¼ 0:87;r2 ¼ 0:03; LB ¼ 0:5; UB ¼ 1:0Þ ð9Þ

Note that the parameters of the variables with continuous dis- tributions can be generally obtained through collecting and evalu- ating historical data. Generally, the truncated normal distribution is an appropriate distribution as it is confined to lie between two determined lower and upper bound values, especially for modeling the amount of cargo handling or similar variables.

4.2. Modeling vulnerability through absorptive capacity

Discussed previously, eight important factors were identified as contributors to the port’s absorptive capacity. The prior probability distribution for six of variables, including space utilization, storm surge protection, communication and coordination, backup utility system, skilled labor and management and extra cargo handling, are represented by two states of either False or True as can be seen on the left side of Fig. 6. The posterior probability distribution for the Reliability and Maintenance variables are obtained by Boolean logic rules.

To calculate port reliability, the time to failure or closure/stop- page of the port in terms of operation hours was considered, denoted by time to failure (TTF). TTF can be simply obtained by his- torical data. If the TTF is greater than or equal to the expected TTF of port, then the port is reliable (On state) and fails (Fail state) otherwise. Similar logic has been used to determine the posterior probability distribution for the on-time repair scheduling variable. The Boolean expressions for these two variables are presented in Table 1. The procedure for calculating reliability is depicted in Fig. 4.

The posterior probability distribution of absorptive capacity node is determined by the weighted sum of probabilities of its par- ent nodes. The weight of each factor represents the importance of that factor in achieving the port’s absorptive capacity. To calculate the probability of absorptive capacity, a labeled type node called Weights of factors contributed to absorptive capacity is defined to incorporate the weight of each factor. Such weights can be obtained from decision makers using any of a number of decision analysis techniques (e.g., Analytic Hierarchy Process, swing weights). The weighted mean (WMEAN) function is shown in Eq. (10), where i is the number of variables connected (eight in this case) to the weighted average node (Absorptive capacity in Fig. 6 in this case), and wi is the weight associated with ith variable. This same weighted average method has been used for adaptive capac- ity and restorative capacity variables.

WMEAN ¼ X i

wiXi; 8i ¼ 1; .. .n; 0 < wi < 1; X i

wi ¼ 1 ð10Þ

The logic used to determine the posterior probability distribu- tion of absorptive capacity is based on Boolean logic discussed ear- lier. For example, the expression used to tie the relationship between the Absorptive capacity node and Maintenance node is IF (maintenance = ‘‘True”, ‘‘True”, ‘‘False”), which denotes that absorptive capacity can be achieved when maintenance is success- fully achieved. The similar interpretation can be used for other contributors of absorptive capacity since their achievement will eventually contributed positively to the achievement of absorptive capacity.

Discussed previously, the adaptive capacity and restorative capacity of a system reflect the capability of system to recover its lost capacity after experiencing a disruptive event. Adaptive capac- ity refers to the temporary solutions to recover the lost capacity (lost cargo handling) of the system, like repositioning of containers and equipment. Restorative capacity refers to the permanent activ- ities to fully restore damaged infrastructure impacted by disrup- tion, such as dock berth and equipment restoration. Adaptive and restorative capacities are modeled similarly to absorptive capacity, as shown in Fig. 6.

Fig. 6. Baseline Bayesian network for measuring resilience.

Table 1 Boolean expressions used to define posterior probability distribution of the Reliability and Maintenance variables.

Variable name

Boolean expression Meaning

Reliability IF (TTF P 7500, ‘‘On”, ‘‘Fail”) If time to failure (closure/ stoppage) of port is greater than or equal to 7500 h (expected time to failure), then port is reliable (On state), otherwise not (Fail state)

Maintenance IF (on time repair scheduling P 85% || Availability of spare equipment P 85%, ‘‘True”, ‘‘False”)

If the probability of on time repair scheduling is greater than or equal to 85% AND the probability of availability of spare equipment is greater than 85%, then maintenance mission is successes (True state), otherwise not (False state)

