An Examination of the Impact of Flexibility and Agility on Mitigating Supply Chain Disruptions

Accepted Manuscript An Examination of the Impact of Flexibility and Agility on Mitigating Supply Chain Disruptions

Mansoor Shekarian, Seyed Vahid Reza Nooraie, Mahour Mellat Parast PII:

S0925-5273(19)30248-8

DOI:

10.1016/j.ijpe.2019.07.011

Reference:

PROECO 7438

To appear in:

International Journal of Production Economics

Received Date:

13 August 2018

Accepted Date:

12 July 2019

Please cite this article as: Mansoor Shekarian, Seyed Vahid Reza Nooraie, Mahour Mellat Parast, An Examination of the Impact of Flexibility and Agility on Mitigating Supply Chain Disruptions, International Journal of Production Economics (2019), doi: 10.1016/j.ijpe.2019.07.011

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An Examination of the Impact of Flexibility and Agility on Mitigating Supply Chain Disruptions

Mansoor Shekarian North Carolina A&T State University 1601 E Market Street Greensboro, NC 27411 E-mail: [email protected] Seyed Vahid Reza Nooraie North Carolina A&T State University 1601 E Market Street Greensboro, NC 27411 E-mail: [email protected] Mahour Mellat Parast Eminent Scholar Arizona State University 660 S. College Avenue Tempe, Arizona 85281 E-mail: [email protected]

* Corresponding author

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An Examination of the Impact of Flexibility and Agility on Mitigating Supply Chain Disruptions Abstract This paper examines the effect of flexibility and agility on improving supply chain responsiveness. We examine a supply chain with multiple sites, multiple transportation channels, and multiple product planning, over multiple periods, under supply risk and demand risk. Using a numerical example, we determine the relationship between three objective functions related to responsiveness, risk, and the cost of new and seasonal products, then discuss the impact of flexibility and agility on mitigating supply chain disruptions. To show a trade-off among objective functions in our numerical example, we solve the multi-objective mixed integer programming (MOMIP) model using three multi-objective optimization methods: the weighted goal programming (WGP) method, the augmented ε-constraint (AUGMECON) method, and the non-dominated sorting genetic algorithm (NSGA-Ⅱ). Our findings help decision makers with these two tasks: anticipate how much improvement in flexibility and agility will lead to an improvement in responsiveness; and create an investment plan to minimize the negative impact of supply chain disruptions by an examination of the trade-offs among responsiveness, risk, and cost. The results show that the NSGAⅡ method outperforms the AUGMECON method in several metric indexes: the spacing metric, the diversity metric, and simple additive weighting. Keywords: Supply chain management, disruption risk, multi-objective mixed integer programming (MOMIP), weighted goal programming (WGP) method, augmented ε-constraint (AUGMECON) method, non-dominated sorting genetic algorithm (NSGA-Ⅱ). 1. Introduction Rapid advances in technology and changes in customer expectations are creating an uncertain environment for firms. In the literature, a well-established strategy to mitigate supply chain disruptions is “don’t put all your eggs in one basket" (Habermann et al., 2015). For example, with a wide geographic distribution of supply chain partners, a single disruptive event will not affect all the entities at the same time or with the same magnitude (Hu and Kostamis, 2015; Kamalahmadi and Parast, 2016a). Firms relying on their supply

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chain to remain competitive in a rapidly changing environment must be more agile in perceiving and developing opportunities, more responsive to disruptions, and more resilient against external threats (Battistella et al., 2017; Yang, 2014). The management of disruption risk in a supply chain has received increasing attention in the last few years (Parast and Shekarian, 2019; Parast et al., 2019; Ho et al, 2015; Gilgor et al., 2015; Purvis et al., 2014; Čiarnienė and Vienažindienė, 2014). This increasing attention is due to widespread recognition that all supply chains are susceptible to a variety of disruptions that can have both immediate and long-term effects on the supply chain (Habermann et al., 2015). Supplier capacity constraints that are caused by supply process breakdowns and supply disruptions show the importance of supply chain risk management (Stank et al., 2011; Manuj and Mentzer, 2008; Christopher and Lee, 2004). Developing contingency plans that select appropriate suppliers with the optimal demand allocation using the best transportation channel is a crucial component of an effective supply chain system in a turbulent and dynamic environment (Kauppi et al., 2016; Kamalahmadi and Parast, 2015; Neiger et al., 2009; Oke and Gopalakrishnan, 2009; Trikman and McCormack, 2009). The cultivation of flexibility, agility, and responsiveness has been mentioned frequently as a key component in managing the risk of disruption (Parast and Shekarian, 2019; Ciccullo et al., 2018; Dubey et al., 2018; Nooraie, 2017; Jimenez et al., 2015; Singh, 2015; Gligor et al., 2015; Purvis et al., 2014; Čiarnienė and Vienažindienė, 2014; Babazadeh and Razmi, 2012; Chiang et al., 2012; Braunscheidel and Suresh, 2009; Bernardes and Hanna, 2008). Chopra and Sodhi (2004) named flexibility and responsiveness as two effective strategies to mitigate supply chain disruptions. Faisal et al. (2006) listed information sharing, supply chain agility, trust, and collaborative relationships as the enablers for supply chain disruption mitigation. Singh (2015) asserted that in order to have a responsive supply chain, top management should be proactive in considering and taking different initiatives to improve resource utilization and strategy implementation. Gunessee et al. (2018) asserted that when facing catastrophic vulnerability, enterprises that have little agility and flexibility exposes themselves to the disastrous consequences of such changes and events. Parast and Shekarian (2019) emphasized the important roles of flexibility, collaboration, agility, 2

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and redundancy in enhancing supply chain resilience. In addition, some studies showed the important role of flexibility and agility as the key antecedents of supply chain responsiveness (Nooraie, 2017; Mohammaddust et al., 2017; Jahre and Costes, 2015; Williams et al., 2013; Malhotra and Mackelprang, 2012; Braunscheidel and Suresh, 2009; Vickery et al., 2010; Bernardes and Hanna, 2009; Reichhart and Holweg, 2007; Holweg, 2005). We aim to provide more clarity about the relationships among flexibility, agility, and responsiveness in a supply chain system, and we will examine how improvement in responsiveness can mitigate supply chain disruptions. According to a literature review by Abdelilah et al. (2018), flexibility and agility are two distinct characteristics that enable a firm to gain a competitive advantage by responding quickly and effectively to changing customer demand. To distinguish the differences between agility and flexibility, we use the definitions of each concept from the literature. The literature on supply chain agility shows an emerging consensus for a definition emphasizing the capability to sense changes, rapidly respond to changes, rapidly reduce product development cycle time or total lead time, rapidly increase the level of product customization, rapidly increase the level of customer service, rapidly improve delivery reliability, and rapidly improve responsiveness to changing market needs (Alfalla-Luque et al., 2018; Lim et al., 2017; Dominik et al., 2015; Blome et al., 2013; Gligor et al., 2013; Hallgren and Olhager, 2009; Swafford et al., 2008; Li et al., 2008; Sharifi and Zhang, 1999). Flexibility is the capability of a firm to respond to longterm or fundamental changes in the supply chain and market environment by adjusting the configuration of the supply chain. Thus, the flexibility of a firm is defined in terms of the capability of the firm to respond to environmental changes, technology changes, demand changes, and supply changes (Dominik et al., 2015; Blome et al., 2014; Li et al., 2009; Overby et al., 2006). Flexibility can also be defined as the capability to make changes in the quantity of orders to suppliers, changes in the time of orders placed with suppliers, changes in production volume, and changes in production mix (Esmaeilikia et al., 2014; Swafford et al., 2008). According to Fayezi et al. (2015), agility is the capability of an organization to respond quickly to external uncertainties, whereas flexibility is the response to uncertainties by means of change.

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Bernardes and Hanna (2009) provided a comprehensive understanding of the relative roles that flexibility, agility, and responsiveness play in the operations strategy of firms to improve the performance of their organizations. They showed that flexibility could be subsumed within agility, and both of these may be subsumed within responsiveness. Um et al. (2017) regarded supply chain flexibility and agility as two distinct concepts. They indicated that supply chain flexibility represents internally-focused manufacturers' capabilities and responsiveness in a firm’s internal functions, while supply chain agility represents externally-focused manufacturers’ competencies that emphasize speed at the organizational level. This manuscript makes a key contribution to the literature on flexibility and agility by examining the associations between supply chain responsiveness, cost efficiency, and risk management in an environment that is exposed to demand and supply risks. This study seeks to contribute to the supply chain management literature by proposing a conceptual model and a mathematical model. Our conceptual model is believed to be the first to relate flexibility, agility, and responsiveness in a supply chain system under demand and supply risk. Our conceptual model is developed based on reviewing the literature (Singh, 2015; Williams et al., 2013; Braunscheidel and Suresh, 2009; Bernardes and Hanna, 2009). Using our conceptual model, we develop a multi-objective model to show how investment in responsiveness in situations involving risk could mitigate demand and supply disruptions. We believe our model is the first to consider agility and flexibility as the enablers of responsiveness, and also to determine how much each of these enablers can improve responsiveness in a supply chain system, considering the trade-off among responsiveness, risk, and cost. By presenting a numerical example and using three optimization methods (AUGMECON, WGP, and NSGA-Ⅱ), we find the solutions for our numerical example and present a trade-off among objective functions. The rest of this paper is organized as follows. First, we discuss supply chain risk management. Next, we review the literature on flexibility, agility, and responsiveness, and then we propose a conceptual model. The model's indices, parameters, and variables are specified, and a multi-objective mathematical model is developed. In order to examine how the model behaves, a numerical example is presented to show the trade-

