Review on Energy Resilience

Int. J. Production Economics 180 (2016) 68–87

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Int. J. Production Economics

http://d 0925-52

n Corr Oklahom

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journal homepage: www.elsevier.com/locate/ijpe

A Bayesian network model for resilience-based supplier selection

Seyedmohsen Hosseini, Kash Barker n

School of Industrial and Systems Engineering, University of Oklahoma, Norman, USA

a r t i c l e i n f o

Article history: Received 3 February 2016 Received in revised form 5 July 2016 Accepted 6 July 2016 Available online 15 July 2016

Keywords: Resilience Supplier selection Bayesian network

x.doi.org/10.1016/j.ijpe.2016.07.007 73/& 2016 Elsevier B.V. All rights reserved.

espondence to: School of Industrial and Syste a, 202 W. Boyd St., Rm. 124, Norman, OK 73

ail address: [email protected] (K. Barker).

a b s t r a c t

Supplier selection is an important strategic decision in the context of supply chain management. Existing literature on the subject of supplier selection is focused on evaluating primary (e.g., cost, quality, lead time) and green (e.g., CO2 emission, environmental practices) criteria. However, the concept of supplier resilience has recently emerged due to advent of competitive and global supply chains (and the opera- tional and disruptive risks to which they are exposed). Several resilience-based supplier selection criteria are developed with respect to absorptive, adaptive, and restorative capacities. This paper further pro- poses a Bayesian network (BN), a paradigm that effectively models the causal relationships among variables but that has not been used in the context of supplier evaluation and selection, to quantify the appropriateness of suppliers across primary, green, and resilience criteria. Some benefits of the BN paradigm, including an ability to handle expert evidence and to perform sensitivity and propagation analyses, are demonstrated with an initial illustrative example of three suppliers.

& 2016 Elsevier B.V. All rights reserved.

1. Introduction and motivation

According to recent estimates (Beli, 2010), the average U.S. manu- facturer spends roughly half its revenue to purchase goods and ser- vices. As such, the choice of suppliers poses an important considera- tion for manufacturers as they have a large financial stake in how suppliers perform. And such a decision is made all along the supply chain, with ramifications to all members of the supply chain.

The supplier selection problem is a challenging multi-criteria de- cision problem that involves tangible and intangible factors (Ho et al., 2010). Gonzalez and Quesada (2004) highlighted the important role of suppliers in meeting the goals of a larger supply chain, particularly in achieving high quality products and customer satisfaction. The sup- plier selection problem aims to select the best supplier among a set of potential suppliers to satisfy certain requirements while subject to their limitations. Traditionally, supplier selection problems account for primary criteria including quality, cost, service level, and lead time, among others (Dickson, 1966).

Given the recent (and perhaps more frequent) occurrence of large- scale disruptions in the form of natural disasters (e.g., earthquakes, tsunamis, floods) and man-made events (e.g., labor strikes, human errors, transportation mishaps), supplier selection criteria should also include the concept of supplier resilience. Resilience is often thought

ms Engineering, University of 019, USA.

of as the ability of a system or organization to withstand the effects of a disruption and to recover to a desired level of performance in a timely manner.

The earthquake and tsunami that struck in Japan in March 2011 caused significant disruptions throughout the supply chains of many industries, leading to massive economic losses (MacKenzie et al., 2012). One significantly impacted industry was automobile manufacturing. Many of Toyota’s part suppliers were unable to deliver parts at their expected volume and suffered from sig- nificant delays. General Motors was forced to halt the production of its vehicles due to the shortage of raw materials from Japanese suppliers (Huffington Post, 2015). Nissan suffered greatly because of its high level of dependency on raw material suppliers in the earthquake zone that supplied about 12% of its engines (BBC News, 2011), forcing Nissan to shut down production at its Sunderland, UK plant for several days (Massey, 2011).

The adverse impacts of natural disasters on the suppliers of auto- motive parts are significant due to the size and complex nature of the automotive supply chain. A car consists of 20,000 parts on average, and if any one of those parts is unavailable, the finished product cannot be shipped. Many of the car’s components, such as engines and transmissions, are supplied by Japanese companies located in regions affected by natural disasters (Business Theory, 2011). Hence, segrega- tion of suppliers geographically from disaster-prone areas could help suppliers to efficiently mitigate the effects of disruptions. For example, Toyota asked their suppliers to either spread production to multiple locations or hold extra inventory buffers as a mitigation strategy to withstand disruptions (Supply Chain Digest, 2012). Nissan also asked

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 69

the same of its suppliers, suggesting the importance of supplier seg- regation and extra buffer inventory to enhance the resilience of auto manufacturing suppliers. Electronics supply chains are also very si- milar to the automotive part supply chains where products such as desktop PC, laptops, smart phones consist of hundreds of components that are commonly supplied by Japan (Monczka et al., 2014).

More recently, Hurricane Sandy struck New York and New Jersey, among other east coast U.S. states, in October 2012, causing the stoppage of normal daily operations of ports and resulting in massive economic losses. For example, the commercial trucking industry was halted due to the effects of the hurricane with losses of approximately $140 million per day (U.S. Department of Com- merce, 2013). This highlights the idea that designing robust pro- tection strategies is not sufficient to withstand against disruptive events, especially large-scale natural disasters.

These recent events suggest that supply chain disruptions are inevitable and their adverse impacts to revenue and productivity can be significant. In general, risks associated with supply chains can be classified into two categories: operational and disruption (Tang, 2006a). Operational risks refer to the inherent “every day” events that occur within a supply chain, including uncertainty in customer demand, transportation cost, and supply uncertainty due to operational problems such as power outages and technical equipment failures. Disruption risks refer to the major event-dri- ven disruptions, including natural disasters, human-made acci- dents, or malevolent attacks. Disruption risks tend to be lower in likelihood but higher in adverse consequences compared to op- erational risks. Resilient suppliers are those that can withstand and recover from multiple sources of risk.

This paper aims to develop a new decision approach for sup- plier selection based on Bayesian network theory, a power tool for handling risk and uncertainty in decision making with the cap- ability of modeling both qualitative and quantitative variables (Fenton and Neil, 2013). Bayesian networks have been used for decision making in a variety of applications such as software de- velopment projects (Perkusich et al., 2015), data classification (Arizmendi et al., 2014), safety management (Hanninen et al., 2014), customer service management (Song et al., 2013), and traffic accidents (Hanninen, 2014), among others. However, there appears to be no use of Bayesian networks for aiding the supplier selection process. We propose a Bayesian network formulation for supplier selection, accounting for operational (e.g., customer de- mand) and disruption (e.g., natural disaster) risks and their effect on resilient suppliers.

2. Literature review

This work accounts for supplier selection criteria from three per- spectives, defined here as primary criteria, green criteria, and resilience criteria. This section highlights literature dealing with primary and green criteria, as well as respective supplier selection problem for- mulations. A summary of recent literature on supplier selection and related methodologies is represented in Table 1. The notation for supplier selection factors used in Table 1 is provided in Appendix.