S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266 259

4.3. Modeling recoverability through adaptive and restorative capacities

Adaptive capacity and restorative capacity both contribute to the system’s recoverability; however their impacts may be differ- ent. Adaptive capacity, or temporary solutions to recover lost capacity, can be viewed as a second line of defense if absorptive capacity is not strong enough to withstand a disruption. Restora- tive capacity, or permanent activities to fully restore damaged infrastructure impacted by disruption, can be thought of third line of defense. The practical experience of planning for disruptions, specifically natural disasters (Lucena-Moya, Brawata, Harrison, Elsawah, & Dyer, 2015), indicate that ports with higher restorative capacity (relative to adaptive capacity) are more resilient, suggest- ing the need to model the link between a post-disaster strategy and its causal factors. The key assumption throughout the Bayesian network model is the conditional independence between the

causal factors, but this assumption can be relaxed by introducing links between them. Although the Boolean expression can be used to express the causal relationship between post-disaster strategy and its contributing factors, (adaptive capacity and restorative capacity), there may be a more effective means to account for the uncertainty associated with a successful post-disaster strategy even if adaptive and restorative capacities are both at their True settings. As such, we address this uncertainty with the NoisyOR function, which allows for a probability of resilient strategy failure even when the contributing conditions are met.

To model the causal influences on post-disaster strategy, we use the NoisyOR function. Suppose that there are n causal factors, X1; . . . ; Xn of a condition, Y, with a probability value for Y being true when one and only one X1 is true, and all causes other than X1 are false. The NoisyOR function is defined Eq. (11), where for each i, vi ¼ PðY ¼ truejXi ¼ true; Xj ¼ false; for each j – iÞ is the probabil- ity of the conditional being true if and only if that causal factor is true (Fenton & Neil, 2013).

NoisyORðX1;v1; X2;v2; . . . ; Xn;vn; lÞ ð11Þ

Term l is the leak factor representing the probability that Y will be true when all of its causal factors are false, as shown in Eq. (12).

l ¼ PðY ¼ TruejX1 ¼ False; X2 ¼ False; . . . ; Xn ¼ FalseÞ ð12Þ In general the conditional probability of Y obtained with the

NoisyOR function can be represented with Eq. (13).

PðY ¼ TruejX1;...;XnÞ ¼ 1� Yn i¼1

½ð1�PðY ¼ TruejXi ¼ TrueÞð1�PðlÞÞ�

ð13Þ The NoisyOR function used in this paper to calculate the condi-

tional probability of post-disaster strategy is defined in Eq. (14), which suggests that the chance of successful achievement of a post-disaster strategy is 70% if only adaptive capacity is met, while this value increases to 95% when only restorative capacity is met,

Table 2 The conditional probability table for inbound and outbound cargo handling under DOC.

False True

Absorptive capacity

TNORM (45,000, 200, 0, 75,000)

TNORM (69,000, 150, 62,000, 75,000)

260 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

where the leak probability is only 0.02. Eq. (14) follows the approach by Vugrin et al. (2011), who suggest that adaptive capac- ity (e.g., repositioning, rerouting) can achieve some level of recov- erability, while restorative capacity (e.g., repair) is required to achieve more.

NoisyORðAdaptive capacity;0:7; Restorative capacity;0:95; 0:02Þ ð14Þ

4.4. Modeling resilience capacity

Inspired by Eq. (3), resilience is modeled as the ratio of recoverability to vulnerability, or the ratio of recovered cargo handling capacity to the lost cargo handling capacity resulting from a disruptive event. Vulnerability is achieved through absorptive capacity, and recoverability is achieved with a combi- nation of adaptive and restorative capacity. The resilience node is represented by in Fig. 7. The lost capacity of the Cargo handling variable is conditioned on expected inbound and outbound cargo handling under normal operating conditions (NOC), and inbound and outbound cargo handling under disrupted operating condi- tions (DOC). The partitioned expression in Table 2 was used to define the probability of inbound and outbound cargo facility under DOC.