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off among three objective functions. We continue the discussion by conducting a sensitivity analysis on several parameters in order to further examine the dynamics and behavior of the model. Finally, we provide theoretical and managerial implications of the study, along with limitations of the study and directions for further research. 2. Literature Review In order to develop a conceptual model for supply chain responsiveness, we first review the literature about supply chain risk management, then we review two antecedents of supply chain responsiveness that have been discussed in prior studies: flexibility and agility (Williams et al., 2013; Braunscheidel and Suresh, 2009; Bernardes and Hanna, 2009). 2.1. Supply Chain Risk Management Supply chain disruption risks have been described as the occurrence of unpredictable and undesirable events such as natural disasters, loss of partnership relationships, and changes in customer preferences (Braunscheidel and Suresh, 2009; Tang and Tomlin, 2008). Events such as hurricane Rita in 2005, the Indian Ocean tsunami in 2004, the Fukushima Daiichi nuclear disaster in Japan in 2011, and the fire at a Philips plant in New Mexico in 2000 that disrupted the supply chains of both Nokia and Ericsson are motivation for supply chain researchers to consider supply chain risk and its effect on the design of supply chains (Kauppi et al., 2016; Hu and Kostamis, 2015; Creighton et al., 2014; Park et al., 2013; Kleindorfer and Saad, 2005; Chopra and Sodhi, 2004). Therefore, risk management for supply chains has become a key industry concern (Blome and Schoenherr, 2011; Khan and Burnes, 2007). Supply chain risk management remains a key managerial challenge that affects the performance of organizations (Altay and Ramirez, 2010). It is “the identification of potential sources of risk and implementation of appropriate strategies through a coordinated approach among supply chain risk members, to reduce supply chain vulnerability” (Jüttner et al., 2003, p. 201). According to Kamalahmadi and Parast (2016), supply chain risk management is concerned with the assessment of sources of risk across the supply chain and the development of strategies to deal with them. Figure 1 shows a classification of

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supply chain risk by Christopher and Peck (2004). Their classification covers five categories: process risk, control risk, demand risk, supply risk, and environmental risk.

Supply Risk

Process Risk

Demand Risk

Control Risk

Environmental Risk

Figure 1. Sources of risk in a supply chain (Christopher and Peck, 2004) For this study, we focus on supply risk and demand risk. Demand risk relates to any interruption in the flow of products or information within the network, between the focal firm and the market. Supply risk relates to disturbances in the upstream part of a supply chain (Christopher and Peck, 2004; Kamalahmadi and Parast, 2015; Li et al., 2015). 2.2. Supply chain flexibility To study supply chain flexibility, Williams et al. (2013) captured capabilities that reflect the way supply chain managers decide to change their production quantity and quality in order to better respond to changes in demand and supply. They found that responsiveness in the literature usually addresses tactical flexibility, which typically occurs at the level of business units, rather than flexibilities that are associated with specific functions or lower-level operations. Brusset and Teller (2017) indicated that flexibility capabilities increase resilience. Swafford et al. (2008) asserted that supply chain flexibility represents the operational capabilities within the supply chain functions, while supply chain agility represents the speed of the aggregate supply chain in providing a responsive supply chain. Some studies showed that flexibility is a driver for agility, and higher levels of supply chain flexibility lead to higher levels of agility (Fayezi et al., 2013; Chiang et al., 2012; Betts and Tadisina, 2009; Swafford et al., 2008). Gilgor (2016) indicated that flexibility is the capability to modify the range of tactics and operations to the extent needed. Shishodia et al. (2019) indicated that investing in creating flexibility is assumed to be more beneficial than investing in creating

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redundancies, because having flexible suppliers helps a firm in day-to-day operations in addition to helping the firm mitigate disruptions. Zhang et al. (2003) considered the external flexibilities comprising mix flexibility and volume flexibilities in their study. In addition, they suggested that flexibility is a concept to address adaptability in production/ delivery quantities and qualities to respond to shifts in customer demand and to changes in supply. Considering internal integration and external integration with key suppliers and key customers, external flexibility is one of the three direct antecedents of a firm’s supply chain agility (Williams et al., 2013; Braunscheidel and Suresh, 2009). 2.3. Supply chain agility In today’s turbulent and uncertain global environment, firms need to manage their supply chain risk to improve the agility and resilience of their supply chain systems (Tang and Tomlin, 2008). The literature suggests that supply chain agility is a concept to address competitiveness in a fast-paced and unpredictable industrial environment (Brusset, 2016; Gligor et al., 2015). Bernardes and Hanna (2009) define agility as the ability of the system to rapidly reconfigure. In addition, agility is needed to enhance the ability of the supply chain to respond more rapidly to changes in customer demand and thus improve the responsiveness of the supply chain (Gunasekaran et al., 2008; Yusuf et al., 2004). Gilgor (2016) asserted that supply chain agility is not equivalent to supply chain responsiveness. Rather, agility is a capability that allows firms to operate in a more efficient and more responsive manner (Gilgor, 2016). Braunscheidel and Suresh (2009) defined supply chain agility as a firm’s internal and external capability for achieving in a timely manner a response to market changes as well as to potential and actual disruptions. Gilgor et al. (2015) indicated that there is a direct relationship between supply chain agility and cost efficiency. They showed that the development of supply chain agility can allow a firm to meet customers' ever-changing expectations and achieve this in a cost-efficient manner. Chiang et al. (2012), in an investigation of 144 US manufacturers, found strategic sourcing and strategic flexibility are pivotal drivers of supply chain agility. Braunscheidel and Suresh (2009) indicated that demand response, joint planning, customer responsiveness, and visibility are the enablers of supply chain agility. Chan et al. (2017) argued that the critical antecedents to supply chain agility are two organizational flexibility factors: strategic flexibility and manufacturing flexibility. 7

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They showed that strategic flexibility and manufacturing flexibility can positively influence supply chain agility. Supply chain agility can be achieved through the synergy of flexibility, and it can facilitate the achievement of resource efficiency, a high level of customer service, and responsiveness in the supply chain (Mohammed et al., 2019; Um et al., 2017; Swafford et al., 2008). 2.4. Supply chain responsiveness Supply chain responsiveness shows how rapidly a firm can respond to a customer’s requirements. Responsiveness can be defined as the ability of a supply chain to respond purposefully and within an appropriate timeframe to customer requests or changes in the marketplace (Nooraie, 2017). Donk and Vaart (2007) described that responsiveness in a supply chain is the speed at which the system can adjust its output within the available range of four types of external flexibility (product, mix, volume, and delivery) in response to an external stimulus such as a customer order. According to Singh and Sharma (2015), a responsive supply chain ensures a reduction in lead time, the right service quality, the right service quantity, a flexible and on-time response to a customer’s requirements, and transportation optimization. Holweg (2005) indicated that supply chain responsiveness is the ability of a firm to identify changes, respond to them quickly (reactively or proactively), and recover from them. Responsiveness is characterized by an action or reaction in the face of modulating stimuli (Bernardes and Hanna, 2009). At the organizational level, supply chain responsiveness is a collection of actions by a business that involves decisions about when and how much to use capabilities to respond to a particular stimuli. Thus, a combination of capabilities that provide flexibility and capabilities that provide agility may form the backbone of the organization’s capability to be responsive to a particular stimulus. Moreover, some studies showed that flexibility and agility are subsumed in responsiveness (Chen et al., 2019; Um et al., 2017; Nooraie, 2017; Kim et al., 2013; Gong and Janssen, 2012; Bernardes and Hanna, 2009). Roh et al. (2014) asserted that the goal of a responsive supply chain is to provide customers with the right product at the right place in the right length of time. They indicated three main objectives for a responsive supply chain: (1) to improve agility in order to enhance responsiveness to customer demands; (2) to increase flexibility by streamlining and centralizing supply chain planning processes for new-product development and market expansion, in order to improve 8

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the response to changing customer demands; and (3) to reduce risk by removing potential sources of supply chain bottlenecks and disruptions. In addition, Saeed et al. (2019) showed that organizations with higher levels of supply chain agility will be more responsive in term of consistently meeting the quantity and delivery requirements of their customers. Um et al. (2017) showed that product variety management influences supply chain responsiveness in terms of supply chain flexibility and supply chain agility, and these both influence cost and service performance. They conceptualized supply chain responsiveness as comprising two components: operating-level responsiveness,

and

organizational

and

inter-organizational

responsiveness.