2.1. Primary criteria for supplier selection

Primary criteria are comprised of the common criteria used for decades in supplier selection, including cost, quality, lead time, and service level, among others. For example, Dickson (1966) introduced 23 supplier selection criteria still found in literature today. Kotula et al. (2015) investigated the supplier assessment criteria from multiple

stakeholder perspectives specific to industry and country. They found that for the construction industry, quality, supplier relationship man- agement, and profit were the important factors for evaluating sup- pliers, while for the electronics industry, quality, a sourcing strategy aligned with corporate goals, and supply flexibility were most important.

Many supplier selection problems have been addressed with multi-criteria decision analysis tools that compare discrete supplier alternatives, including TOPSIS (Wang et al., 2009), ELECTRE (Sevkli, 2010), and data envelopment analysis (DEA) (Toloo and Nalchigar, 2011). Generally, these approaches provide a ranked order of alter- natives (i.e., suppliers) given a set of weighted criteria, where weights are elicited through the analytic hierarchy process (AHP) or a similar approach. Fazlollahtabar et al. (2011) integrated AHP and TOPSIS to evaluate suppliers based on cost, quality, service, delivery, and in- novation. Liu and Zhang (2011) applied the ELECTRE III method for supplier selection considering technology available, service, manage- ment capability, and enterprise environment. Hague et al. (2015) ap- plied an interval-value TOPSIS approach with importance measure- driven weights to select suppliers based primarily on part reliability and maintainability. Memon et al. (2015) applied a combination of grey system theory and uncertainty theory for evaluating supplier criteria of quality, delivery capability, logistics service, and risk factors. Pitchipoo et al. (2015) also applied a grey decision model for supplier assessment and selection in the process industry where cost, delivery, capacity, and warranty of potential suppliers were evaluated. Saghiri and Barnes (2016) addressed the relationship between supplier flex- ibility and postponement as a strategy for managing demand under uncertainty through an empirical analysis.

Mathematical programming formulations have also been de- veloped for the supplier selection problem. Jadidi et al. (2014) proposed a goal programing approach for multi-objective joint supplier selection and order allocation. Ustun and Demitras (2008) integrated ANP and multi-objective mixed integer linear pro- gramming for selection of suppliers with consideration of finance, quality, delivery, customer relationships, service, and risk. Sawik (2010) introduced a mixed integer programming formulation to consider supplier finance, quality, delivery, management, and or- ganization. Yucenur et al. (2011) considered quality, cost, and risk with AHP and analytical network process (ANP) approaches under a fuzzy environment. Mohammaditabar et al. (2016) developed a game theoretic analysis for capacity-constrained supplier selection to analyze selected suppliers and agreed-upon prices in decen- tralized supply chains. Rezaei and Davoodi (2011) developed a mixed integer nonlinear programming to integrate lot sizing and supplier selection problem together where the main primary cri- teria are quality, service, and supplier cost of supplier. Zhang and Zhang (2011) proposed a mixed integer program for the supplier selection and purchase problem under stochastic demand. Zhang et al. (2016) explored how supplier selection can be empirically integrated with services and co-creation with customers.

2.2. Green criteria for supplier selection

The threat of increased greenhouse gas emissions has led some governments to impose stricter regulations and standards. These re- quirements, as well as environmental consciousness on the part of industry decision makers, have led to green considerations in doing business, including supplier selection. There has been a recent in- crease in supplier selection work that addresses both primary and green criteria.

Lee et al. (2009) extended a fuzzy AHP approach for green supplier selection with five primary criteria (quality, finance, organization,

Table 1 Recent literature on supplier selection and analysis methodologies.

Reference Selection factor Methodology

a b c d e f g h i j k l m n o p q r s t u v w x y z ra scc fl rd in bs

Huang and Keskar (2007), ✓ ✓ ✓ ✓ ✓ ✓ AHP Ustun and Demitras (2008), ✓ ✓ ✓ ✓ ✓ ✓ ANP and multi-objective programming

Lee et al. (2009), ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Fuzzy AHP Wang et al. (2009), ✓ ✓ ✓ ✓ ✓ ✓ Fuzzy TOPSIS

Sawik (2010), ✓ ✓ ✓ ✓ ✓ Mixed integer programming Kumar and Jain (2010), ✓ ✓ DEA

Zhang and Zhang (2011), ✓ Mixed integer programming Fazlollahtabar et al. (2011), ✓ ✓ ✓ ✓ ✓ Multi-objective programming, AHP, and TOPSIS Toloo and Nalchigar (2011), ✓ DEA

Liu and Zhang (2011), ✓ ✓ ✓ ✓ ELECTRE III Rezaei and Davoodi (2011), ✓ ✓ ✓ ✓ Multi-objective nonlinear programming

Yucenur et al. (2011), ✓ ✓ ✓ AHP and ANP Zhang et al. (2013), ✓ ✓ ✓ ✓ ✓ Multi-objective programming

Sawik (2013), ✓ ✓ ✓ Mixed integer programming Jadidi et al. (2014), ✓ ✓ ✓ ✓ Fuzzy multi-objective optimization Kuo et al. (2014), ✓ ✓ Binary integer programming

Karimi and Rezaeian (2014) ✓ ✓ ✓ ✓ Multi-stage goal programming Theiben and Spinler (2014), ✓ ANP

Haldar et al. (2014), ✓ ✓ ✓ Fuzzy TOPSIS Memon et al. (2015), ✓ ✓ ✓ ✓ Grey theory

Akman (2015), ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Fuzzy c-means and VIKOR Pitchipoo et al. (2015), ✓ ✓ ✓ ✓ Grey theory

Kotula et al. (2015), ✓ ✓ ✓ ✓ ✓ ✓ ✓ Empirical analysis Torabi et al. (2015), ✓ ✓ ✓ ✓ ✓ Mixed integer stochastic programming

Hashemi et al. (2015), ✓ ✓ ✓ ✓ ✓ Grey relation analysis and ANP Rajesh and Ravi (2015), ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Grey relational analysis Mahdiloo et al. (2015), ✓ ✓ DEA

Saghiri and Barnes (2016), ✓ Empirical analysis Mohammaditabar et al. (2016), ✓ ✓ ✓ ✓ Game theory

Sawik (2016), ✓ ✓ ✓ Mixed integer programming

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technology capability, and service) and four green criteria (total pro- duct life cycle cost, green image, pollution control, and environmental management). Hashemi et al. (2015) proposed an a grey relation analysis and ANP for green supplier selection, accounting for primary criteria of cost, quality, and technology and green criteria of pollution production, resource consumption, and management commitments. Huang and Keskar (2007) applied AHP with carbon footprint con- siderations, along with finance, delivery, service, and organizational performance. Zhang et al. (2013) developed a nonlinear multi-objec- tive optimization model for green supplier selection that accounted for pollution emitted by gasoline consumption during transportation, cost, delivery rate, transportation time, and service level, solved with a Pareto genetic algorithm. Akman (2015) integrated fuzzy c-means and VIKOR methods to evaluate green suppliers based on green design, pollution prevention, green image, green capability, and environ- mental management. Kumar and Jain (2010) developed a DEA model considering carbon footprint monitoring. Mahdiloo et al. (2015) also applied DEA considering technical and environmental criteria, referred to as an eco-efficiency measurement. Theiben and Spinler (2014) evaluated the efficiency of green suppliers based on their CO2 emis- sion level using ANP. Kuo et al. (2014) developed a carbon footprint inventory route model based on the vehicle routing problem.

