Rethinking the role of partnerships in global supply chains: A risk-based perspective

Author’s Accepted Manuscript Rethinking the Role of Partnerships in Global Supply Chains: A Risk-Based Perspective Bingcong Zeng, Benjamin P.-C. Yen

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To appear in: Intern. Journal of Production Economics Received date: 21 May 2016 Revised date: 28 June 2016 Accepted date: 17 November 2016 Cite this article as: Bingcong Zeng and Benjamin P.-C. Yen, Rethinking the Role of Partnerships in Global Supply Chains: A Risk-Based Perspective, Intern. Journal of Production Economics, http://dx.doi.org/10.1016/j.ijpe.2016.12.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Rethinking the Role of Partnerships in Global Supply Chains: a Risk-Based Perspective Dr. Bingcong Zenga1*, Prof. Benjamin P.-C. Yenb2 a

Application and Business Services, Hewlett Packard Enterprise, HK SAR Limited, City Plaza One, 1111 King’s Road, Taikoo Shing, Hong Kong b Faculty of Business and Economics, The University of Hong Kong, Hong Kong, Pokfulam Road, Hong Kong [email protected] [email protected]

Abstract Growing global operations on one hand drive cost down substantially but on the other hand make the supply chain more vulnerable to numerous risks. Confronted with increased risks, companies are more inclined to form partnerships and engage in supply chain collaboration consciously. Such inclination for partnerships simulates thinking of its incentives behind in association with risk management. However, traditional literature, confining its focus to individual enterprise, echoes inadequately on the role of partnerships in supply chain risk management. To bridge this gap, this paper refines the notion of risk in supply chains and proposes a model of supply chain risk system which is able to convey a risk-based view of partnerships in global supply chains. Through analytical inference it is shown that the level of collaboration among partners contributes to the resilience of supply chains. This implies that partnerships can positively affect the integration of supply chain risk system, thus benefiting

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operations in supply chains. A simulation program has been developed with aim to demonstrate the practical feasibility of the proposed model. Implemented in simulation, two sets of experiments have been conducted for testing the model in actual business scenarios. The experimental results manifest high consistence with the analytical prediction. Key words: partnerships; supply chain risk management; resilience; modeling and simulation

1. Introduction Nowadays, a high degree of collaboration is required along global supply chains in order to optimize cost structure, leverage service level and improve profit generating ability (Horvath 2001; McCarter and Northcraft 2007; Kauppi et al. 2016). The interconnections between supply chain partners cause numerous new risks, of which the impacting magnitude and scope are larger than ever before. In fact those risks today are not just limited to operations, but have already expended to relationship-related aspects, influenced by partnerships. Under partnerships the risk of an individual company is no longer just the risk of itself and it actually the risk of all the partners (Hallikas and Varis 2009). For instance, if an upstream supplier broke down because of a strike occurring in workplace, it would probably jeopardize the operations of manufacturers in the middle stream and further negatively affect the sales of retailers in the downstream. In other words, the risk of a company is not limited within the boundary of enterprise any longer. Partnerships have been expanding the scope of risk management from enterprise level to supply chain level. It demonstrates new features that deserve extensive investigation.

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Although risks and partnerships have independently been the focus of academic and industry, the existing literature seldom links them together and fails to reflect their recent combined relevance. Therefore, this research project is proposed, with aim to improve understanding of risks in the context of today’s collaborative supply chains where inter-organizational linkages are strengthened through partnerships. Given the context of global supply chains, risks among partners are linked with each other in worldwide scale. In attempt to echo the correlation of risks resulting from partnerships and to construct more accurate notion of it, we draw from the theories of system science and the literatures of risk management to propose a model of supply chain risk system (SCRS). SCRS organizes supply chain risks in a network according to their causal relationships and reflects the partnerships delicately in a risk-based view by topological distribution of risk nodes and a series of chain influencing processes. Through modeling and simulation, our analysis on SCRS reveals that the partners’ collaboration can significantly contribute to the resilience of supply chains. This offers a novel explanation from the perspective of risk management for why nowadays an increasing number of companies are consciously engaged in partnerships in supply chains.

Our next section is devoted to the literature review on partnerships and

supply chain risk management with intention to identify the key issues as well as the research gap in the existing literature. In section 3, the proposed model of SCRS is presented and the impact of partnerships upon supply chains in terms of topological structure of SCRS is analyzed through mathematical inference. The verification experiments and the related results are disclosed in section 4. The main conclusions of the paper are summarized in section 5.