Operating-level

responsiveness is an internal capability referred to as supply chain flexibility; organizational and interorganizational responsiveness are external capabilities referred to as supply chain agility. This is in general agreement with Bernardes and Hanna (2009), who concluded that flexibility is an operating characteristic and agility is a business-level characteristic. 3. Conceptual Model Based on our findings from the literature, we develop a conceptual model for supply chain responsiveness to examine two antecedents of responsiveness: external flexibility (or flexibility) and supply chain agility (Um et al., 2017; Williams et al., 2013; Braunscheidel and Suresh, 2009; Bernardes and Hanna, 2009). Eckstein et al. (2015) and Kim et al. (2013) showed that both supply chain agility and flexibility are positively related to supply chain responsiveness. Zhang et al. (2003) and Swafford et al. (2006) statistically proved that mix and volume of external flexibility are intended to improve responsiveness in an organization. In addition, Braunscheidel and Suresh (2009) and Qrunfleh and Tarafdar (2013) showed that supply chain agility improves responsiveness. Moreover, Braunscheidel and Suresh (2009) showed that external flexibility improves a firm’s supply chain agility. Several researchers showed that there is a relationship between responsiveness and the risk of disruptions in a supply chain (Babazadeh and Razmi, 2012; Tenhiala and Ketokivi, 2012; Hum and Parlar, 2012). In order to mitigate disruptions of supply and demand in a supply chain, we need to improve supply chain responsiveness through investment in its enablers: agility and flexibility (Gligor et al., 2015; Čiarnienė and 9

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Vienažindienė, 2014; Braunscheidel and Suresh, 2009). Each of these enablers have a positive effect on improving supply chain responsiveness. Since improvement in supply chain responsiveness mitigates the effects of supply chain disruptions, supply chain responsiveness has a negative effect on supply chain disruption risks (Nooraie, 2017). Moreover, for firms that are exposed to disruption risks, managers need more investment in enablers of responsiveness to mitigate the negative effects of disruptions (Nooraie and Parast, 2015). Therefore, supply chain disruption risks have a positive effect on the expected total cost of the supply chain. Finally, supply chain responsiveness can be improved by investing in flexibility and agility. In other words, through appropriate investments in flexibility-enhancing capabilities (i.e., responding to expected changes in product volume, demand, and supply) and agility-enhancing capabilities (i.e., improving delivery time, product quality, and service quality) while keeping within budget constraints, the destructive effect of supply chain disruptions can be mitigated. Thus, by increasing investment in antecedents of supply chain responsiveness (i.e., flexibility and agility), supply chain responsiveness can be improved. These relationships are used to design a conceptual model to show how risk, cost, and responsiveness influence each other, and then to show how to improve responsiveness by investing in its enablers, flexibility and agility (see Figure 2).

+

Cost

+ Agility

Risk

+

-

+

+ Flexibility

Responsiveness + `

Figure 2. Proposed Conceptual Model for Supply Chain Responsiveness To measure key terms (flexibility and agility), we desire to capture the extent to which a firm’s supply chain is responsive to changes in customer expectation (flexibility), the speed of response (agility), and the degree to which a firm is able to meet customer demand based on product quality, delivery time, and number of 10

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products delivered (responsiveness) (Nooraie, 2017). For this study, we consider changes in production volume and changes in demand or supply as the enablers of flexibility, and we consider delivery time, customer service, and product quality as the enablers of agility, as suggested in previous studies (Chan et al., 2017; Esmaeilikia et al., 2014; Bernardes and Hanna, 2009; Swafford et al., 2008; Zhang et al., 2003). The next step is to design a model for our conceptual model in terms of supply chain responsiveness, cost, and risk, in order to examine their relationships in a supply chain exposed to demand and supply risk. 4. Mathematical Model Our model is an extension of Nooraie and Parast (2015), which examined the relationship between visibility, supply chain cost, and supply chain risk of disruption. This study differs from Nooraie and Parast’s (2015) in the following aspects: 1. We believe this is the first study to show the relationship between responsiveness, risk, and cost using multi-objective mathematical programming. 2. We aim to investigate how different levels of flexibility and agility (as two important antecedents of supply chain responsiveness) lead to different levels of responsiveness. 3. We consider both supply risk and demand risk in our model as sources of disruption risk. 4. We assume there are different transportation channels in our supply chain system. Thus, when a disruption occurs, choosing the appropriate transportation channel can help mitigate the negative effects of the disruption on supply chain responsiveness. 5. We use a numerical example to examine our model's efficiency. We aim to solve our model with three different methods: the WGP method, the AUGMECON method, and the NSGA-Ⅱ method. We use the WGP method by introducing the decision maker’s preferences into the objective function to obtain an optimum solution for our model’s decision variables. We use the AUGMECON and NSGA-Ⅱ methods to present a Pareto optimal solution and show a trade-off among objective functions, which helps decision makers and managers to better understand and

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predict the interaction among objective functions (Mohammed and Wang, 2017; Fahimnia et al., 2017; Feng et al., 2014; Deb et al., 2002). Using our conceptual model, we develop a mathematical model by incorporating supply chain responsiveness, supply chain risk, and supply chain cost. The model is for a single-echelon supply chain system where supply chain participation and production varies from period to period. Using this multiobjective model and appropriate constraints, we aim to allocate each type of product to appropriate suppliers, choosing the best transportation channels during different time periods by considering supply risk and demand risk as sources of disruption in the supply chain system. It is assumed that there is only one demand point in the supply chain system. Our multi-objective mixed integer programming (MOMIP) model aims to maximize responsiveness, minimize risk, and minimize cost. Table 1 presents the indices, decision variables, and parameters of our model. Table 1. Indices, Variables, and Parameters of the Mathematical Model Symbol Description Indices I index of products J index of suppliers H index of transportation channels T index of time periods Decision Variables a binary variable determined by whether product i is supplied by supplier j using Yijht transportation channel h in period t quantity of product i supplied by supplier j using transportation channel h in Qijht period t BOit quantity of backorder for product i during period t Input Parameters Bit budget available to enhance supply chain responsiveness for product i in period t CBOit cost of backorder for one unit of product i during period t Cjt production capacity of supplier j in period t CRijht cost of reducing one unit in supply risk and demand risk for product i supplied by supplier j using transportation channel h in period t CRSPijht cost of improving one unit in supply chain responsiveness by investment in its enablers (agility and flexibility) for product i supplied by supplier j using transportation channel h in period t. Dit demand of product i in period t Mijt minimum order quantity for product i required by supplier j in period t Pijht purchase price for product i supplied by supplier j using transportation channel h in period t IRijht financial loss impact caused by supply and demand risks for product i supplied by supplier j using transportation channel h in period t 12

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Symbol Rijht Rit RSPijht

EFijht

EAijht EDTijht ECSijht EPQijht EPFijht EDFijht ESFijht RSPit EFit EAit SUPRijht DEMRijht SUPRit DEMRit αF αA

Description risk for product i supplied by supplier j using transportation channel h in period t. The risk comes from a summation of effective factors, which are the expected supply risk and the expected demand risk. maximum allowable risk (supply and demand risks) for product i in period t supply chain responsiveness incurred if product i is supplied by supplier j using transportation channel h in period t. Responsiveness comes from weighted summation of two effective factors: expected flexibility and expected agility. expected flexibility for the supply chain (it is determined by its enablers: expected changes in product volume, expected changes in demand, and expected changes in supply) if product i is supplied by supplier j using transportation channel h in period t. expected agility for the supply chain (it is determined by its enablers: expected delivery time, expected product quality, and expected customer service) if product i is supplied by supplier j using transportation channel h in period t. Expected delivery time for product i supplied by supplier j using transportation channel h in period t Expected customer service for product i supplied by supplier j using transportation channel h in period t Expected product quality for product i supplied by supplier j using transportation channel h in period t Expected production volume flexibility for product i supplied by supplier j using transportation channel h in period t Expected demand flexibility for product i, supplied by supplier j, using transportation channel h, in period t Expected supply flexibility for product i supplied by supplier j using transportation channel h in period t minimum amount of responsiveness needed for product i in period t expected supply chain flexibility for product i in period t. expected supply chain agility for product i in period t. supply risk for product i supplied by supplier j using transportation channel h in period t demand risk for product i supplied by supplier j using transportation channel h in period t supply risk of product i in period t demand risk of product i in period t impact factor of flexibility on improving responsiveness impact factor of agility on improving responsiveness

In our model, we assume that different products (i) are supplied by different suppliers (j) to one demand point, using different transportation channels (h) in different time periods (t). We have two decision variables: Yijht represents whether product i is supplied by supplier j using transportation channel h in period t; and Qijht represents the amount of product i that is supplied by supplier j using transportation channel h in period t. 13

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The impact factors of flexibility and agility on improving supply chain responsiveness are αF and αA, respectively. These parameters show the level of investment in each enabler of responsiveness in order to improve supply chain responsiveness. It is assumed that they are determined by supply chain managers and αF + αA <=1. Here is the mathematical formulation of our model. Objective functions (maximize Responsiveness, minimize Risk, and minimize Cost): Max ( Responsiveness )   i  j  h  t RSPijht  F EFijht   A EAijht  Y