3. Development of resilient supplier selection criteria

The ability to withstand, adapt to, and recover from a disrup- tion is generally referred to as resilience, a definition with which many would largely agree (Haimes 2009, Aven 2011, Barker et al., 2016). Resilience is a concept that is increasingly gaining traction in government, industry, academia, and popular science (Park et al., 2013, Zolli and Healy, 2013, Hosseini et al., 2016).

Resilient supply chain practices have been a well-studied topic for the last decade or so. Particularly in a supply chain context, Sheffi (2005) defined the resilience of a firm within a supply chain as its inherent ability to maintain or recover its steady state be- havior, thereby allowing it to continue normal operations after a disruptive event. Rice and Caniato (2003) highlighted that supply chain resilience in the upstream level could be enhanced with the multiple-sourcing of suppliers, sourcing strategies to allow switching of suppliers, and commitment to contracts for material supply. Christopher and Peck (2004) emphasized that developing visibility to a better view of upstream inventories and supply conditions would positively contributes to the resilience of supply chain context, while Tang (2006b) pointed out the importance of flexible supply base (sourcing).

However, in contrast to the extensive work to explore the role of primary and green criteria in the supplier selection problem, accounting for the concept of resilience in supplier selection is relatively new and with no consensus on factors contributing to the resilient characteristics of suppliers. Rajesh and Ravi (2015) proposed a grey relational analysis method for selecting suppliers considering vulnerability, collaboration, risk awareness, supply chain continuity management for selection of resilience suppliers. Torabi et al. (2015) developed a two-stage stochastic programming model to solve a resilient supplier selection and allocation pro- blem under operational and disruption risks, accounting for four resilience-building strategies including supplier business con- tinuity plans, extra inventory maintained by the supplier, for- tification of suppliers, and contracting with backup suppliers. Sa- wik (2013) investigated the problem of developing a resilient supply portfolio, including the pre-positioning of emergency in- ventory as a primary strategy to mitigate the effects of a

disruption, using a mixed integer programming model with con- cepts from value-at-risk and conditional value-at-risk. Sawik (2016) proposed a risk-averse optimization model in the presence of a supply chain disruption with two different service levels measures: the expected worst-case demand fulfillment rate and the expected worst-case order fulfillment rate with consideration that suppliers are geographically dispersed. Haldar et al. (2014) proposed a fuzzy group decision making approach for resilient supplier selection where the importance degrees of supplier at- tributes are expressed in terms of linguistic variables. Reyes and Nof (2015) proposed resilience by teaming (RBT) association de- cisions, inspired in the “fault-tolerance by teaming” principle from collaborative control theory to form network and re-configure mechanisms. The main findings of their research show that supply chain networks using RBT association rules result in increased quality of service with no significant cost increases for normal operations.

Vugrin et al. (2011) defined the resilience capacity of a system as a function of the absorptive, adaptive, and restorative capacities of the system, clearly identifying pre-disruption and post-disrup- tion planning. We make use of this concept of resilience capacity and its three dimensions to explore the factors contributing to a resilient supplier in the supplier selection problem.

Absorptive capacity is the extent to which a system (or a sup- plier in the context of this study) is able to absorb shocks from disruptive events, implying proactive planning for resilience or the development of pre-disaster strategies that can be considered as a first line of defense. Absorptive capacity can be viewed as being endogenous to the system (Vugrin et al., 2011). It is similar to the concept of inherent resilience described by Rose (2009) as the “ordinary ability to deal with crises.” Features of absorptive capa- city in the context of supplier selection are proposed here.

� Geographical segregation: Segregation or separation of a supplier geographically from natural disasters can reduce the likelihood of adverse impacts on the supplier if the disaster occurs. Al- luded to previously in the discussion of automakers after the Japanese earthquake and tsunami, Nissan and Toyota requested that their part suppliers establish facilities that are geo- graphically separated from disaster prone areas. Note that not only should the location of suppliers be segregated from natural disasters but also the location of suppliers in a multi-sourcing supply chain network (Vugrin et al., 2011).

� Surplus inventory: Although maintaining more on-hand in- ventory may increase holding costs, it can also enhance the ability of the supplier to absorb a disruptive event. Note that pre-positioned inventory levels are restricted by space avail- ability. Torabi et al. (2015) discussed that pre-positioning extra inventory can enhance the resilience of a supplier. Turnquist and Vugrin (2013) developed a stochastic model for design of resilience in infrastructure distribution networks, and they treat extra inventory as a feature of absorptive capacity in a distribu- tion center. Little (2005) suggests that New York City’s recovery following the terrorist attacks of September 11, 2001, would have been hampered had more organizations taken an inven- tory reduction (e.g., just-in-time) philosophy.

� Backup supplier contracting: A disrupted supplier may contract with a backup supplier to fulfill manufacturer orders. Such a contract is assumed to be in place prior to a disruption. Con- tracting with a backup supplier can be viewed as a form of re- dundancy, a common absorptive capacity enhancement philo- sophy in infrastructure systems (Vugrin et al., 2011).

� Physical protection: Physical protection and facility safety can

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reduce the initial impact of disruptive consequences. Physical protection refers to the security of supplier’s facility from dis- ruptive events that could cause serious losses or damage to a supplier’s facility. To protect from attacks, this could include security cameras, or for natural disasters, a form of physical protection is system hardening. Hosseini and Barker (2016) define physical protection strategies for inland waterway port infrastructure as a form of absorptive capacity.

Adaptive capacity is the extent to which a supplier can adapt itself after a disruption to minimize adverse consequences on the performance of system. Adaptive capacity is considered to be a second line of defense against disruption as a part of a temporary post-disaster strategy.

� Rerouting: Redundant transportation usually allows supplier to use nonstandard, but more expensive, rerouting options if the original transportation mode is disrupted. A recent example of rerouting through a different transportation mode occurred when a drought on the Mississippi River caused a considerable portion of the waterway to be unusable by barges (National Geographic News, 2013). Shipping companies were forced to lighten their load or switch to railway or highway modes suitable for long distance bulk transportation.

Restorative capacity is the extent to which a supplier is able to recover permanently from disruption. Restorative capacity differs from adaptive capacity in that restorative capacity is longer term in nature. Restorative capacity can be thought of the last line of defense against disruption. In cases where the impact of extreme event is significant, the supplier’s facility site may be disrupted partially or entirely. The supplier's facility site or equipment needs to be repaired to fully recover to its normal operating conditions in a permanent way. Hosseini and Barker (2016) highlighted the re- storation budget and technical resource restoration as the main factors of restorative capacity of long-term recovery for inland waterway port infrastructure.

� Restoration budget: Monetary capital is typically required for a supplier to restore its productivity. Therefore, restoration could be hampered by a lack of budget resources.

� Technical resource restoration: The capability of a supplier to restore its damaged equipment and facilities is dependent on the availability of equipment resources (e.g., repair vehicles) and human resources (e.g., repair crews).