2. Partnerships and Supply Chain Risk Management: Major 3

Issues in the Literature 2.1 Traditional Theories Regarding the Incentives for Partnerships In contrary to traditional arm-length type of buyer-supplier relationships, partnerships are portrayed by industry observers as “becoming closer” (Heide and John 1990). The formation of such close relationships is about “timing”, but more importantly is the matching of “desire” (Dyer et al. 2001). Regarding “desire” the inward force behind driving companies towards alliance and partnerships, academia holds different explanations. Generally there are two theories dominating the understanding of incentives for partnerships: Resource-Based View (RBV) and Transaction Cost Theory (TCT). RBV believes that competitive advantage of a firm stems from the quantity, quality and effective application of strategic resource at the firm’s disposal (Wernerfelt 1984). Unlike TCT proposing to minimize transaction cost as possible, RBV considers a company as a repository of resources, emphasizing making full use of the resource on hand to realize its maximum value (Barney et al. 2001). However, strategic resource is rare, inimitable and non-substitutable, and the resource on hand may not satisfy the requirements of company’s strategic goal, thus inevitably causing so-called “strategic gap” (Crook et al. 2008). Spekman et al. (1998) and Holweg and Pil (2008) both advocated that the natural property of strategic resource makes it unable to obtain through trading in the market. Given that, partnerships emerge as a form that allows companies to share strategic resource on the basis of mutual trust. For supply chain risks, according to RBV, the robustness and resilience of supply chain, some scholars argued, can be treated as a type of strategic resource able to help companies sustain their competitive advantages (Christopher and Peck 2004). Thus, partnerships, from

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risk management point of view, is to more effectively reduce and mitigate supply chain risks, so enhancing the robustness and resilience of supply chains. Nevertheless, this assertion is still very conceptual. It is lacking of strong empirical supporting evidences, and seldom tested by academic research. TCT is established based on the key concept of transaction cost which is referred to a cost incurred in an economic exchange (Ariño and Torre 1998). Its believers assert that partnerships are the best choice for most companies as they are the most efficient option in terms of transaction cost when compared with either traditional buyer-supplier market relationships or vertical integration through acquisition (Kogut 1988). Partnerships enjoy advantage over traditional market relationships by avoiding severe uncertainty and reducing risk, and excel vertical integration structure in saving supreme management expense and daily operation cost (Dyer 1997; Uzzi 1997). Therefore by using TCT partnerships can be interpreted as a form trying to achieve an optimal balance between risk and transaction cost. Applied under the context of supply chains, this assertion conveys an important message that partnerships do impose some effect on supply chain risks. However, the detail regarding “how” is still ambiguous in the literature.

2.2 Research Review on Supply Chain Risk Management Today, managing risks within the enterprise boundary is far from enough (Ritchie and Brindly 2007). Companies start to notice that a number of risks impacting upon them may not exist in the companies but come from their supply chain partners. Therefore, while continuously improving enterprise risk management (ERM) within companies, they gradually pay more attention upon the risks in supply chains. Supply chain risk management (SCRM),

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compared to ERM, no doubt is a relatively new discipline. It is more interested in the coordination and collaboration of processes and activities across functions within a network of companies, with intention to ensure that supply chains are performing effectively and efficiently as normal (Olson and Wu 2008). To cope with the uncertainty from the supply side and the demand side, upstream risk management and downstream risk management have emerged, forming two major research areas in SCRM. Regarding upstream risk management, the main issues include supply network design, supplier relationship management, supplier order allocation and supply contract management. Helper (1991) reported that supplier relationships in U.S. have experienced a great shift from common market transaction relationships to long-term cooperative partnerships in 1990s. Dyer and Ouchi (1996) confirmed the similar situation happed in Japan also. Spekman and Davis (2004) pointed out that interdependency resulting from partnerships is the main source of risks in the supply side, but it is not unmanageable . Zsidisn (2003) provided some useful suggestions to mitigate the upstream risks, including: 1) establishing buffer stock and enhancing inventory management; 2) avoiding single sourcing and using alternative sources of supply; 3) utilizing supply contracts to manage the fluctuation in sourcing price; and 4) adopting quality initiatives to implement comprehensive quality management Normally in supply chains the supply capacity is fixed in most cases whereas the demand is changing all the time. Thereby companies are required to apply various downstream risk management strategies to lower the probability of mismatch between the static constant supply and the dynamic uncertain demand. The literature is abundant in this area. Carr and Lovejoy (2000) developed a mathematical model to identify an optimal portfolio of demand