Min ( Risk )   i  j  h  t Rijht  DEMRijht + SUPRijht  Y

Min (Cost )   i  j  h  t Pijht Qijht   i  j  h  t IRitY

ijht

ijht

(1) (2)

ijht

  i  t CBOit BOit

  i  j  h  t RSPijht  F EFijht   A EAijht  CRSPijhtYijht

(3)

  i  j  h  t Rijht  DEMRijht  SUPRijht  CRijhtYijht 

Subject to:

 j  h RSPijht  F EFijht   A EAijht  CRSPijht Y

for each i, t

(4)

 j  h RSPijht  F EFijht   A EAijht  Yijht  RSPit  F EFit   A EAit 

for each i, t

(5)

 j  h Rijht  DEM ijht  SUPijht  Yijht  Rit  DEM it  SUPit 

for each i, t

(6)

 j  h Qijht = BOi ( t 1)  BOit  Dit*

for each i, t

(7)

ijht

 Bit

* it

D is the expected value of demand, which is equal to Dit*P (corresponding probability)  i  h Qijht   i  h C jtYijht

for each j, t

(8)

Qijht  C jtYijht

for each i, j, h, t

(9)

for each i, j, h, t

(10)

Qijht  0

for each i, j, h, t

(11)

BOit  0, BOi 4  BOi 0  0

for each i, t for each i, j, h, t

(12) (13)

Q

ijht

h

 mijt  Yijht

Yijht  (0,1)

h

Equation (1) represents the first objective function, which is maximizing responsiveness through investing in flexibility and agility. Equation (2) aims to mitigate expected supply chain disruption risks by minimizing expected demand and supply risk. Equation (3) represents minimizing total supply chain cost, which includes production cost, financial loss cost, backorder cost, cost of improving responsiveness, and cost of reducing supply chain risk. Constraint (4) restricts the cost of supply chain responsiveness to be under a planned budget for each product in each time period. Constraint (5) sets a minimum amount of responsiveness for each product in each time period. Constraint (6) limits the maximum allowable demand and supply risk for each product in each time period. Constraint (7) presents the relationship between 14

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demand, production, and backorder variables. Constraint (8) serves as the capacity constraint for each supplier in each time period. Constraint (9) ensures that there is no conflict in decision variables, so supplier j will not be able to supply more than its capacity in period t, Cjt, for product i by using transportation channel h. Constraint (10) specifies the minimum order quantity of each product for each supplier that uses transportation channel h in period t. Constraint (11) and (12) indicates the non-negativity of each decision variable. Constraint (13) indicates binary decision variables. Regarding responsiveness, its terms (i.e., flexibility and agility) are qualitative parameters that were converted to quantitative values. For this purpose, we calculated each of these terms as the sum of their enablers:

EAijht  EDTijht  ECSijht  EPQijht

(14)

EFijht  EPFijht  EDFijht  ESFijht

(15)

All parameters in Table 1 are provided in Appendix A. 4.1. Demand risk calculation We assume that demand comes from different scenarios with different probabilities. The possible scenarios are defined as forecasting, benchmarking, and market analysis data (Nooraie and Parast, 2015). Therefore, since each scenario has its approximation to forecast future demand, we consider Pi as the probability of the ith scenario with the quantity of demand. Therefore, to consider demand uncertainty in our mathematical model, we propose the following equations: Dit*  PS

D

S it

for each i and t

(16)

S

P

S

1

(17)

S

5. Numerical Example In this section, we provide a numerical example to show how the model works and provide further insight. We use the example and data provided by Nooraie and Parast (2015), based on the observation of a global manufacturing firm. They assumed that there is one transportation channel in their example. However, to mitigate disruption in the supply chain, we assume there are two kinds of transportation channels (h=1, 2) in our example. In order to adjust the example to new conditions, we modify some of the parameters. The 15

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first transportation channel (h=1) is road type, which is cheaper than the second transportation channel (h=2), an air transportation channel that is faster. Also in our numerical example, we have two types of products (i=1, 2) and two suppliers (j= 1, 2), during four periods of time (t=1, 2, 3, 4). It is assumed that there is one demand point. We obtain our solutions for responsiveness, risk, and cost in terms of decision variables, using the AUGMECON, WGP, and NSGA-Ⅱ methods. 5.1. Solution methods Most real-life problems are multi-objective problems for which the objective functions under consideration have some sort of conflict with each other (Moghaddam, 2013). The difficulty of multi-objective problems is to find a solution that optimizes simultaneously all the objective functions of each single problem, since in most cases, it rarely happens to find a solution that optimizes all the objective functions. Therefore, this kind of problem requires a set of non-dominant solutions (Rubem et al., 2017; Ghasemi et al., 2014). Mavrotas (2009) has one of the most widely accepted methods for classifications of solutions to multiobjective mathematical programming problems; it classifies solutions according to the stage at which the decision maker expresses his/her preferences: the a-prior methods, such as the goal programming method and the weighted-sum method; the interactive methods, such as the Zionts-Wallenius method; and the generation (a-posterior) methods, such as the ε-constraint method. Although the a-prior methods are the most popular due to a much faster computational process, the interactive methods and the a-posterior methods convey more information to the decision makers. The a-posterior methods provide an entire picture of the solutions (the Pareto set) for the decision maker (Najjarbashi and Lim, 2015). The weighted-sum method is one of the most widely used methods for optimizing multi-objective problems. This method converts a multi-objective problem into a single-objective problem by considering a weighted summation of objective functions. Consider a multi-objective problem with the m objective functions as below: Max { f1 ( x ), f 2 ( x ),..., f m ( x )}

(18)

S .t. xS

16

(19)

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where x is the vector of decision variable, S is the feasible region, and fi(x) is the ith objective function,

i  {1, 2,..., m} . This is the mathematical model of the weighted-sum method: m

Max Z   Wi f i ( x )

(20)

i 1

S .t.

m

W i 1

i

1

xS

(21) (22)

where wi is the weight of each objective function, and wi≥0, i=1, 2, … m indicates that objective function’s relative importance in decision making (Balaman, 2016; Yu and Solvang, 2016; Tian et al., 2012). The ε-constraint method to solve a multi-objective problem is a known method that aims to optimize one of the m objective functions (usually the most preferable one) and transform the other m-1 objective functions into constraints by integrating them into the initial constraint set. The constraints derived from the objective functions are constructed according to their bounds, which should be determined. According to this procedure, a multi-objective problem can be transformed into a single-objective problem (Fahimnia et al., 2017; Feng et al., 2014). Balaman (2016) showed that there are some advantages for the ε-constraint method over the weighted-sum method: 1- In linear programming, the weighted-sum method is applied to the original feasible region and results in only extreme solutions, while the ε-constraint method alters the region of feasible solutions and generates Pareto solutions (or non-extreme solutions). Pareto solutions are the solutions that cannot be improved in one objective function unless the performance of at least one of the other objective functions is decreased. Thus, in the weighted-sum method, there can be many combinations of weights that result in the same efficient extreme solution. With the ε-constraint method, we can exploit every run to produce a different efficient solution (due to the existence of the Pareto set), thus obtaining a richer representation of the efficient set (Mavrotas, 2009). 2- For a-posterior decision making, the weighted-sum method is unable to generate either a complete set of points at the Pareto frontier or evenly Pareto distribution solutions. Figure 3 illustrates the inability of the weighted-sum method to determine the Pareto frontier points for a non-convex feasible region, while the ε-constraint method is an efficient method to identify the 17

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Pareto frontier points for non-convex feasible regions (Yu and Solvang, 2016). According to Figure 3, the weighted-sum method is unable to indicate the feasible region between point A and point C (containing point B), while the ε-constraint method can efficiently illustrate the feasible region between A and C. 3- The weighted-sum method cannot produce unsupported efficient solutions in multi-objective integer programming and multi-objective mixed integer programing, while the ε-constraint method does not suffer from this deficiency (Norouzi et al., 2014; Feng et al., 2014). 4- In the weighted-sum method, the scale of each objective function has a great influence on the results, so it is important to scale them to a common scale. This is not important for the ε-constraint method (Mavrotas, 2009). 5- In the ε-constraint method, we can control the number of the generated efficient solutions by properly adjusting the number of grid points in each of the objective function ranges. This is not easy in the weighted-sum method (Mavrotas, 2009). f2(x)

A feasible region

B C D

f1(x)

Figure 3. Graphical comparison of the Pareto frontier for the weighted-sum and the ε-constraint method Another applicable optimization method for a multi-objective problem is the goal programming method. This method has been the most widely used technique in solving multi-objective problems for several reasons: robustness, mathematical flexibility, and the possibility of introducing many system constraints (Jadidi et al., 2014). In this method, the decision maker first indicates the ideal levels (aspiration levels) for each objective function, then the model aims to minimize the deviation between the achievements of goals and their aspiration levels. There are three basic approaches to the goal programming method: (1) the weighted goal programming (WGP) method, (2) the lexicographic or preemptive goal programming method, and (3) the min-max goal programming method. We selected the WGP approach as the modeling 18