Fig. 1. An example BN with five variables (nodes).

4. Background of Bayesian networks

Bayesian networks (BNs), structured based on Bayes' theorem for calculating conditional probabilities, is a powerful for handling risk assessment and decision making under uncertainty (Fenton and Neil, 2013). BNs have been widely used as a decision support tool in a diverse set of application domains such as risk analysis (Song et al., 2013, Khakzad, 2015), safety management (Hanninen et al., 2014, Wu et al. 2015), and reliability engineering (Chai et al. 2012, Liu et al. 2015), among others, including some initial work in modeling infrastructure resilience (Hosseini and Barker, 2016). BNs are a popular method of modeling uncertain and complex do- mains (Uusitalo, 2007) and are capable of integrating different sources of information such as observed data and expert judg- ment. As BN models focus on the relationship between informa- tion and uncertainty with action, the consequences of various management decisions can be modeled (Uusitalo, 2007). Unlike black-box models (e.g., neural networks), there are no hidden variables in the BN model. Further, BNs can handle both qualitative

and quantitative variables. More details about advantages of BNs can be found in Uusitalo (2007) and especially (Fenton and Neil, 2013) for risk applications.

BNs graphically describe networks of causes and effects using a set of variables (nodes) and a set of causal relationships (edges) that exist among the variables. The causal relationship between variables can be expressed in terms of conditional probabilities. BNs are capable of encoding qualitative (low/medium/high), Boo- lean (yes/no, true/false), or continuous variables. Data describing these variables can come from historical data, expert knowledge, or a combination of the two.

From a mathematical standpoint, BNs are acyclic graphs with a set of variables (nodes), represented by { }= …V X X X, , , n1 2 , and a set of edges whose structure determines interdependencies among variables. An outgoing edge from Xi to Xj indicates a relationship that value of variable Xj is dependent of the value of Xi. Further, if there is an 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. 1, nodes X1 and X2 are root nodes, X3 and X4 are intermediate nodes, and X5 is a leaf node.

The causal relationship among variables of a BN can be mea- sured through conditional probability distributions. The full joint probability distributions of the BN given in Fig. 1 can be expressed in Eq. (1), which can be thought of as a representation of the to- pology of the BN and dependencies among variables. In the ex- ample above, two priori probabilities, ( )P X1 and ( )P X2 , and three conditional probabilities, ( )|P X X3 1 , ( )|P X X X,4 2 3 , and ( )|P X X5 4 , must be defined. Each variable (node) is associated with a node probability table, or NPT, which lists the probability of the occur- rence of a realization of a variable given the values of other vari- ables. NPTs contain probability information that underpins the structural relationship in a model.

( ) ( ) ( )( ) ( ) ( ) ( )= 1P X X X X X P X P X P X X P X X X P X X, , , , ,1 2 3 4 5 1 2 3 1 4 2 3 5 4 The joint probability distribution can be used for calculating

the probability of an individual variable in a BN. Suppose that we are interested in calculating X3, then ( )P X3 can be written with Eq. (2) using marginalization.

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 73

( )( ) ( ) ( ) ( ) ( )∑= | | ( )

P X P X P X P X X P X X X P X X, 2X X X X

3 , , ,

1 2 3 1 4 2 3 5 4

1 2 4 5

Marginalization is a distributive operation over combinations of local joint probabilities, meaning that we can marginalize the global joint probability by marginalizing local NPTs (Fenton and Neil, 2013). In the example given in Fig. 1, the marginalization of

( )P X3 consists of factors in Eq. (3). More details about the technical aspects of marginalization, among other topics related to Bayesian networks, can be found in Fenton and Neil (2013).

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Note that Eqs. (1)–(3) hold true when all the variables in the BN are binary (e.g., True/False). In fact, the theory of BN discussed above can be expressed in terms of binary variables, but in many real case studies such as the one studied in this paper, different type of variables, including continuous and fixed variables, must be taken into account.

5. Proposed BN for supplier evaluation and selection

BNs provide flexibility to construct a causal structure based on expert judgment, an important trait when evaluating the perfor- mance of suppliers as a function of some available data but also expert knowledge about supplier behavior and the conditional dependencies among variables related to supplier performance. The proposed BN in this study is used for evaluating the perfor- mance of candidate suppliers in terms of primary, green, and re- silience criteria to eventually guide the selection of the best supplier.

The primary steps of model development include: (i) identifying model variables that contribute to the supplier se- lection problem, and then (ii) building the causal model structure based on conditional dependencies among those variables. The proposed general framework for supplier selection is illustrated in Fig. 2. As shown, the target variable is Supplier evaluation, which is conditioned on primary, green, and resilience criteria variables (derived from Sections 2 and 3), as well as a Weighting factor that captures the importance of each criterion.

Fig. 2. General BN framework for eval

The supplier selection model, the complete BN for which is depicted in Fig. 8, was built using the AgenaRisk BN tool (AgenaRisk, 2005). AgenaRisk supports standard discrete, labeled, and continuous state variables approximated using dynamic dis- cretization (Fenton et al. 2010). There are four types of variables used in the proposed BN model:

1. Boolean variables (BVs) have a binary response whose two states of True and False are used to represent positive and ne- gative outcomes, respectively.

2. Continuous variables (CVs) capture uncertainty associated with a variable that can take on continuous realizations via a prob- ability distribution.

3. Fixed variables (FVs) represent a variable whose value is constant.

4. Labeled variables (LVs) can have a number of discrete states.

These variables are explained subsequently in the context of a particular supplier, referred to as Supplier 1. The parameters of the variables will change from supplier to supplier for the ultimate purpose of assessing and comparing each supplier.

5.1. Modeling primary criteria

The primary criterion, defined by a Boolean variable for which a probability measures whether criterion is met (True) or not (False), is measured as a collection of Delivery robustness, Quality of pro- ducts, Service, and Total costs variables. The relationships among these variables and depicted in Fig. 5.

5.1.1. Delivery robustness The ability of the supplier to meet the predefined delivery

schedule is an often-used criterion for supplier selection (Mwikali and Kavale, 2012). The supplier must be able to respond to the customer order with short lead time. Lead time is defined with a truncated normal distribution (TNORM) as shown in Eq. (4) and depicted in Fig. 3. Assume Supplier 1 has an expected lead time for delivery of raw materials of 16 days with a variance of 1.5 day. The shortest and longest lead time are 1 day, denoted by LB (lower bound) and 21 days, denoted by UB (upper bound), respectively. These data can be obtained through empirical observation over a specified time period. The Delivery robustness variable is

uating the selection of a supplier.

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8774

conditioned on response rate and lead time as represented in Fig. 3

σ~ (μ= = = = ) ( )Lead time TNORM 16, 1.5, LB 1, UB 21 42

Note that TNORM is an extension of the normal distribution in which occurrences are bounded to values that lie within a speci- fied range (Burkardt, 2014). TNORM is an appropriate distribution to use when the data are normally distributed on a finite range. TNORM can be presented by four parameters: mean, average, lower bound, and upper bound respectively.