It is assumed that the port’s absorptive capacity can fully absorb the shocks from a disruptive event if it is in its True state, and as a result, its inbound and outbound cargo handling capacity under DOC would be the same under NOC. That is, when absorptive capacity is in its True state, inbound and outbound cargo handling is assumed to follow a truncated normal distribution, TNORM (69,000, 150, 62,000, 72,000), which suggests that monthly ton- nage has an average of 69,000 with standard deviation of 150, with minimum and maximum tonnage of 62,000 and 75,000 tons, respectively, due to restrictions on yard space and cargo handling equipment. When the absorptive capacity is in its False state, the amount of inbound and outbound cargo handling in terms of monthly tonnage follows TNORM (45,000, 200, 0, 75,000). The lost capacity of cargo handling in terms of tonnage can be obtained by calculating the difference between the inbound and outbound cargo handling under DOC and NOC as represented in Eq. (15).

maxf0; difference between inbound and outbound cargo handling under DOC and NOCg ð15Þ

Note that the estimated resilience distribution is bimodal because resilience is calculated as a function of lost and recovered cargo handling capacity. Lost capacity of cargo handling is condi- tioned on inbound and outbound cargo handling. Inbound and out- bound cargo handling itself determined depending whether

Expected resilience

Fig. 7. The resilience value measured for the baseline model.

absorptive capacity is on either False state or True state which results in two different modes.

4.5. Improving resilience capacity

The ultimate usefulness of the Bayesian network approach to modeling resilience capacity is to determine the efficacy of differ- ent strategies to strengthen absorptive, adaptive, and restorative capacities. This is addressed through a set of hypotheses that determine how similar desired resilience, 0 < Zdesired 6 1, is to the actual resilience, Zactual, calculated from the Bayesian network. The null hypothesis is that desired and actual resilience are similar to each other, that is the difference between Zdesired and Zactual (as the ratio of recovered to lost cargo handling capacity follows a probability distribution) is within e, a small acceptable threshold. Alternatively, the difference between Zdesired and Zactual would be sufficiently large to conclude that the simulated strategy does not meet the desired resilience level. These hypotheses are found in Eq. (16), the notation used by Fenton and Neil (2013).

H0 : Zdesired � Zactual 6 e H1 : Zdesired � Zactual > e

8 >< >:

ð16Þ

In this study, Zdesired is generated by TNORM (l ¼ 0:85, r2 ¼ 0:01, LB = 0, UB = 1), and e is set to 0.05, as represented in Fig. 8.

For the example in Fig. 8, it is found that with probability of 73.7%, the current port resilience strategy being analyzed may not necessarily need any urgent improvement actions to enhance resilience. However, with probability of 26.3% the port’s resilience strategy should be improved.

4.6. Sensitivity analysis

A useful means to examine the validity of an expert-built model is to perform sensitivity analysis, whereby it is possible to graphi- cally analyze the greatest impact of a set of variables on a selected (target) node. To analyze the impact of causal factors of Absorptive capacity, we set the Absorptive capacity to be the target node, and the impacts of its factors are measured in term of conditional prob- ability. The sensitivity analysis of Absorptive capacity’s factors is represented in Figs. 9 and 10. From a purely visual inspection, we can think of the length of the bars in the tornado graphs as being the measure of the impact of that variable on absorptive capacity. Fig. 9 illustrates the impacts of a set of selected nodes including reliability, maintenance, communication and coordina- tion, skilled labor and management, extra cargo handling, and space utilization on the absorptive capacity when absorptive capacity is being ‘‘False”. Fig. 10 shows the impacts of those variables when the absorptive capacity is being ‘‘True”. From these figures, it is obvious that reliability and space utilization have

If (desired resilience – actual resilience ≤ 0.05, “No”, “Yes”)

TNORM ( =0.85, 2 =0.01, LB=0, UB=1)

Fig. 8. Hypothesis modeling through Bayesian networks to determine the efficacy of port resilience strategies.

Fig. 9. Tornado graph depicting the impact on several variables when Absorptive capacity is set to ‘‘False”.

S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266 261

the greatest and lowest impact on the absorptive capacity, respec- tively. The formal interpretation is that the probability of adaptive capacity given the result of reliability goes from 0.649 (when reli- ability is ‘‘Fail”) to 0.899 (when reliability is ‘‘On”), shown in Fig. 10. Despite the wide impactful range of reliability, the impact of space utilization is limited to narrow range, from 0.846 to 0.876. This implies that improvement in port reliability will have an impact on improving the absorptive capacity of port, while this impact would be negligible for utilizing the space of ports.