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framework for our study, since it is flexible enough to accommodate large numbers of objective functions and provides a way of striving toward several objective functions simultaneously, without intractable computation. It is rather straightforward to explain to potential users. Also, this method has been successfully implemented in various areas, which supports its credibility (Jones and Tamiz, 2010; Fine et al., 2005). In this research, the WGP, AUGMECON, and NSGA-Ⅱ methods are used as approaches to the solution. The WGP method needs the decision-maker to determine two parameters: an acceptable level of achievement (aspiration level) for each objective function and the weight of each deviation between the objective function and its aspiration level. Thus, when this information can be determined by the decision maker, this method works efficiently. The major drawback of the WGP method is its inability to illustrate the Pareto solutions, because it can obtain only one non-dominant solution (Moghaddam, 2015) and therefore cannot provide a trade-off among objective functions for decision makers. Therefore, we use the AUGMECON and NSGA-Ⅱ methods to overcome this weakness and provide a trade-off among objective functions while avoiding subjective weighting from the decision maker. 5.2. Weighted goal programming (WGP) method The goal programming method was first proposed by Charnes and Cooper (1961). According to Ransikarbum and Mason (2016), in this method, the decision maker specifies the desired level for each objective function separately. Usually, the desired levels can be determined by considering each of the objective functions and their related constraints as a single-objective function, then by solving separately each of the problems and finding the optimum solutions as the desired levels. The goal programming method treats these desired levels as the aspirations to achieve, not as absolute constraints. This method seeks to find the solutions that are closest to each objective function’s desired levels. The goal programming method contains two types of constraints: system constraints and goal constraints. System constraints are formulated following linear programming, while goal constraints seek to obtain the best possible solution regarding the aspirations for the objective functions. The weighted goal programming (WGP) method is

19

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one of the most common techniques in goal programming. The WGP method needs the decision maker to indicate the most-desired value for each objective function as the aspiration level, and also to determine the weight of each deviation (the deviation between each objective function and its aspiration level), in order to minimize the weighted summation of deviations for each objective function. This is the mathematical formulation of the WGP method (Aalaei and Davoudpour, 2016; Jadidi et al., 2014): m

Min Z   wi ( d i  d i )

(23)

i 1

S .t.

f i ( x )  d i  d i  g i

for i  1, 2,..., m

xS  i

d ,d

 i

(24) (25)

0

for i  1, 2,..., m

(26)

where Equation 24 is the goal constraint and Equation 25 is the system constraint, wi is the weight of each objective function, gi indicates the desired level for each objective function, and di and di are positive variables that indicate positive and negative deviation from the desired level of the ith goal, respectively. Our mathematical model can be reformulated with the WGP method as follows: Min Z  w1d1  w2 d 2  w3 d 3

(27)

S .t.  i  j  h  t RSPijht  F EFijht   A EAijht  Y  i  j  h  t Rijht  DEMRijht + SUPRijht  Y  i  j  h  t Pijht Qijht   i  j  h  t IRit Y

ijht ijht

ijht

 d1  d1  g1

 d 2  d 2  g 2

(28) (29)

  i  t CBOit BOit 

  i  j  h  t RSPijht  F EFijht   A EAijht  CRSPijht Yijht   i  j  h  t Rijht  DEMRijht  SUPRijht  CRijht Yijht  d 3  d 3  g 3  i

 i

d ,d  0

for i  1, 2,..., m

(30) (31)

along with Equations 4 through 13, where the constraints in Equations 4 through 13 are the system constraints, and gi for i=1,2,3 is the optimum level of each objective function in a single-objective programming problem. Using a General Algebraic Modeling System (GAMS) for our numerical example (all the data for our numerical example are provided in Appendix A), we solve our primary mathematical model for each of the objective functions separately. The desired level for each objective function is calculated as follows: g1=284.932 units, g2=21.3 units, and g3=$139,527,800 (we assumed αF = αA =0.5). We notice that total cost is defined as a monetary value ($), while responsiveness and risk are numbers. In order to have an effective and reliable solution for this model, we need to evaluate each wi more precisely. 20

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In line with previous studies such as Nooraie and Parast (2015) and Yu and Goh (2014), we assume each unit of total responsiveness is equivalent to $1,000,000 profit, and each number of total risk is equivalent to $100,000 cost. Thus, we assume w1=1,000,000, w2=100,000, w3=1, and αF = αA = 0.5. Table 2 shows the results from solving our model using a GAMS. Table 2. Results for the Numerical Example With the WGP method Y1111=1 Q1111=13,500 Y2111=1 Q2111=19,550 Y1121=1 Q1121=10,000 Y2121=1 Q2121=15,000 Y1122=1 Q1122=27,500 Y2212=1 Q2212=24,000 Y1222=1 Q1222=12,500 Y2222=1 Q2222=17,500 Y1213=1 Q1213=38,275 Y2213=1 Q2213=18,450 Y1223=1 Q1223=9,250 Y2223=1 Q2223=16,500 Y1124=1 Q1124=20,000 Y2214=1 Q2214=26,925 Y1214=1 Q1214=10,000 Y2224=1 Q2224=7,750 Y1224=1 Q1224=10,000 BO12=4,500 BO13=7,000

Z1*  284.709 or Z1*  $284, 709, 000 Z 2*  57 or Z 2*  $5, 700, 000 Z 3*  $197, 270, 720 In accordance with Table 2, the total savings in cost by the investment in responsiveness is

Z1*  Z 2*  Z 3*  $81, 738, 280 . The optimum levels of the numerical values of responsiveness, risk, and cost are 284.709 units, 57.0 units, and $197,270,720, respectively. In addition, return on investment (ROI) would be 41.43%. Figure 4 shows that for period 1, supplier 1 is preferable, and for period 3, supplier 2 is preferable. Due to the great importance for managers of improving responsiveness (as indicated by the value of w1 being much higher than w2 and w3), the WGP method looks for solutions that are sufficiently close to the desired level of responsiveness (g1=284.932). Therefore, the model looks to allocate each product to those suppliers that select the right transportation channels to lead to a highly responsive supply chain system in each period.

21

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T=1

T=2

Supplier 1

Supplier 1

Supplier 2

T=3

T=4

Supplier 1

Supplier 2

Supplier 2

Figure 4. The solution for the numerical example with the WGP method 5.3. Augmented ε-constraint (AUGMECON) method The ε-constraint method is one of the most popular methods for solving multi-objective optimization problems; it was first introduced by Haimes et al. (1971). In this method, we optimize one of the objective functions, generally the most preferable one, while considering the other objective functions as constraints with an upper/ lower bound limitation. This is the mathematical formulation of the traditional ε-constraint method (Zhang and Reimann, 2014): min / max f1 ( x)

(32)

S .t. f 2 ( x)   2 for max functions

(33)

f 3 ( x)   3 for min functions

(34)

... f m ( x)   m

(35)

xS

(36)

where εi is the vector of satisfaction levels. By changing each εi, the Pareto set can be obtained. Despite the ε-constraint method’s advantages over the weighting method discussed earlier, this method has three points that need attention in its implementation: (a) the calculation of the range of objective functions over the efficient set; (b) the guarantee of the efficiency of the solution obtained; and (c) the increased solution time for problems with more than two objective functions. According to Feng et al. (2014), the AUGMECON method can successfully demonstrate the complete Pareto front. Therefore, by using the

22

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AUGMECON method and the pay-off table, we try to address these three mentioned issues (Hassannayebi et al., 2016; Mavrotas, 2009). We use lexicographic optimization to generate the pay-off matrix. Generally, the lexicographic optimization of a series of objective functions is to optimize the first objective function and then, among the other possible alternative optima, optimize for the second objective function, and so on (Mavrotas, 2009). The structure of the pay-off matrix is shown below. (We assume that all objective functions are to be maximized.) Table 3. The Structure of the Pay-Off Table f1 * Max f1(x) f ( x* ) 1

1

f2

f2 ( x )

… …

f m ( x1* )

…

f m ( x2* )

* 1

Max f2(x)

f1 ( x2* )

f 2* ( x2* )

. . . Max fm(x)

. . .