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distributions, and Van Mieghem and Dada (1999) from an economic view made an in-depth analysis on how to through dynamic pricing make an appropriate response to the unstable demand. Regarding the phenomena that companies set different price at different time, the literature explained this as a strategy of risk mitigation. Pricing higher in peak seasons is actually to shift demand to off seasons rather than to grasp high profit margin from the customers (Dana 1999). It is found that the pricing mechanism is not only able to shift the demand across the time but also to shift the demand across the products. Chod and Rudi (2005) showed us a vivid case in which a higher profit can be obtained through adopting differential pricing strategy to entice customers to shift the demand from one product to another . In the context of supply chains, physical experimentations suffering from technical and cost related limitations are difficult to implement in risk research (Law 2007). Simulation is considered as an effective method to model and analyze risk cases of large scale. There are a number of good studies of SCRM using simulation in the literature. E.g. Swaminathan et al (1998). It adopted agent-based simulation to model supply chain dynamics and provided a rapid decision supporting tool for risk management. Deleris and Erhun (2005) presented in their paper a Monte Carlo simulation with which different levels of risks in supply chains can be analyzed sophisticatedly. Jain and Leong (2005) viewed supply chains as a complex system and demonstrated the advantages of constructing supply chain simulations to “stress test” the system and investigate its performance under risk situations. After an extensive literature review above, we are aware that the previous literature more or less has propensity to focus SCRM upon discrete sectors, mainly confined in either upstream

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or downstream risk management. Most of research is concentrating upon solely one area, and there are few studies that provide an integrated view of the whole supply chain from risk management perspective. Furthermore, although a variety of risks, e.g. inventory risks, delay and quality risks have been carefully investigated, researchers maybe in order to retain the focus on the major problem prefer to treat them isolated, and hence their internal correlations are seldom studied in the literature. Yet, increasing engagement in partnerships generates interdependency among partners, and their risks are twisted with each other tightly with progression of their close relationships. This study contributes in bridging those gaps by investigating supply chain risks as a system, reflecting the correlation effect among risks and offering a risk-based view of partnerships in supply chains. Considering the scale as well as the constraints of this study, simulation is chosen as the research’s confirmatory methodology, for its fitness to SCRM studies suggested by the literature.

3. Conceptual Development and Model Building 3.1. Modeling Individual Supply Chain Risk What is a risk? It is the fundamental problem every study of risk has to confront. Although countless answers subjected to various perceptions are conferred by the literature, their essence is not out of the below four interpretations, including viewing risk as hazard (Mlynczak and Sipa 2008), as probability (Dani 2009), as consequence (Hendricks and Singhal 2003), and as potential adversity or threat (Kleindorfer and Saad 2005; Li et al. 2015) . Whatever hazard, probability consequence, or potential threat, they all agreed risk is uncertain, which may occur sometimes and not occur in other time. There must be a law of

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probability governing its occurrence (Knight 1965). Once the risk happens it should cause some negative consequence like adversity or hazard. The reasons leading to the risk were grasping people’s attention. Researchers were searching all possible approaches for the origin of the risk. However, it turned out to be a tantalizing conundrum at the end when traced back to the root of the reasons of the reasons. The origin seemed to be an unknown black box or too complicated to be understood by people; thereby researchers gave it a name “uncertainty”. Despite there used to be a period of time when academia argued for “does uncertain produce risk or risk begets uncertain?”, today scholars have reached a consensus nearly that it is the uncertainty that causes the risk (Dani 2009). Through the previous discussion it is revealed that risk as an entity is not simple. It should be a complicated object consisting of multiple components (Lewis 2009). In the model proposed in Kaplan (1997), the risk portrayed as a triplet with the combination of probability, consequence and scenario. Following this way of thinking, we argue that risk is at least made up of three essential components: (1) a driver or drivers which trigger the risk to happen; (2) an event with probability that signifies the occurrence of the risk; and (3) a consequence or consequences resulted from the risk. By considering the three critical elements of risk and incorporating the conception of correlation among risks, we propose a model named Risk with Casual Relationship (RCR) to describe an individual risk. Figure 1 shows it graphically.