The sensitivity analysis of the lost capacity of cargo handling in respect to six contributors of port’s absorptive capacity is illus- trated in Fig. 11. Note that the lost capacity of cargo handling dras- tically drops when the state of reliability variable changes from Fail to On, which points out the high impacts of reliability on reduction of lost cargo facility, while the range of changes on lost capacity of cargo handling slightly varies for the space utilization variable which indicates the low impact of this variable on the loss of capacity of cargo handling.

4.6.1. Forward propagation analysis A useful feature of Bayesian networks is the ability to propagate

the effect of evidence through the network, referred to as

‘‘propagation analysis” (Fenton & Neil, 2013). Forward propagation implies the propagation of an observed variable and measures its impact on the target variable. If there exists enough evidence that an observation occurs, then the observation can be entered into the model, and the probabilities of all unobserved variables can be updated. The junction tree algorithm (Jensen, 1996) is used for propagation analysis, where the joint probability for the model from the Bayesian network’s conditional probability structure is calculated in a computationally efficient manner.

Four different forward propagation scenarios were designed, with results reported in Table 3. Four decision variables were cho- sen such that contributions were believed to be significant to the port resilience: Maintenance, Backup utility system, Quick evacua- tion, and Restoration resource. Variables were chosen to fall into each of absorptive (Maintenance, Backup utility system), adaptive (Quick evacuation), and restorative (Restoration resource) capacities.

The first scenario refers to the case when there observation is made that Maintenance is not successful (its ‘‘False” state), which eventually increased the lost capacity of cargo handling. In Sce- nario 2, two failure events of Maintenance and Restoration resource are assumed, leading to a reduction recovered capacity due to the reduction in restorative capacity which eventually results in

Fig. 10. Tornado graph depicting the impact on several variables when Absorptive capacity is set to ‘‘True”.

0 800

1600 2400 3200 4000 4800 5600 6400

E xp

ec te

d va

lu e

(l os

t c ap

ac ity

of

c ar

go h

an dl

in g)

States of maintenance variable

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

False True Fail OnE xp

ec te

d va

lu e

(l os

t c ap

ac ity

o f

ca rg

o ha

nd lin

g)

States of reliability variable

0 800

1600 2400 3200 4000 4800 5600 6400

False TrueE xp

ec te

d va

lu e

(l os

t c ap

ac ity

of

c ar

go h

an dl

in g)

States of backup utility system

0

1000

2000

3000

4000

5000

6000

7000

False TrueE xp

ec te

d va

lu e

(l os

t c ap

ac ity

of

c ar

go h

an dl

in g)

States of storm surge protection

0

800

1600

2400

3200

4000

4800

False TrueE xp

ec te

d va

lu e

(l os

t c ap

ac ity

of

c ar

go h

an dl

in g)

States of skilled labor and management

0 400 800

1200 1600 2000 2400 2800 3200 3600 4000

False TrueE xp

ec te

d va

lu e

(l os

t c ap

ac ity

of

c ar

go h

an dl

in g)

States of space utilization

Fig. 11. Sensitivity analysis of lost capacity of cargo handling with respect to six contributors to the port’s absorptive capacity.

262 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

Table 3 Forward propagation scenarios.

Scenario Maintenance Backup utility system

Restoration resource

Quick evacuation

Absorptive capacity

Adaptive capacity

Restorative capacity

Expected resilience

Failure events

1 F – – – 0.56 0.83 0.83 0.81 One 2 F – F – 0.56 0.83 0.40 0.67 Two 3 – F – F 0.62 0.47 0.83 0.76 Two 4 F F F F 0.43 0.46 0.40 0.55 Four

Fig. 12. Forward propagation analysis for Scenarios 1, 3, and 4.

Fig. 13. Backward scenario when the expected resilience is set to 90%.

S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266 263

0

0.3

0.6

0.9

Absorp�ve capacity

Adap�ve capacity

Restora�ve capacity

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Fig. 14. Radar chart for comparison absorptive, adaptive, and restorative capacities of four scenarios.