. . .

f1 ( xm* )

f 2 ( xm* )

fm

. . . …

f m* ( xm* )

The AUGMECON method transforms the inequality constraints of the ε-constraint method into equality constraints by introducing non-negative slack/surplus variables, and then it augments the objective function with the weighted sum of the slack/surplus variables (Zhang and Reimann, 2014). This is the mathematical formulation of the AUGMECON method: Max f j ( x)  eps *  k j

S .t.

sk rk

f k ( x)  sk   k

(37) k  j

xS sk  0

(38) (39) (40)

Where eps is an adequate small number (usually between 10-3 and 10-6), sk denotes a slack variable for the kth constraint, and rk denotes the range for the kth objective function (Hassannayebi et al., 2016). For determining rk, we should first indicate the utopia point (fU) and the pseudo nadir point (fND) as below (Nezhad et al., 2014):  f i ND  f i ( x )  f iU   ND *  min  f i ( x1* ),..., f i * ( xi* ),..., f i ( xm )  fi  U * *   fi  fi ( x )

23

(41) (42) (43)

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where the pseudo nadir point for objective function i, f i ND , is the lowest amount of column i in the pay-off matrix. Since finding the worst value (the nadir point) over the efficient set is not always possible, we usually find f i ND from Equation 42 as an approximation alternative for the nadir point (Amirian and Sahraeian, 2015). The utopia point for objective function i, f iU , is the corresponding amount in row i and column i in its pay-off matrix. We can also obtain the utopia point by optimizing the objective function i as a single-objective problem. This is our mathematical model reformulated with the AUGMECON method: Max Z   i  j  h  t RSPijht  F EFijht   A EAijht  Y

3

ijht

 eps *  k 2

sk rk

(44)

S .t.  i  j  h  t Rijht  DEMRijht + SUPRijht  Y  i  j  h  t Pijht Qijht   i  j  h  t IRit Y

ijht ijht

 s2   2

(45)

  i  t CBOit BOit

  i  j  h  t RSPijht  F EFijht   A EAijht  CRSPijht Yijht   i  j  h  t Rijht  DEMRijht  SUPRijht  CRijht Yijht  s3   3

(46)

sk  0

(47)

along with Equations 4 through 13, where constraints 4 through 13 are the system constraints. We follow the algorithm from Amirian and Sahraeian (2015) for the AUGMECON method in our numerical example. By solving our model with the AUGMECON method in GAMS, we obtain the results shown in Table 4. Table 4. The Pay-Off Table for Our Numerical Example Pay-off Responsiveness Risk Cost (*108 $) Responsiveness 284.932 45.400 2.524863 Risk 151.998 21.300 2.587764 Cost (*108 $) 202.016 49.000 1.395278 Table 4 shows the trade-off among responsiveness, risk, and cost. Considering the main diagonal of the matrix, we notice that the optimum value for responsiveness, regardless of the other objective functions, is 284.932 units. The optimum amounts for risk and cost are 21.3 units and $139,527,800, respectively. The pay-off table also shows that the objective values differ from 151.998 units to 284.932 units for responsiveness, from 21.3 units to 49.0 units for risk, and from $139,527,800 to $252,486,300 for cost. A decision maker cannot have the optimum value for all the objective functions simultaneously, since it makes

24

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the main problem infeasible. Therefore, it is left to the decision maker how to trade off among the objective functions. In order to make a comparison between the Pareto set solutions and select one of the solutions, according to the previous section, we again convert the units of responsiveness and risk to monetary units by considering w1=1,000,000 and w2=100,000 for responsiveness and risk, respectively. As an example, considering the first row of Table 4, with 284.932 units for responsiveness, 45.4 units for risk, and $252,486,300

for

cost,

the

total

savings

in

cost

by

investment

in

responsiveness

is

* * * Z responsiveness  Z risk  Z cos t  $27,905, 700 .

5.4. Trade-off among objective functions In this section, we aim to illustrate the trade-off among responsiveness, risk, and cost. First, to determine the size of changes in responsiveness that occur with simultaneous improvement in both risk and cost, we change the objective values for both risk and cost between their nadir point (worst point) and their optimum point together. (These points are extracted from the GAMS; namely, the grid points that are used to build the pay-off table.) Then we calculate the objective value for responsiveness (Table 5). Table 5. Trade-Off Among Objective Functions When Risk and Cost Improve Together Responsiveness 284.9 284.9 284.9 275.7 256.7 229.4 197.8 Risk 49.0 46.3 43.6 40.9 38.2 35.5 32.8 Cost (*$10^6) 258.7 247.9 237.2 226.4 215.6 204.8 194.0

Z1*  Z 2*  Z 3* (*$106 )

21.3

32.37

43.34

45.21

37.28

21.05

0.52

166.8 30.1 183.3 (19.51)

Considering the data from Table 5, Figure 5 shows the trade-off among responsiveness, cost, and risk when cost and risk improve simultaneously. According to Figure 5, when the objective values for cost and risk change from their nadir points (49.0 units for risk and $258.8*106 for cost) to 43.6 units for risk and $237.2 *106 for cost, the objective value for responsiveness remains at its optimum amount (i.e., 284.9 units). Then, by improving the objective value for both risk and cost, the objective value for responsiveness decreases, gradually. To compare these objective values with each other, we again convert the units of responsiveness and risk to the monetary unit by considering w1=1,000,000 and w2=100,000 for responsiveness and risk, respectively. By comparing the total savings in cost for each solution that is shown in Table 5, with 275.7 units for responsiveness, 40.9 units for risk, and $226,400,000 for cost, the best total savings in cost by 25

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* * * investment in responsiveness is: Z responsiveness  Z risk  Z cos t  $45, 210, 000 . Therefore, ROI would be

19.97%.

Responsiveness

Responsiveness 300 250 200 150 100 (49, 258.8) (46.3, 248) (43.6, 237.2) (40.9, 226.4) (38.2, 215.7) (35.5, 204.9) (32.8, 194.1) (30.1, 183.3)

(Risk, Cost*$10^6)

Figure 5. Trade-off among objective functions when risk and cost improve together To determine the size of changes in cost that occur by simultaneous improvement in both responsiveness and risk, we change the objective values for both responsiveness and risk between their nadir points (worst points) and their optimum points together. Then we calculate the objective value for cost (Table 6). Table 6. Trade-Off Among Objective Functions When Responsiveness and Risk Improve Together Responsiveness 152.0 164.1 176.2 188.3 200.5 212.6 224.7 Risk Cost (*$10^6)

Z  Z  Z (*$10 ) * 1

* 2

* 3

6

49.0

46.3

43.6

40.9

38.2

35.5

32.8

139.5

139.5

139.5

139.4

158.9

187.9

232.5

7.79

20.19

32.59

44.87

37.271

21.17

(11.04)

Considering the data from Table 6, Figure 6 shows the trade-off among responsiveness, cost, and risk when responsiveness and risk improve simultaneously. According to Figure 6, whenever the objective values for risk and responsiveness change from their nadir points (49.0 units for risk and 152.0 units for responsiveness) to 43.6 units for risk and 176.2 units for responsiveness, the objective value for cost remains at its optimum amount (i.e., $139,527,800). Then, by improving the objective value for both risk and responsiveness, the objective value for cost increases gradually. To compare these objective values with each other, we again convert the units of responsiveness and risk to the monetary unit by considering w1=1,000,000 and w2=100,000 for responsiveness and risk, respectively. By comparing the total savings in cost for each solution that is shown in Table 6, with 188.3 units for responsiveness, 40.9 units for risk, and

26

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$139,431,900 for cost, the most total savings in cost by investment in responsiveness is * * * Z responsiveness  Z risk  Z cos t  $44,870, 000 . Therefore, ROI would be 32.19%.

Cost * 10^6

Cost 250 200 150 100 (49, 152.0) (46.3, 164.0) (43.6, 176.3) (40.9, 188.4) (38.2, 200.5) (35.5, 212.6) (32.8, 224.8)

(Risk,Responsiveness)

Figure 6. Trade-off among objective functions when responsiveness and risk improve together To determine the size of changes in risk that occur by simultaneous improvement in both responsiveness and cost, we change the objective values for both responsiveness and cost between their nadir points (worst points) and their optimum points together. Then, we calculate the objective value for risk (Table 7). Table 7. Trade-Off Among Objective Functions When Responsiveness and Cost Improve Together Responsiveness 152.9 164.9 176.9 189.0 201.0 213.1 225.1 237.2 Risk 21.3 24.4 27.5 30.4 33.4 37 40.4 43.6 Cost (*$10^6) 258.8 248.4 237.6 226.7 215.9 205.1 194.3 183.4 4.3 26.8 49.4 Z *  Z *  Z * (*$106 ) (108.0) (85.9) (63.4) (40.8) (18.2) 1

2

3

Continued below Responsiveness Risk Cost (*$10^6)

Z1*  Z 2*  Z 3* (*$106 )

249.2 48.9 172.6 71.7

261.3 49.0 161.8 94.6

Considering the data from Table 7, Figure 7 shows the trade-off among responsiveness, cost, and risk when responsiveness and cost improve together. According to Figure 7, when we improve the objective values for both responsiveness and cost by starting from their nadir points (152.9 units for responsiveness and $258.8*106 for cost), the objective value for risk increases gradually. To compare these objective values with each other, we change the units of responsiveness and risk to the monetary unit by considering w1=1,000,000 and w2=100,000 for responsiveness and risk, respectively. By comparing the total savings in

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cost for each solution that is shown in Table 7, with 261.3 units for responsiveness, 49.0 units for risk, and $161,797,900 for cost, the greatest total savings in cost by investment in responsiveness is * * * Z responsiveness  Z risk  Z cos t  $94,557,100 . Therefore, ROI would be 58.10%.