The model of RCR gives an understanding of risk with causal relationships, which depicts the causation process instead of offering a static definition. Keeping in line with traditional interpretations regarding risk, RCR contains “drivers”, “event” and “consequences” in the

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conception. The model defines risk as an event that occurs in probability. It is denoted as a circle in the middle (See Figure 1). Nonetheless the isolated circle itself is unable to constitute a risk. It is qualified as a real risk only when it occurs with causes (those are referred to drivers) and effects (those are referred to the negative consequences). Given that, when judging the risk, we shall not make decision solely based upon whether it is an event with probability or not. It will be confirmed as a risk if it can result in some negative consequences. In addition, the occurrence of such an event needs drivers, the antecedents that generate the risk. Noticing the correlation among risks, we infer that the drivers should not just involve the factors that lead to the risk event, but it is also possible that some other risks which took place antecedently could create a ripple effect and thus trigger the risk event to occur. Therefore, the drivers can be either factors or other risks: Driver (D) = Factor (F) | Risk (R) In the expression above, the factors are mainly referred to the causes which are uncontrollable or immeasurable. They can be perceived in abstract ways. It is hard to capture those using specific indicators. The main difference between a factor and a risk in our model is that a risk occurs in probability whereas a factor is like uncertainty which is almost impossible to be quantified, and even if it can to some extent, it is always unchangeable. One of the typical examples of “factor” is political climate. It is surely uncontrollable for supply chain firms. An unstable political climate can produce numerous risks, for instance a strike risk in the factory that will make serious disruptions in supply chains. However, firms can do very little to political situation. In most cases they have to accept the factor and adapt to it. Consequences in RCR model are referred to the negative result brought by the risk. There are

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two possible situations. One consequence is that it results in a direct harmful impact which can be quantified financially. The other one is that it causes another subsequent risks being triggered which may make other bigger loss in the later time. Therefore, put into a mathematical expression, it is Consequence (C) = Impact (I) | Risk (R) In the expression above the impact is defined as the ultimate loss able to be quantified financially caused by the risk. To sum up briefly, the model of RCR conceptualizes individual risk as a stochastic event with reasons and consequences. The risk event happens, requiring antecedent drivers that can be either factors or other risks. If the drivers has been activated, in other words, the conditions of triggering the event are satisfied, it does not imply the risk will occur at once. It only reflects that the probability of its occurrence is extremely high. While some risks will generate negative impact which directly causes financial loss, others will lead to certain harmful damage in an indirect manner through activating another risk in a consequence.

3.2. Modeling Supply Chain Risk System When risks are linked up according to their causal relationships, those will constitute a risk causality network (RCN). RCN is a general aggregation model on the basis of RCR. To secure the causality in between, we suggest the risks in RCN should be at the same level. Up to specific application, RCN can be aggregated to a more strategic level or drilled down to certain operational level. In fact, its organization is not arbitrary and there are 3 rules governing its construction: 1) the initial risk node of RCN must be triggered solely by factor(s); 2) RCN should end with risk nodes that result in negative impacts only; 3) the

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causality among risks involves the time sequence. So the antecedent risk must happen before the triggered risk. This property determines that RCN must be an acyclic graph. RCR and RCN are two fundamental concepts that assist us in modeling risks in supply chains. Although conceived in a general level that ignored the application context, they have been conceptualized with the key features of supply chain risks. The correlation of risks in supply chains can be reflected fully in the casual relationships both in RCR and in RCN. RCR provides an appropriate template for supply chain risks modeling, and supply chain risks can easily be specified following the conception of RCR. Table 1 shows a list of supply chain risks in the process of sourcing. It demonstrates a well fitness of applying RCR in the context of supply chains. Similarly, the supply chain risk system (SCRS) can be engendered by a specific application of RCN in supply chains (Please see Figure 2).