The response rate, or the ratio of satisfied ordered items of product to ordered items of product (Rezaei and Davoodi, 2011), is also modeled with a truncated normal distribution shown in Eq. (5).

For Supplier 1, the mean response is 94%.

~ (μ= σ = = = ) ( )Response rate TNORM 0.94, 0.01, LB 0.87, UB 1 52

A Boolean expression is used to calculate the probability of successful Delivery robustness, as represented in Table 2. The Boolean expression defines the probability of Delivery robustness being True when the lead time is less than 17 days and response rate is at least 90%. Note that the probability of Delivery robustness being true reduces if the lead time threshold is shorter and the response rate threshold approaches 1. A schematic representation for modeling of delivery robustness variable is illustrated in Fig. 4.

Note that the prior probability of response rate and lead time can be obtained by fitting appropriate distribution to the historical data, or in the cases which a little data are available, expert jud- gements can be incorporated (Constantinou et al., 2016).

5.1.2. Quality of products The quality of delivered raw materials or products has been an

important factor in the selection of suppliers in many studies (Fazlollahtabar et al., 2011; Chai and Ngai, 2015; Chan and Chan, 2010). The likelihood that items from a supplier are of sufficient quality, as measured by True or False states, is conditioned on the probability of the product being faulty during inspection by the manufacturer. The NPTs of these two variables are described in Table 3 for the illustrative Supplier 1.

Fig. 3. Lead time node for Supplier 1.

Table 2 Boolean expression used to calculate the NPT of delivery robustness.

Variable name NPT Meaning

Delivery robustness

IF (Lead time o17 and response rate 40.9, “True”, “False”)

If lead time is less than 17 days and response rate is greater than 90%, then delivery and response is being met (True), otherwise not being met (False)

5.1.3. Service A supplier's service level is defined as all those activities pro-

vided by the supplier to enhance or augment the product and have value for the buyer, thus increasing customer satisfaction and better relationship between supplier and manufacturer (Do- naldson, 1994) and is a commonly used criterion in supplier se- lection (Mwikali and Kavale, 2012). Fazlollahtabar et al. (2011) considered after-sales service and technical support as attributes of service level for the selection of best supplier, and these char- acteristics are also used in this study. The NPTs for the Service variable and its prior nodes (technical service and after-sale ser- vice) are represented in Tables 4–6 for Supplier 1.

5.1.4. Total costs Supplier costs are perhaps the most common criterion in the

supplier selection problem (Ho et al., 2010; Lee et al., 2009; Fa- zlollahtabar et al., 2011). The total costs of a supplier are re- presented here as the sum of order cost, total transportation cost, purchase cost, and tardiness penalty cost. The NPT for total cost variable is represented in Table 7. The NPT suggests that the Boolean variable for cost is acceptable below some budget value, which is $127,000 for this illustrative example.

From Fig. 5, the probability of total costs of the first supplier being True (satisfactory) is about 56% while the probability of about 44% is False (unsatisfactory). The components of total cost of the supplier are: (i) Order cost, a constant in Fig. 5, set at $45 for Supplier 1 in this example, (ii) Purchase cost, the multiplication of the purchase cost per item and the number of purchased items, where the purchased cost per item is a constant set to $125 in this example and the number of items purchased from the supplier is dependent on customer demand and capacity of supplier whose NPTs are shown in Table 8, (iii) Tardiness penalty cost, a penalty for delayed delivery that is assigned if the actual order completion time is beyond its expected due time as calculated in the NPT is found in Table 9, and (iv) Total transportation cost, calculated as the sum of fixed and variable transportation costs.

5.1.5. Primary criteria variable The posterior probability of the primary criteria variable being

either True or False depends on the probability of its prior vari- ables: delivery robustness, quality of products, service, and total cost. One way to model the NPT for the primary criteria node is similar to that of the service variable, represented in Table 6. However, the NPT for the service variable requires only eight en- tries since it is conditioned on only two variables, but as the pri- mary criteria variable has five Boolean variables (and thus =2 325

entries), its calculation can be tedious and error prone. Moreover, many of those 32 entries may be unnecessary as the effects of the parent nodes on the child node may be essentially independent.

An alternative, perhaps more effective approach, is called the NoisyOR function. NoisyOR has been well established as a standard means of encoding expertise in large NPTs (Huang and Henrion, 1996). Suppose there are n causal factors, …X X, , n1 of a condition, Y, with a probability value for Y being true when one and only one Xi is true, and all causes other than Xi are false. The NoisyOR function is defined in Eq. (6), where for each i,

= ( = | = = ≠ )v P Y X X j itrue true, false, for eachi i j is the probability of the conditional being true if and only if that causal factor is true (Fenton and Neil, 2013).

( … ) ( )X v X v X v lNoisyOR , , , , , , , 6n n1 1 2 2

Term l is referred to as the leak probability representing the probability that Y will be true when all of its causal factors are false, as shown in Eq. (7).

( )= = | = = … = ( )l P Y X X Xtrue false, false, , false 7n1 2

Fig. 4. The modeling procedure for the variable describing delivery robustness.

Table 3 NPTs of the variables describing the quality of products and probability of the product being faulty.

Variable names NPT Meaning

Probability of product being faulty

(α= β= = = )Beta 0.8, 30, UB 0, LB 1 The probability of a product being shipped by the supplier to the manufacturer follows a beta distribution.

Quality of products IF (prob. of product being faulty o7%, “True”, “False”) If the probability of a product being faulty is less than 7%, then the quality of the product is acceptable (True state), otherwise not (False state)

Table 4 NPT of the variable describing after-sale service.

False 0.1 True 0.9

Table 5 NPT of the variable describing technical service.

False 0.15 True 0.85

Table 6 NPT of the variable describing service.

After sale service False True

Technical service False True False True

False 1.0 0.4 0.45 0.0 True 0.0 0.6 0.55 1.0

Table 7 NPT of the variable describing total cost.

Variable name NPT Meanin

Total cost IF (order costþtotal transportation costþpurchase cost þ tardiness penalty cost o127,000, “True”, “False”)

If the su then the (unsatis

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 75

In general, the conditional probability of Y obtained with Noisy OR function can be represented with Eq. (8).

⎡⎣ ⎤⎦)( ) ( ( )∏ ( )

= | … = − ( − ( = | = ) − = 8

P Y X X X P Y X P ltrue , , , 1 1 true true 1n i

n

i1 2 1

The NoisyOR function is used here to calculate the conditional probability of the primary criteria as defined in Eq. (9), which suggests that the likelihood of Supplier 1 successfully achieving the primary criteria is 0.15 if only the desired service level of the supplier is met, while this probability changes to 0.30, 0.40, and 0.25 when total cost, quality of products, and delivery robustness, are individually met, respectively. Finally, the values associated with the leak will be 0.05. In general a leak probability is a non- zero probability for the effect to be triggered even if all the causes are false (Antonucci, 2011), generally used to reflect when another factor not considered causes the trigger. In this case, there is a 5% likelihood of the primary criteria being met while delivery ro- bustness, quality, service, and total costs are all false. There might be other factors that contribute to the primary criteria (e.g., ease of communication with supplier, supplier's profile, performance history of supplier) that are not included among the four defined primary criteria. Note that when more primary criteria factors are considered, the leak probability reduces. These parameters could realistically be obtained through decision maker experience, per- haps combined with historical data.

g

m of supplier costs is less than the budget limitation of the buyer (manufacturer), cost of the supplier is in a True state (satisfactory), otherwise is in a False state

factory).