Risk 60

Risk

50 40 30

) .3

,1 61

.8

) 61 (2

.2

,1 72

.7

) 49 (2

.2

,1 83

.4

) 37 (2

25

.1

,1 94

.2

) .1 (2

,2 05 .1 13 (2

,2 16 .0 01 (2

.0

,2 26

.0

)

,7 )

) 89 (1

(1

77

.0

,2 37

.6

) .4 ,2 48 .9 64

(1

(1

52

.9

,2 59

.2

)

20

(Responsiveness,Cost * 10^6)

Figure 7. Trade-off among objective functions when responsiveness and cost improve together Among the solutions that we obtained through trade-offs among responsiveness, risk, and cost, we choose the best solution as the solution that makes the most total savings in cost by investing in responsiveness. * * * By comparing the objective values for Z responsiveness  Z risk  Z cos t and the corresponding ROI percentages

from Table 5, Table 6, and Table 7, Table 8 shows the best solution with highest ROI percentage and profit amount for the firm. Table 8. Test Solution for the Numerical Example With the AUGMECON Method Y1111=1 Q1111=13,500 Y2111=1 Q2111=19,550 Y1121=1 Q1121=10,000 Y2121=1 Q2121=15,000 Y1212=1 Q1212=32,000 Y2112=1 Q2112=24,000 Y1222=1 Q1222=12,500 Y2212=1 Q2212=17,500 Y1213=1 Q1213=40,775 Y2113=1 Q2113=18,450 Y1223=1 Q1223=9,250 Y2213=1 Q2213=16,500 Y1214=1 Q1214=23,000 Y2214=1 Q2214=26,925 Y1224=1 Q1224=10,000 Y2224=1 Q2224=7,750 * Z responsiveness  261.255 or $261, 255, 000 * Z risk  49.0 or $4,900, 000 * Z cos t  $161, 797,900

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* * * So the total savings in cost by investing in responsiveness are Z responsiveness  Z risk  Z cos t  $94, 007,100 ,

for which the optimum levels of the numerical values of responsiveness, risk, and cost are 261.255 units, 49.0 units, and $161,797,900, respectively. This solution provides 0.58 unit return on each unit of investment for the firm. The result for our numerical example is shown in Figure 8. T=1

T=2

T=3

Supplier 1

Supplier 1

Supplier 2

Supplier 2

Supplier 2

T=4

Supplier 2

Figure 8. The best solution for the numerical example with the AUGMECON method According to Figure 8, for period 1, only supplier 1 is preferable and for period 4, only supplier 2 is preferable. For periods 2 and 3, both suppliers are selected to meet the demand. 5.5. NSGA Ⅱ The non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) was designed by Deb et al. (2002). In order to optimize the multi-objective mathematical problems, this algorithm uses two key concepts: ranking and crowding distance. The following steps are required to develop an NSGA-Ⅱ (Deb et al, 2000): Step 1: Create a random parent population. Step 2: Sort the random parent population based on non-domination. Step 3: Assign a fitness (rank) equal to the non-domination level for each non-dominated solution. Step 4: Create an offspring population using binary tournament selection, recombination, and mutation operators. Step 5: From the first generation onwards, create a new generation considering the following steps: a) Create a mating pool by combining the parent population and offspring population.

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b) Sort the combined population, according to the fast non-dominated sorting procedure to identify all non-dominated fronts. c) Generate the new parent population by adding non-dominated solutions starting from the first ranked non-dominated front until the total non-dominated solutions exceed the population size. This is achieved through a sorting procedure based on the crowding distance operator. d) Perform the selection, crossover, and mutation operations on the newly generated parent population to create the new offspring population. Step 6: Repeat Step 5 until the maximum number of iterations is reached. Matlab R2018b (version 9.5) was used to solve our numerical example using the proposed NSGA-Ⅱ algorithm. Table 10 shows the Pareto solutions after using the AUGMECON and NSGA-Ⅱ methods. According to Table 10, while the optimum amount for responsiveness using either AUGMECON or NSGAⅡ are the same (Responsiveness=284.9 units), NSGA-Ⅱ outperforms in term of proposing better optimum solutions for cost and risk objective functions. Table 9. Comparing Pareto solution using AUGMENCON and NSGA II methods AUGMECON

Pareto

NSGA-II

solutions

Responsiveness

Risk

𝑪𝒐𝒔𝒕 (* 106)

Responsiveness

Risk

Cost (* 106)

1

166.8

30.1

183.3

152.1

25.5

142

2

197.8

32.8

194.1

155.7

26.1

148

3

229.4

35.5

204.9

160.6

27.0

157.3

4

256.7

38.2

215.7

164.2

29.9

170.6

5

275.7

40.9

226.4

165.1

30.1

182.4

6

284.9

43.6

237.2

173.6

31.0

187.1

7

284.9

46.3

248.0

184.5

31.5

190.8

8

284.9

49

258.8

196.5

32.9

194.2

9

-

-

-

201.1

33.2

195.5

10

-

-

-

210.5

33.6

199.8

11

-

-

-

231.7

34.5

203.9

12

-

-

-

239.6

35.3

205.1

13

-

-

-

250.0

36.0

211.2

14

-

-

-

255.4

36.8

212.3

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AUGMECON

Pareto

NSGA-II

solutions

Responsiveness

Risk

𝑪𝒐𝒔𝒕 (* 106)

Responsiveness

Risk

Cost (* 106)

15

-

-

-

270.3

37.2

218.8

16

-

-

-

280.4

38.9

220.4

17

-

-

-

283.5

39.7

225.1

18

-

-

-

284.0

40.6

228.9

19

-

-

-

284.9

41.1

231.5

5.5.1. Comparison Metrics To validate the reliability of the proposed NSGA-Ⅱ method, three comparison metrics are used: (1) Spacing metric (SM): The uniformity of pareto solutions can be indicated by using this metric. It can be defined by: 𝑆𝑀 =

∑𝑛 ― 1|𝑑 ― 𝑑𝑖| 𝑖=1

(48)

(𝑛 ― 1)𝑑

where di is the Euclidian distance between solutions i and i+1 in sorted pareto solutions, and 𝑑 is the arithmetic average of di. (2) Simple Additive Weighting (SAW): This metric calculates an evaluation score for each metric. It can be defined by: SAWi= ∑𝑗𝑤𝑗𝑛𝑖𝑗

(49)

where wj is the weighted criterion and nij is the normalized decision matrix for each criterion. (3) Diversification metric (DM): This metric measures the spread of the solution set and is defined by: 𝑛 𝐷𝑀 = ∑𝑖 = 1max (||xit ― yit||)

(50)

where ||xit ― yit|| is the Euclidean distance between the non-dominated solutions xit and yit. Considering the three proposed metrics to evaluate the validation of the proposed NSGA-Ⅱ, Table 11 shows the obtained scores of these indexes for the obtained frontier by the AUGMECON and NSGA-Ⅱ methods for the numerical example. The value of DM for NSGA-Ⅱ is considerably greater than this value for AUGMECON, which means NSGA-Ⅱ finds non-dominated solutions with more diversity. In addition, 31

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the SM value shows that NSGA-Ⅱ obtains more pareto solutions that are closer to each other. Finally, running time for the NSGA-Ⅱ algorithm is less than for the AUGMECON method. Therefore, NSGA-Ⅱ outperforms the AUGMECON method. Table 10. NSGA-II and AUGMECON methods validation

Method/Index

SM

DM

AUGMECON 0.95 623.5 NSGA-II

1.08 997.5

SAW Running time (S) 1.05

100.3

1.04

15.7

6. Sensitivity Analysis In the previous section, we allocated equal budgets to flexibility and agility (α1= α2= 0.5) to improve supply chain responsiveness. In the next section, we examine the impact of different transportation channels on improving supply chain responsiveness. After that, we conduct sensitivity analyses by changing the impact factor of each of supply chain responsiveness’s enablers, to investigate the effect of each enabler on improving supply chain responsiveness. 6.1. The impact of different transportation channels on improving responsiveness In this section, we conduct a sensitivity analysis to examine how different transportation channels can improve responsiveness when disruption occurs in the supply chain. We assume that supply risk and demand risk, as the sources of disruption, increase substantially in our model. Table 9 shows the results from solving the model with the WGP method. Table 11. Sensitivity Analysis When Disruption Risk Increases Y1121=1 Q1121=23,500 Y2121=1 Y1222=1 Q1222=44,500 Y2222=1 Y1223=1 Q1223=50,025 Y2223=1 Y1224=1 Q1224=33,000 Y2224=1

Q2121=34,550 Q2222=41,500 Q2223=34,950 Q2224=34,675

Z1*  160.04 or Z1*  $160, 040, 000 Z 2*  47 or Z 2*  $4, 700, 000 Z 3*  $260,196,300 The optimum levels of the numerical values for responsiveness, risk, and cost are 160.04 units, 47 units, and $260,196,300, respectively. Figure 9 indicates that in a highly uncertain environment, in which 32

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demands and suppliers have a higher risk of disruption, the model selects the second transportation channel for each period; the second channel is more reliable and more responsive (while more expensive) in comparison with the first transportation channel. Therefore, choosing the best transportation channel can help managers to mitigate disruption risk in their supply chain and improve supply chain responsiveness. T=1

T=2

T=3

T=4

Supplier 1

Supplier 2

Supplier 2

Supplier 2

Figure 9. Sensitivity analysis when disruption risk increases 6.2. The impact of flexibility and agility on improving responsiveness In this section, we conduct a sensitivity analysis to examine how flexibility and agility can affect responsiveness, risk, and cost, and how much it can influence the total cost of investment. We change α1 from 1 (which means a full investment in flexibility) to 0 (which means to invest in the other enablers of responsiveness) and solve our model. Table 10 shows the results. Table 12. The effect of flexibility and agility on cost investment α1, α2 Responsiveness Risk Cost (*106 USD) Total saving ($) ( Z *  Z *  Z * ) 1