Essentially SCRS is a network constructed by a number of individual risks in supply chains following their casual relationships. Unpredictable environmental factors will trigger the initial nodes to be realized. For instance, price instability of raw material will give rise to the realization of flawed co-forecasting risk on the supply side. Then the manufacturer may shrink its purchase order of the inventory if the price is too high to be afforded. It could cause the occurrence of inventory shortage risk when the customer demand is strong, and the chain effect may result in manufacturing stoppage, leading to serious disruptions of operations in supply chains. The state of a risk node of SCRS at time t is determined by two key factors. They are the marginal probability of the risk node and its correlations with other risk nodes. The node state

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therefore can be expressed as below in a set form with time property: RSt ={Pi, corrij}t

(1)

where RSt denotes the state of SCRS at time t, pi is marginal probability of a risk node i, and corrij is the causal correlation between risk node i and j. pi measures the likelihood of risk node to happen. The other key factor corrij depicts the relationships among the nodes and it also reflects the topological information of SCRS. The value of both factors can be computed using the statistical data available in nowadays’ ERP system. Even though the enterprise database does not have the required data, it can be suggested and estimated by supply chain risk management experts. At different time t, RSt changes with the risk occurrence probability pi and SCRS layout structure corrij. There are a number of factors, like economic climate, industrial practices and partnerships which impose influence on it (See Figure 2). In this paper, we mainly focus on how the topological structure of SCRS is impacted by supply chain partnerships.

3.3. Measuring Resilience of Supply Chain Risk System Robustness and resilience are two key concepts in SCRM. To large extent, they indicate the performance of risk management in supply chains. Robustness of supply chain is referred to the ability of supply chain to resist the impact of risk and retain the same stable situation as it had before the occurrence of risk (Asbjørnslett 2009). Confronted with risk, a robust supply chain is able to cope with it so that the negative impact of risk will cause very little harm to supply chain operations. In contrary to robustness, resilience is referred to ability of supply chain to return to a new stable or desirable situation after the impact of risk (Asbjørnslett 2009). A resilient supply chain is able to adapt very quickly to the new change brought by

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risks and then operate in a stable manner again. In this paper, our focus is more on resilience and we would like to measure it quantitatively within SCRS. A risk node in SCRS has two states. To make the concepts more understandable we borrow the terms in epidemiology. The two states are named the “healthy” state and “infected” state by analogy with virus infection. The healthy state indicates that the risk event remains inactive whereas the infected state means the risk event has been triggered by environmental factors or other supply chain risks. The risk node that is healthy has the probability to be turned into the infected state for each time point t. The infecting mechanism involves two cases. In the first case when the antecedent nodes are not infected, the healthy risk will be triggered by its marginal probability. However, in case two, if one or more of its antecedents have been infected, the probability of the risk to be triggered, by reasoning, must be higher than the first case. So it is by conditional probability that the risk in the second case is triggered. When risk nodes are infected in SCRS, they may cause troubles in supply chain operations. Therefore the companies involved have to take actions to restore the infected nodes back to the healthy state. The effort they made may succeed or fail, determined by the recovery rate that is a probability by which the risk node is able to return from chaos to normality. In general the infected risk node can come back to health more quickly as the recovery rate increases. Hence, the recovery rate of SCRS should be a good measure to reflect supply chain resilience. To some degree, the recovery rate shows the level of resource the companies devote in supply chain risk management. Its improvement takes cost. It requires significant input of capital in risk analysis and mitigation method development. But in the real world, on one hand very

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few companies can afford it; on the other hand they are all noticed that it is important to maintain an acceptable level of the recovery rate otherwise they will suffer a huge loss for the chaos in supply chains. In the model of SCRS, a minimum requirement for the recovery rate, we are aware, must exist. If this threshold value is failed to be catch up with, the supply chain will persistently suffer from chaos. In Chaos, healthy risk nodes are triggered by conditional probability instead of marginal probability, and thus the chain effect of infection will go on and on and never stop, since the recovery rate is too low to suppress the spawning chaos. It will result in a disaster to the whole supply chain. In the following parts, the recovery rate is analyzed using a mathematical model which is developed based on SCRS, and the threshold value of the minimum requirement is obtained by analytical reasoning. Below is the detail of the model settings. We suppose n risk nodes in SCRS, and pi(t) is defined as the probability by which risk node i is triggered at time t. Assume that j=1,2,…,k are the antecedent nodes of node i, and Δ is the average recovery rate of the supply chain. We denote the triggered rate matrix of n  n as Г. Its mathematical definition is shown as follows:  11  12   =  21  22  ... ...   n1  n 2

...  1n   p11 d ...  2 n    p 21 ... ...   ...   ...  nn   p n1

p12

...

p 22 ... ...