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8776

(

) ( )

NoisyOR total cost, 0.3, quality of products, 0.4, service,

0.15, delivery robustness, 0.25, 0.05 9

Fig. 5. Graphical depiction of the B

Table 8 NPTs of the variables describing customer demand, capacity of supplier, and purchased

Variable names NPT Meaning

Customer demand (μ= σ = = = )TNORM 1000, 20, LB 980, UB 10202 The customer dem 20, and lower m

Capacity of supplier Constant value (1000) The capacity of S Purchased items Min (customer demand, capacity of supplier) The number of p

demand and sup

Table 9 NPTs of the variable describing tardiness penalty cost and its parents.

Variable names NPT Meaning

Tardiness penalty cost ×Tardy penalty Tardiness Tardiness penalty cost Tardiness Max (0, completion time – due date) Tardiness occurs when Completion time (μ= σ = = = )TNORM 18, 1.5, LB 15, UB 242 The average order com

earliest completion tim Due date Constant value (20) The order due date is t

5.2. Modeling green criteria

The use of green supplier selection criteria has grown in the recent literature (e.g., Hashemi et al., 2015; Dobos and Vorosmarty,

N model for primary criteria.

items.

and follows a truncated normal distribution with an average of 1000, variance of inimum and maximum of 980 and 1020 respectively. upplier 1 is 1000. urchased items is determined by taking the minimum values between customer plier’s capacity.

is calculated as product of tardy penalty by tardiness. the order competition time is greater than order due date.

pletion time on average is the 18th day of the month with variance of 1.5 days. The e is not earlier than the 15th, and the latest not beyond the 24th. he 20th day of the month.

Table 10 NPTs of the green criteria variables.

Variable names NPT Meaning

CO2 emission (g/km) Triangular distribution (25, 120, 150)

Amount of emitted CO2 depends on many factors such as mode of transportation. The first supplier uses roadways for the shipping of products. The CO2 emitted by truck may varies depending on the age of truck, slope of roads, among others. It is assumed that the emitted CO2 by truck follows a triangular distribution (Kahn Ribeiro et al., 2007) with minimum, most likely, and maximum estimates of 25, 120, and 150 g/km, respectively.

Distance between supplier and customer (manufacturer)

Constant (1450) The distance between the supplier's location and manufacturer’s location is a constant 1450 kilometers.

Total emitted CO2 Distance × CO2 emission Total emitted CO2 is calculated as the product of distance between supplier and manu- facturer and the amount of CO2 (gram) per kilometer.

Green criteria If (total emitted CO2 o170,000, “True”, “False”)

If the total emitted CO2 is less than some carbon capacity limitation (170,000), then green criteria is met (True state), otherwise not (False state).

Fig. 6. Graphical depiction of the BN model for green criteria.

Fig. 7. Graphical depiction of the BN model for resilience criteria.

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 77

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S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8778

2014; Scott et al., 2015; Lee et al., 2009; Akman, 2015). As en- vironmental awareness increases, manufacturers today are more interested in purchasing goods and services from suppliers with environmental responsibility (Lee et al., 2009). Different green factors including product life cycle, green image, CO2 emission and environment management, reusability among others have been used to evaluate green suppliers. Among aforementioned factors, CO2 emission is among the more common factors (Lee et al., 2009; Dobos and Vorosmarty, 2014). In this study, the green performance of supplier is assessed based on the amount of CO2 emitted by that supplier. The NPTs of green criteria are found in Table 10, and a depiction of the portion of the BN is represented in Fig. 6. The total amount of CO2 emitted by the supplier depends on the distance between customer and supplier (km), as well as CO2 emission (g/ km). Note that the level of CO2 emission depends on the type of transportation mode used for the shipment of commodities.

Note that in this paper, the focus of the green criteria is given to CO2 emission only, as it contributes to over 95% of greenhouse gas emissions (Marufuzzaman et al., 2014). Carbon capacity is one of the carbon regulatory mechanisms that limit carbon emissions produced by transportation activities in the supply chain, and the aim of the carbon capacity constraint is to diminish carbon emission produced by supplier companies.

5.3. Modeling resilience criteria

Discussed previously, the idea of resilience in the supplier se- lection problem is relatively new and becoming more important due to the vulnerabilities of an increasingly global supply chain. The contributors to the supplier resilience, identified in Section 3, are modeled using the Bayesian network illustrated in Fig. 7. The NPTs of the resilience criteria and its contributors are listed in Table 11.

5.4. Modeling the supplier evaluation variable

The ultimate target node is the Supplier evaluation variable provides a probability statement about whether the supplier should be selected, conditioned on the primary, green, and resi- lience criteria nodes, as well as the weighting factor. The weight- ing factor is a labeled variable with three states that captures weights of three criteria. Initially, it is assumed that the weight of each factor is equally distributed, 33.33%. As illustrated in Fig. 8, the probability of selecting Supplier 1 (the Supplier evaluation variable being True) is 66.8%, with the probability that Supplier 1 not being selected of 33.2% (the False state).

BN models were similarly developed for Suppliers 2 and 3, whose BNs were developed similarly to that of Supplier 1. The resulting probability of selection of Suppliers 2 and 3 are 59.6% and 53.5%. The BN model for only Supplier 2 is illustrated in the Appendix and BN model for supplier 3 is eliminated due to space limitation.

Ta b le

11 N P Ts

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ce cr it er ia

an d it s co

n tr ib u to rs .

V ar ia b le

n am

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T N O R M

(0 .0 2 , 0

Se g re g at io n

If (p ro . o f to rn

ad

Su rp lu s in ve

n to ry

Tr u e ¼ 9 0 % , Fa ls

B ac k u p su

p p li er

av ai la b il it y

T N O R M

(0 .9 6 , 0

B ac k u p su

p p li er

If (b ac k u p su

p p

P h ys ic al

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R er o u ti n g

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A d ap

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Fa ls e

Tr u e

Te ch

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Tr u e ¼ 8 0 % , Fa ls e

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Tr u e ¼ 7 5 % , Fa ls e

R es il ie n ce

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N o is y O R (a b so rp

0 .1 )

6. Results and analysis

The results of the illustrative example built around Supplier 1, as discussed in the previous sections, are provided here.

6.1. Sensitivity analysis

A useful method to investigate the validity of an expert-built model is to perform sensitivity analysis to get a sense of how the model’s output is affected by uncertainty in input parameters. Resilience criteria is set as the target node, and the impacts of its causal factors are measured in terms of conditional probability. The sensitivity analysis

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 79

of resilience factors is represented in Figs. 9 and 10, which represent the probability of resilience of Supplier 1 being “True” and “False” re- spectively given a set of its contributors respectively.