α1=1, α2=0 α1=0.9, α2=0.1 α1=0.8, α2=0.2 α1=0.7, α2=0.3 α1=0.6, α2=0.4 α1=0.5, α2=0.5 α1=0.4, α2=0.6 α1=0.3, α2=0.7 α1=0.2, α2=0.8 α1=0.1, α2=0.9 α1=0, α2=1

260.1 261.814 262.442 264.782 267.770 270.768 273.943 277.118 281.098 284.226 284.932

49.0 49.0 49.0 46.2 48.8 45.9 45.9 45.9 45.9 45.9 45.9

202.3570 202.3570 229.1509 219.6681 203.9615 232.5220 232.5220 232.5220 232.9660 232.9660 232.9660

52,843,000 54,557,000 28,391,100 40,493,900 58,928,500 33,656,000 36,831,000 40,006,000 43,542,000 46,670,000 49,799,000

2

3

ROI (%) 26.11 26.96 12.39 18.43 28.89 14.47 15.84 17.17 18.69 20.03 21.38

According to Table 10, regardless of the cost and risk objective functions, by increasing investment in flexibility and consequently decreasing investment in agility (since α1+ α2<=1), the supply chain responsiveness will decrease. Thus, if managers aim to increase responsiveness, investing in agility is an 33

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effective approach for them, rather than investing in flexibility. In addition, according to Table 10, when there is no investment in flexibility (α1=0), the result is the best objective value for responsiveness, which is 287.355 units. However, by considering the other objective functions through trade-offs among them, the result may be changed. Again, to compare each solution of Table 10, we convert each objective function unit to a monetary unit by considering w1=1,000,000 and w2=100,000 for responsiveness and risk, respectively. These results are shown in Figure 10. According to Figure 10, by investing 60% of the budget in flexibility and 40% in agility, we expect the most profit of investing in responsiveness for the firm: $58,928,500. This solution provides a return on investment of about 0.29 unit of investment. We also notice that the firm should not have an investment of 80% of the budget on flexibility, because that provides the least profit for the firm.

Profit (*10^6USD)

The effect of flexibility and Agility on Profit 70 60 50 40 30 20 10 0 (1,0)

(0.8,0.2)

(0.6,0.4)

(0.4,0.6)

(0.2,0.8)

(0,1)

(α1, α2)

Figure 10. The effect of flexibility and agility on cost investment 7. Discussion This study provides several contributions to the theory and practice of supply chain risk management that are discussed in the following sections. 7.1. Theoretical contributions The proposed multi-objective model was chosen for several purposes: 1) to model supplier selection and demand allocation using appropriate transportation channels under the risk of disruptions in suppliers and demand in different time periods; 2) to provide insight into the influence of flexibility and agility on 34

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improving supply chain responsiveness; and 3) to investigate trade-offs among responsiveness, risk, and cost to determine how they interact. Our study provides several contributions to the theory of supply chain risk management. First, we extended the previous study by Nooraie and Parast (2015) in several ways. We analyzed the relationship between responsiveness, risk, and cost by incorporating supply risk and demand risk in our model. We used different transportation channels to improve supply chain responsiveness, to help mitigate disruptions in demand and suppliers. The numerical example showed that when we use the WGP method to solve our problem, due to the major importance of responsiveness for managers (as indicated by the relative values of the wi parameters), the model selects the most responsive transportation channel in each period for each product allocation and supplier selection. Using the AUGMECON and NSGA-Ⅱ methods to solve the problem, the model provides managers with different solutions as the subsets of the Pareto set. Using trade-offs among the objective functions, a manager is able to choose the appropriate solutions. For our second theoretical contribution, our sensitivity analysis provides some important insights. First, for a supply chain that is exposed to disruption, planning some disruption mitigation strategies can greatly help managers to address the problem. In the case of our numerical example, we considered two transportation channels in the problem. We showed that when a disruption occurs in the supply chain, the more responsive and reliable transportation channel can help to mitigate the supply chain disruption. Second, for a supply chain that is exposed to supply and demand risk, risk reduction depends on how much improvement can be made in flexibility and agility. We showed by increasing the investment in supply chain agility (while decreasing investment in flexibility), supply chain responsiveness will increase. But, by increasing investment in supply chain flexibility (while decreasing investment in agility), supply chain responsiveness will decrease. Therefore, for managers who are looking to increase supply chain responsiveness, investing in agility’s enablers is the best strategy to cope with demand and supply disruption risks. The third contribution of the study is our mathematical model. To the best of our knowledge, we believe our model is the first mathematical model to investigate how flexibility and agility interact in order to

35

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improve supply chain responsiveness. By doing so, we were able to illustrate the trade-offs among responsiveness, risk, and cost to help decision makers make adjustments. In studying the trade-offs among objective functions, we noticed that the optimum value for our multi-objective problem is different from the optimum values of each single objective problem, so managers cannot improve responsiveness without diminishing at least one of the other objective functions. The trade-off among objective functions showed that investing in flexibility is more profitable for the firm in comparison with investing in agility. Therefore, for managers who are looking to increase their firm’s profit, investing in flexibility’s enablers is the best strategy. In addition, based on the two solution methods for our numerical example, we showed when the objective functions are comparable to each other and their units are changeable to a common unit (for example, a monetary unit), the WGP method is preferable for managers, because this method provides an optimum solution (if one exists) and these solutions can be easily used and interpreted by managers. However, if finding a common unit for comparing objective functions is not possible, the AUGMECON or NSGA-Ⅱ methods are preferable for managers. These methods provide a trade-off among objective functions that can help managers to decide properly about the available resources and decision variables. Finally, we proposed an NSGA-Ⅱ method for solving the numerical example. The results showed that the NSGA-Ⅱ method outperforms the AUGMECON method in several metric indexes: the spacing metric, the diversity metric, and simple additive weighting. In addition, this method is preferable for large-sized problems, since its running time is comparatively less than the AUGMECON method. Moreover, the NSGA-Ⅱ method could achieve a greater number of pareto-optimal solutions with higher qualities than AUGMECON and WGP; this can provide a better perspective for managers to plan about the available resources and also allocate resources to appropriate decision variables to satisfy the objective functions. 7.2. Managerial implications Although our results are limited by our particular experiment setting, our model provides important managerial implications for supply chain managers. First, while previous studies showed flexibility and 36

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agility have a positive effect on improving supply chain responsiveness, our results indicated that agility’s effect is greater than flexibility’s effect in improving responsiveness to disruptions in supply and demand. Thus, for managers who are looking to improve responsiveness regardless of the other objective functions, investing in supply chain agility provides the most improvement on supply chain responsiveness for the firm. For managers looking to decrease the total cost by investing in responsiveness, our study showed that the best strategy is investing 60% in flexibility and 40% in agility. Considering this strategy, the best result of our multi-objective problem has 6.41% deviation from the optimum value of responsiveness, 129.11% deviation from the optimum value of risk, and 46.19% deviation from the optimum value of cost. Moreover, we showed that adding different transportation channels to help improve responsiveness will change the set of suppliers in our supplier selections. Because the primary goal of our model is to improve responsiveness, our model suggests that supply chain managers need to work with a different set of suppliers that have access to the most responsive transportation channels when they are concerned with improving responsiveness and mitigating the effects of disruptions. Finally, the results indicate that when supply chain managers plan to improve responsiveness and appropriately respond to customer demands if a disruption occurs in the supply chain system, the managers should consider responsiveness enablers and the trade-offs among them, and also assess the use of different transportation channels with different suppliers for their firm. When customers are not satisfied with the delivery time and service, managers should invest in supply chain agility. When customer expectation is order size that changes from time to time, supply chain managers should invest in flexibility. 7.3. Limitations and future research There are several limitations in our study. First, we only investigate the effect of supply and demand disruption in the supply chain. Future studies can consider the other sources of risk (process, control, and environmental risk of disruptions) and examine different contingency plans for each type of disruption. In addition, according to Singh (2015), there are 17 important factors that influence supply chain responsiveness. For this study, we only considered two of them; that can be extended in further studies. Moreover, we considered deterministic parameters in our model, without any correlations with each other. 37

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For example, we considered α1 and α2 as parameters that are predetermined by managers and also did not have any correlation with each other. Studies could use them as decision variables and solve a multiobjective non-linear programming (MONLP) problem. In addition, further work can extend the supply chain risk management model presented in this study for service-based companies. In addition, we could consider risk mitigation plans such as inventory planning, regionalization strategies, and back-order policy for our model to address the risk of demand and supply disruptions. We can also utilize scenario-based modeling and the fuzzy method to provide more realistic results about supply and demand risk (Torabi et al., 2015; Jabbarzadeh et al., 2018; Song et al., 2018). Finally, considering more suppliers, various transportation channels, and each supplier’s location can further test the reliability of the proposed NSGAⅡ method for large-sized problems. Acknowledgments This research is based on work supported by the National Science Foundation (NSF) under Grant No. 123887 and 1533681. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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