...

pn2

...

p1n  p 2 n  ...   p nn 

where pii which is the diagonal element in the matrix represents the marginal probability of risk node i, and pij the non-diagonal element denotes the conditional probability given that node j is infected. According to the theory of statistics, pij is positively associated with corrij (Please refer to Formula 1). It implies that given other condition unchanged, when the correlation between node i and node j becomes stronger, the probability of node i to be triggered will be higher if node j has been infected. In other words, γij the triggered rate of 15

node i given that node j has been infected is equal to the conditional probability of node i given that node j has been infected. In case that risk node i is not infected at time t-1, the probability of infection at time t is the sum of probabilities of being triggered by the k antecedent nodes. By definition, the probability that node i is not infected at time t-1 is [1-p(t-1)], and thus the probability of being triggered by its antecedents is

k

 γi j pj(t-1).

Hence the probability of being trigged from its

j

k

neighbors should be [1  pi (t  1)]  ij p j (t  1) . j

In case that node i has already been infected at time t-1, the probability that it remains in the infected state at time t is the joint probability that it was infected at time t-1 and the probability that it fails to recover. Therefore the probability of failure to recover when already inflected should be (1-Δ)pi(t-1). By adding up the two events (including the case of being triggered and the case of remaining inflected), we can obtain the probability that node i is in the infected state at time t: k

pi (t ) = [1  pi (t  1)]  ij p j (t  1) (1   i ) pi (t  1) where i=1,2,…,n j

Put it into matrix form, the equation will be P(t ) = [1  pi (t  1)]P(t  1)  (1  ) P(t  1) = {[1  pi (t  1)]  (1  ) I }P(t  1)

where i=1,2,…,n, and p(t ) is a column vector [ p1 (t ), p2 (t ),..., pn (t )]T

(2)

A dynamical system with Markov chain property is shown in an elegant form in Formula 2. The state equation is ideal except for the term [1-p(t-1)] that does not fit nicely into the formulation. If p(t-1) is assumed to be very small, so 1-p(t-1)≈1, then the simplified equation will be: P(t )  [  (1  ) I ]P(t  1) 16

(3)

It is reasonable to have the above assumption in the model of SCRS. Normally, risk occurs in supply chains in small probability (Ovdiu and Dekker 2005; Zikopoulos and Taharas 2007). According to Ovidiu and Dekker (2005), this feature does not change along the time. For SCRS, in usual cases risk nodes are triggered in marginal probability which should be small. When antecedent nodes have been infected, conditional probability is as the triggering probability, but it is still very small in most occasions. Thereby, assuming P(t-1)≈0 will not cause big loss of accuracy in P(t), and Formula 3 should be a good estimation for computing P(t). To further simplify the form, we let [  (1  )I ] be S and name it to be the system matrix. Then we obtain the first order difference equation as below: P(t)=SP(t-1)

(4)

When P(0) is given P(t)=StP(0)

(5)

We use ρ(S) to denote the largest nontrivial eigenvalue (spectral radius) of system matrix S and ρ(Г) to represent the largest nontrivial eigenvalue (spectral radius) of triggered rate matrix  .Through a mathematical inference, it is found that ρ(S) and ρ(Г) have the following relationship: ρ(S)= ρ(Г)+(1-Δ)

(6)

(For the proof, please refer to the appendix) P(t) depicts the system state. As shown in Formula 5, SCRS is a dynamic system and it reflects convergent property in terms of system state if ρ(S) <1. Formula 6 further reveals that the convergence happens when Δ is larger than ρ(Г). To be more specific, it means supposing at time t=0 the supply chain falls into the chaos state which is P(0), and then as time passes by, the system state P(t) will converge and return to a stable state if the recovery rate Δ>ρ(Г). 17

In the stable or normal state, the risk nodes of SCRS are triggered by marginal probability. Given that the convergent speed to some extent measures the supply chain resilience. SCRS can recover from chaos to normality more fast when the spread increases between Δ and ρ(Г). However, in case that Δ<ρ(Г), the supply chain will continuously remain in chaos where most of risk nodes in SCRS are triggered by conditional probability rather than marginal probability. Under this situation risks are realized by higher chance, probably causing serious disruptions and catastrophic loss in supply chains. In order to prevent persistent chaos, Δ should be kept above the level of ρ(Г). In other words, Δ* =ρ(Г) is the threshold value of the minimum requirement for the recovery rate.