264 S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266

reduction of expected port’s resilience. Scenario 3 simulates the impacts of failures of Backup utility system and Quick evacuation, and results indicate that the reduction in restorative capacity has a larger adverse impact on resilience compared to adaptive capac- ity as the resilience value of Scenario 2 drops to 67% when the restoration resource fails, while in Scenario 3 this value reduces to 76% when quick evacuation is not successful. Scenario 4 accounts for failure of all four variables, dropping the expected resilience of the port to 55%. The results of observations generated by those aforementioned scenarios on absorptive capacity, adap- tive capacity, restorative capacity and finally expected resilience of port are determined and summarized in Table 3.

A comparison of the forward propagation analysis Scenarios 1, 3, and 4 is illustrated in Fig. 12. The absorptive, adaptive, and restorative capacities of those four scenarios are visually illustrated in Fig. 14. Fig. 15 shows the comparison of the probability distribu- tions of port resilience among Scenarios 1, 3, and 4. We can con- clude that the distribution of resilience is skewed to the left when adaptive and restorative capacities are reduced, suggesting that adaptive and restorative strategies are important to building resilience.

Two key results are gathered from the propagation analysis dis- cussed above:

Scenario 4

Fig. 15. The comparison of resilienc

– Setting any contributor to the absorptive capacity to be ‘‘False” or ‘‘Fail” will reduce the ‘‘True” probability of absorptive capacity.

– Setting any contributor to the adaptive and restorative capaci- ties to be ‘‘False” will reduce the ‘‘True” probability of absorp- tive and restorative capacity, respectively.

4.6.2. Backward propagation analysis Backward propagation is another useful feature of Bayesian net-

works. In backward propagation, observation is made for a specific variable, usually a target variable (e.g., the resilience node in this study) and then the Bayesian network calculates the marginal probabilities of unobserved variables by propagating the impact of the observed variable through the network in a backward fash- ion. For example, if the resilience value is set to 90%, as shown in Fig. 13, that the adaptive capacity should enhance from 82.75% to 85.47% and the restorative capacity from 82.5% to 88.29% under such a scenario. Several analyses could be performed for different desired outcomes.

5. Concluding remarks

The importance of resilience in the context of planning for infrastructure systems is inescapable. Infrastructure systems such as electric power, communication, and supply chains, are dealing with different types of threats ranging from natural disasters to malevolent human-made events to accidents, and hence are required to be rigorously designed to withstand and recover from disruptions rapidly and efficiently. This is especially true of the components of an intermodal transportation network, including inland waterway ports.

In this paper, we relate the resilience capacity of an inland port to the three components of absorptive capacity (a means to with- stand a disruptive event, or a reduction in vulnerability), adaptive capacity (a means to temporarily adapt to maintain performance), and restorative capacity (a means to restore performance in a long term manner, which with adaptive capacity constitutes recover- ability). Various pre-disaster and post-disaster strategies can improve the three capacities to varying extents, all combining to improve the resilience capacity of the port.

We employ Bayesian networks to quantify the resilience capac- ity of an inland waterway network. Bayesian networks have the ability to combine historical data and expert knowledge, using

Scenario 3

Scenario 1

e among Scenarios 1, 3, and 4.

S. Hosseini, K. Barker / Computers & Industrial Engineering 93 (2016) 252–266 265

calculation of prior and posterior conditional probability. Bayesian networks provide a rigorous tool for handling risks and decision making under uncertainty environments based on configuration of graphical framework. Although the Bayesian networks have been applied in a number of fields, their application to quantifying resilience is sparse. Our motivating example is the Port of Catoosa, among the ports along the Mississippi River Navigation System and located in Tulsa, Oklahoma.

The objective of this work is to provide an initial framework for studying resilience with a Bayesian network, highlighting areas for data or expert elicitation and demonstrating how sensitivity anal- yses can help guide and compare pre-disaster and post-disaster strategies for building resilience. Reports released by the National Cooperative Freight Research Program (NCFRP) (2014) highlight that many contributors to resilience are qualitative in nature (e.g., maintaining frequent communication and information flow, skilled level of port’s labor and management, physical protec- tion), rather than quantitative. Quantifying and assessing resilience from such qualitative variables are difficult when relying on the result of a mathematical optimization model, though such a task is relatively straightforward in a Bayesian network (when underly- ing variables are effectively assessed).

Bayesian networks are also powerful tools for generating risk scenarios. Backward propagation scenario analysis is especially beneficial for port decision makers as it provides insights to achieve a specific level of resilience.

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