From a purely visual inspection, the length of the bars in the tor- nado graphs can be thought of as the measure of the impact of that variable on the resilience criteria. Fig. 9 illustrates the impacts of six Boolean variables including Technical resources, Budget resources, Seg- regation, Backup supplier, Surplus inventory, and Physical protection when the resilience criteria is True. Fig.10 shows the impacts of the six variables when the resilience criteria is False. It is clear that technical

Fig. 8. The BN model to

Fig. 9. Tornado graph to analyze the sensitivity of Supplie

resources and physical protection have the greatest and lowest impact on the resilience of supplier, respectively. The formal interpretation is that the probability of resilience of Supplier 1 being "true" given the results of technical resources goes from 69.6% (when technical re- source is Fail) to 87.6% (when technical resource is True), as shown in Fig. 9. The impact of physical protection on the resilience of Supplier 1 is limited to narrow range, from 83.1% to 84.2%. This suggests en- hancing the availability of technical resources is more impactful than any other factor in improving the resilience of Supplier 1.

A sensitivity analysis was also performed for the Supplier evaluation

evaluate Supplier 1.

r 1’s resilience: P (Resilience criteria ¼ True) ¼ 84%.

Fig. 10. Tornado graph to analyze the sensitivity of Supplier 1’s resilience: P (Resilience criteria ¼ False) ¼ 16%.

Fig. 11. Tornado graph to analyze the sensitivity of Supplier 1’s evaluation across primary, green, and resilience criteria: P (supplier evaluation ¼ True) ¼ 66.8%.

Fig. 12. Tornado graph to analyze the sensitivity of Supplier 1's evaluation across primary, green, and resilience criteria: P (supplier evaluation ¼ False) ¼ 33.2%.

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8780

Fig. 13. The impact of the weights of the three criteria when all are equally distributed.

Fig. 14. The impact of the weights of the three criteria when resilience is weighted twice as much as primary and green criteria.

Table 12 Forward propagation scenarios.

Surplus inventory Rerouting Quality Technical resources

Scenario 1 None False None False Scenario 2 False None False None Scenario 3 None None False False Scenario 4 False False False False

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 81

node with respect to some key factors including Restorative capacity, Quality of products, Total cost, Delivery robustness, Absorptive capacity, Service, and Adaptive capacity. The probability of supplier selection being True and False is 66.8% and 33.2%, respectively, as illustrated in the tornado graphs in Figs. 11 and 12. From these figures, it can be concluded that the probability selecting Supplier 1 is more sensitive to the changes in the states of restorative capacity and least sensitive to changes in adaptive capacity.

6.2. Weighting factor analysis

Discussed previously, the weights of each of the three supplier selection criteria (primary, green, and resilience) are assumed to be equally distributed of 33% in the baseline BN. Fig. 13 shows that P(selection of the Supplier 1 | resilience, green, primary, weight of each criteria ¼ 33%) ¼ 66.8%, while this probability for Suppliers 2 and 3 are 59.6% and 53.5%, respectively. Hence, the first supplier is selected as the most appropriate when primary, green, and re- silience criteria are aggregated and considered to be equally

important. In the second scenario illustrated in Fig. 14, emphasis is placed on the supplier’s resilience, which receives a 50% weight relative to primary and green criteria, both equally set to 25%. The results of this scenario shows that the probability of selection of Supplier 1 increases from 66.8% to 71.1% and still remains as the highest ranked supplier, while the probability of selection for Suppliers 2 and 3 increase from 59.6% to 64.7% and 53.5% to 59.4%, respectively.

6.3. Inference process analysis

The inference process in Bayesian networks generally requires obtaining the posterior probabilities for a set of variables ⊂X vI given evidence e. This probability is shown in Eq. (10). This is ty- pically referred to as propagation analysis. Forward propagation analysis aims to propagate the impact of observing one or set of variables and measure its impact on the target node. Such “what- if” analyses can be performed in a backward fashion, where a value can be entered in a target node, and information is propagated to update the distributions of all remaining unknown variables. Note that forward propagation is a type of reasoning from cause to ef- fect, while backward propagation describes effect-to-cause.

( )| ∀ ∈ ( )P X e X X 10i i I

6.3.1. Forward propagation analysis A number of observations can be entered in the BN, and for-

ward propagation can be used to update the marginal probabilities of any unobserved variables, primarily a target node. If, for ex- ample, sufficient evidence suggests that surplus inventory is un- available (in its False state), forward propagation can be used to determine the impact on the supplier’s resilience and ultimately its overall evaluation.

To perform a forward propagation analysis, four factors including Surplus inventory, Rerouting, Quality, and Technical resources were cho- sen, and four scenarios were defined for the supplier with the highest overall evaluation (Supplier 1). Scenario 1 contains False states for Re- routing and Technical resources, Scenario 2 contains False states for Surplus inventory and Quality, Scenario 3 contains False states for Quality and Technical resources, and Scenario 4 includes False states in all four variables, as shown in Table 12. The change in the probability selecting Supplier 1 for each of the scenarios, including the baseline, is desired. For example, in the probability of interest in Scenario 1 is P (selection of supplier 1 | Rerouting ¼ False, Technical resources ¼ False).

The junction tree algorithm (Jensen, 1996) is used for the pur- pose of propagation analysis, where the joint probability for the model from the BN's conditional probability structure is calculated in a computationally efficient manner. As illustrated in Fig. 15, the probability of selecting Supplier 1 under scenarios 1, 2, 3, and 4 is reduced to 62.1%, 61.3%, 56.9%, and 56.4% respectively, relative to the baseline of 66.8%. Different suppliers could also be compared under these four scenarios.

Fig. 15. Four scenarios of forward propagation analysis.

Fig. 16. Backward propagation analysis.

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8782

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–87 83

6.3.2. Backward propagation analysis Backward propagation analysis is a unique capability of Baye-

sian networks, increasing the scope of what-if scenarios especially giving insight to less competitive suppliers on how the compo- nents of their performance criteria (primary, green, resilience) can be improved to reach an overall evaluation level.

To demonstrate backward propagation analysis, the overall supplier evaluation for Supplier 1 was increased from 66.8% to 100% (that is, the probability of Supplier evaluation equating to True being 100%), and the distributions of the remaining variables were updated using the junction tree algorithm (Jensen 1996). As a result, the probability of primary, green, and resilience criteria must be improved to 68.09%, 72.32%, and 90.72% respectively as highlighted in green in Fig. 16.

7. Concluding remarks

This work proposes a novel Bayesian network model for evaluating and selecting the best supplier across criteria falling into primary (or traditional), green, and resilience categories. The concept of resilience in the supplier evaluation and selection process has become more im- portant due to the emergence of global supply chains and the (see- mingly more frequent) events that can disrupt them. The BN model quantifies resilience in terms of absorptive, adaptive, and restorative capacities. This initial implementation was illustrated with a simple example of the comparison of three suppliers with realistic para- meters, and the sensitivity analysis capabilities of the BN paradigm were explored. The capability of BN approach was compared with other existing supplier selection approaches, as shown in Table 13. Highlighted in Table 13 are different criteria selected in all approaches, as well as their ability to handle (i) both qualitative and quantitative variables, and (ii) sources of risk. Further shown in Table 13 is the ability of the different approaches to analyze different disruptive sce- narios (referred to as “disruption analysis”) and to target areas for improvement to increase a supplier’s evaluation (referred to as “im- provement analysis”). Only the BN paradigm allows for both disruption and improvement analysis through propagation analysis.