3.4. Supply Chain Resilience and Partnerships As we discussed in the previous section, the threshold value of the recovery rate Δ* is equal to the largest nontrivial eigenvalue of triggered rate matrix Г. It is determined not only by the marginal and conditional probability of each risk node but also by the topological structure of SCRS, which is referred to how the risk nodes are organized and through what patterns they are distributed. There are two typical network structures in terms of the orderliness and regularity. They are named random graph and scale-free network. For random graph it is a network whose components are organized in a random manner, and no distribution pattern can be recognized in the topological structure (Edelsbrunner and Harer 2010). For scale-free network it is a system in which a regulation holds regardless the scale of the system, that is a small portion of its components has high degree of connections whereas the large portion has very low degree of connections with other components (Edelsbrunner and Harer 2010; Lewis 2009). To construct a scale –free network, when adding a new node each time into the system,

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the nodes with higher degree of connections will more probably be chosen to connect with. On the contrary, the nodes with lower degree of connections will have less chance to be connected with. Following this mechanism we can obtain a scale-free network. As partnerships are growing tremendously in supply chains, companies have higher propensity to be engaged in collaboration. They enjoy cooperating with each other through a series of joint activities to accomplish key operations. Normally those joint activities are located in the core modules of supply chain operations which are associated with a number of processes, thus able to impact the supply chain in a large extent. If they encounter problems, the operations in the supply chain will be greatly jeopardized. In the model of SCRS, the risks hidden in joint-activities are categorized into collaboration risks. When the partnership goes deep, partners will collaborate more frequently and they prefer to co-work in form of joint-activities rather than working individually (Fynes et al. 2005b). Therefore more collaboration risks will be generated. For most of collaboration risks are key nodes with high degree of connections, the change brought by partnerships reflected in SCRS in terms of topological structure is a process of transformation from random graph to scale-free network (See Figure 3).

System science uncovers a fact that compared with random graph, scale-free network is a more organized system (Edelsbrunner and Harer 2010). According to the theory of topology, ρ(Г) of scale-free network is smaller than the one of random graph. Hence, Δ*, the minimum requirement of the recovery rate for scale-free network is lower than the one for random graph. It implies that partnerships cause SCRS to transform towards a more organized system

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so that the minimum threshold Δ* required for the recovery rate becomes lower. Furthermore, Formula 6 ρ(S) = ρ(Г)+(1-Δ) shows that when ρ(Г) drops, ρ(S) will decrease from 1 to 0 given Δ>ρ(Г). In this case, the smaller ρ(S) is, the faster the dynamic system converges. It means the decrease of ρ(Г) can speed up the recovery process of SCRS from chaos to its normal state. Thus, we can reach a conclusion that the supply chain resilience is negatively associated with ρ(Г). The impact of partnerships upon SCRS is to make the risk network evolve from a relatively random structure towards to a more organized system, finally resulting in smaller ρ(Г). Such an influence can benefit the recovery process and make positive contribution to the resilience of supply chains.

4. Verification Experiments Based on the analysis above, we have drawn two important conclusions as below: (1) There is a minimum requirement for the recovery rate that prevents SCRS from persistent chaos, and the threshold value Δ* is equal to ρ(Г) (2) The effect of partnerships can make SCRS more likely evolve towards a more organized and regular system (transforming from random graph to scale-free network). It results in lower ρ(Г) and Δ*, so that it can speed up the recovery process and contribute to the resilience of supply chains. The two conclusions are largely based on analytical reasoning, and they lack empirical evidence to verify their reliability. In addition, some simplification is made in the analytical model, for example it assumes that the probability to trigger the risk event is very small. Its effect on accuracy needs to be tested further. Therefore, in this study simulation is employed as the verification method to test the conclusions mentioned above. In fact, simulation is the

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only feasible choice under the rigorous research requirement of this study. First, empirical data is difficult to collect in practice. Although the concept of risk management has been raised for nearly 20 years, few companies record down and store the risk data in their database (Melnyk et al. 2009). Second, our research target is on the supply chain which involves multiple companies. Obtaining consistent historical data across different companies is extremely difficult. Moreover the key research scenario is set upon making the supply chain recover from chaos back to normality. Only simulation is able to construct such a specific scenario that the research requirements are fulfilled.