Our findings indicate that incorporating and modeling the prob- ability of a disruption is a key issue in resilient supplier selection. Sawik (2010) and Sawik (2013) considered the likelihood of local and global disruptions that may cause the “failure” of a supplier. We also modeled the likelihood of disruptions in the Bayesian network re- presentation. Noted previously, an important advantage of BNs is their ability to handle expert knowledge or judgment, especially important when such disruptions occur infrequently or have never occurred.

7.1. Benefits of the BN formulation

The major methodological benefits of the BN model proposed here include the following.

1. Flexibility of variable types: In contrast to mathematical model- ing approaches such as a mixed integer programming based approach, the proposed BN captures both tangible and in- tangible factors that contribute to the selection of a resilient supplier. Different types of variables including Boolean,

continuous, constant, and labeled extend the flexibility of this modeling approach. Further, different sources of data ranging from historical observations to expert evidence can be in- corporated in the BN framework.

2. Inference analysis: Different what-if scenarios can be analyzed, providing insights to the decision maker as to how the prob- ability of the selection of a supplier varies under different sce- narios. By performing inference analysis, a decision maker can evaluate the performance of a supplier, or compare multiple suppliers, under extreme conditions. Inference analysis can be performed on both subjective beliefs and objective data. Baye- sian networks are capable of performing both cause-to-effect analysis, or forward propagation analysis, and effect-to-cause analysis, or backward propagation analysis. Such backward pro- pagation analysis is not proposed by other approaches.

3. Accounting for uncertainty: The uncertainty associated with the modeling of system variables can be captured using BNs models. In this paper, two types of uncertainty have been captured: operational uncertainty (e.g., demand uncertainty) and disrup- tion uncertainty (e.g., natural disasters).

7.2. Limitations of the BN formulation

The methodological limitations can be summarized as follows.

1. Necessary use of subjectivity: Relying on expert judgment in cases where data are sparse or not available implies inevitable subjectivity and possible bias (Constantinou et al., 2015). This can be partially addressed by using multiple experts.

2. Complexity: Developing causal expert-driven Bayesian networks requires significant development, as they are usually complex due to a large number of variables that capture causality. Although Bayesian networks are conceptually easier than regression and rule- based predictors, they are generally not very simple to build (Fenton and Neil, 2013).

7.3. Future work

The future research directions of this study are as follows.

1. Further green criteria beyond CO2 emission could be accounted for, including environmentally friendly product design, packing, and warehousing, among others.

2. More detail could be given to the important decision of how suppliers choose transportation modes. Qualitative and quan- titative factors involved in the selection of the best transporta- tion mode include total cost of transportation (fixed cost þ variable cost), reliability of transportation mode, transport time, and air emission, among others.

3. Bayesian networks can be used to study the resilience of various infrastructure sectors, from physical infrastructure networks (e.g., energy, telecommunications) to service networks (e.g., emergency services, humanitarian relief). The interaction among physical and service networks, as well as community networks that require the services of both, is a growing concern in the face of more frequent large-scale disruptions (Barker et al., 2016).

Appendix

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8784

See Fig. 17 and Table 13

a b c d e f g h i j k l m n o p q

cost r green image

quality s pollution control

service t resource consumption

delivery u green capability

innovation v green design

finance w recovery and strategy fit

organization x safety

technology capability y vulnerability

environmental management z collaboration

warranty ra risk awareness

managing ability scc supply chain continuity

enterprise environment

fl flexibility

lead time rd R&D

risk factor in inventory

relationship bs Backup supplier

capacity

product life cycle cost

Fig. 17. BN model for S

upplier 2.

Table 13 Comparisons among supplier selection studies.

Reference Criteria Type of variable Type of uncertainty Type of scenario Methodology

Primary Green Resilience Qualitative Quantitative Operational risk Disruption risk Disruption scenario Improvement scenario

Lee et al. (2009) ✓ ✓ ✓ ✓ Fuzzy approach Wang et al. (2009) ✓ ✓ ✓ Fuzzy hierarchical TOPSIS Sevkli (2010) ✓ ✓ Fuzzy ELECTRE Sawik (2010) ✓ ✓ Multiobjective programming Chan and Chan (2010) ✓ ✓ ✓ ✓ AHP Kumar and Jain (2010) ✓ ✓ ✓ ✓ Data envelopment analysis Fazlollahtabar et al. (2011) ✓ ✓ ✓ Goal programming and TOPSIS Yucenur et al. (2011) ✓ ✓ ✓ Fuzzy AHP and fuzzy ANP Zhang and Zhang (2011) ✓ ✓ ✓ Mixed integer programming Liu and Zhang (2011) ✓ ✓ ELECTRE-III and entropy weight Toloo and Nalchigar (2011) ✓ ✓ Data envelopment analysis Rezaei and Davoodi (2011) ✓ ✓ Multiobjective programming Sawik (2013) ✓ ✓ ✓ ✓ ✓ ✓ Mixed integer programming Karimi and Rezaeinia (2014) ✓ ✓ Goal programming Jadidi et al. (2014) ✓ ✓ Goal programming Dobos and Vorosmarty (2014) ✓ ✓ ✓ ✓ Data envelopment analysis Haldar et al. (2014) ✓ ✓ ✓ ✓ Fuzzy TOPSIS Tsui and Wen (2014) ✓ ✓ ✓ Hybrid group decision making Akman (2015) ✓ ✓ ✓ Fuzzy c-means and VIKOR Chai and Ngai (2015) ✓ ✓ ✓ Hesitant Fuzzy Hague et al. (2015) ✓ ✓ TOPSIS Hashemi et al. (2015) ✓ ✓ ✓ ✓ ANP and GRA Kotula et al. (2015) ✓ ✓ ✓ Empirical analysis Mahdiloo et al. (2015) ✓ ✓ ✓ Data envelopment analysis Memon et al. (2015) ✓ ✓ ✓ ✓ ✓ ✓ Grey approach and uncertainty theory Pitchipoo et al. (2015) ✓ ✓ Grey approach Scott et al. (2015) ✓ ✓ ✓ ✓ Chance constrained, AHP, and QFD Rajesh and Ravi (2015) ✓ ✓ ✓ ✓ ✓ ✓ Grey approach Torabi et al. (2015) ✓ ✓ ✓ ✓ ✓ ✓ Two-stage stochastic programming Mohammaditabar et al. (2016) ✓ ✓ Game theory Saghiri and Barnes (2016) ✓ ✓ ✓ Empirical analysis Sawik (2016) ✓ ✓ ✓ ✓ Risk-averse optimization This paper ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Bayesian network

S. H o ssein

i, K . B a rker

/ In t. J. P ro d u ctio

n E co n o m ics

18 0 (2 016

) 6 8 – 8 7

8 5

S. Hosseini, K. Barker / Int. J. Production Economics 180 (2016) 68–8786

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