4.1. Design of Simulation Experiments We have developed a simulation program to implement the attributes and behaviors of the model of SCRS. To provide the required degree of scalability, Java has been chosen as the programming language for its powerful multi-threading features which can make the simulation process more close to the reality. Figure 4 shows a snapshot of the system. It is developed as a Java applet and thus can be run on Java Virtual Machine in OS environment or be embedded in Internet Browsers. The simulation program provides a platform that enables researchers to create the business scenarios they are interested in and conduct simulation experiments to study the risks in supply chains.

In order to verify the two key conclusions we derive from the analytical model, two set of experiments are designed in this study. The first set of experiments is called threshold tests. Its aim is to confirm whether Δ* is equal to ρ(Г) by simulating the process of SCRS from

21

chaos to normality. There are four core steps involved. Step one is to construct the SCRS to model the real scenario in business. To obtain the empirical data, from 2009-2012, we visited a Fortune 500 manufacturing company in Shenzhen, P.R. China several times and conducted interview with the supply chain experts there. The experts who were selected to participate in our study should meet three criteria. First, the participant should have more than 10 years of working experience in supply chain management; second, he/she now is working in the position related to supply chain risk management; and third, he/she has to agree and understand our model of SCRN. There were four experts qualified. For the information regarding the position of risk nodes and the causal linkages in SCRN settings, it is suggested by the experts. In order to guarantee the data representativeness in the study, we held the group interview instead of interviewing the expert individually. The benefit is that the data suggested must be agreed by four experts; otherwise it would not be used in the study. The agreement in group can tremendously increase the data representativeness. For the marginal probability and conditional probability of risks, due to unavailability of the data, they are generated by the computer algorithm. Lewis (2009) suggested that a small probability should be below 0.3. Adopting this suggestion, we generate the marginal probability following the uniform distribution within the interval of (0, 0.2) and conditional probability within the interval of (marginal probability, 0.3) for conditional probability must be larger than the marginal one. In this network settings the value of ρ(Г) can be obtained by computing the largest eigenvalue of  matrix. A positive value of ρ(Г) is assured by Frobenis-Perron theorem. It has proved that for a positive square matrix (  matrix is a positive square matrix) there must be at least one positive real eigenvalue. In the second step the normal state of

22

SCRS is recognized and recorded down. The simulation program allows us to simulate the process when SCRS operates in a normal state. In the simulation of the normal state, the number of the active nodes at each time t is marked down and stored in the database. For each time t we call it a run. In each experiment we simulate the process for 20000 runs in order to capture sufficient time series data to depict the normal state of SCRS. Step three simulates the process of SCRS from chaos to normality and its goal is to obtain Δ*. We refer the chaos state to the situation in which SCRS is overwhelming with risk events and most of the risk nodes are triggered by conditional probability. This situation can be simulated with the program. When the system is already in chaos, we can assign different recovery rates to check the system state and see whether it has been recovered back to normality. In order to make the correct judgment, we compare the current state with the normal state which has been captured in step two, using two-sample t-test. If the p-values of t statistic (t-test is to test the means) and F statistic (F-test is to test the variances) both exceed 0.05, we can confirm that the SCRS has returned to normality. Through try-and-error, we can obtain Δ* which is the minimum requirement of the recovery rate that makes the system from chaos back to the normal state. In the last step, the correlation between Δ* and ρ(Г) is examined. Given ρ(Г) obtained in step one and Δ*in step three, we can check their relationship and verify whether there really exists a strong correlation between them as predicted in the mathematical model. The second set of experiments is called topological tests. They are designed to test whether Δ*of a scale-free network is actually smaller than Δ* of a random graph system through simulation. First, SCRS with topological structure of scale-free or random graph is generated. Barabasi-Albert (BA) approach is chosen as the network generating algorism for scale-free

23

system whereas Erdos-Renyi (ER) approach is used to construct the random graph (for detail about BA algorithm, please refer to Barabasi et al. (1999); for ER, please take a reference to Bollobás (2001)). The major goal of this simulation is to test the effect brought by the topical structure, not the probability factor of the risk node. Thus in order to guarantee the comparability of the two types of networks, the program developed for topological experiments by default generates the same amount of links, and the same amount of risk nodes with constant marginal probability of 0.1 and constant conditional probability of 0.15. After that, we can carry out the similar procedure as in threshold tests to obtain Δ*, and then make comparison of Δ* of the two type of network. Theoretically speaking, Δ*of scale-free network should be less than the one of random graph, implying that it is easier for an organized system to recover from the chaos.

4.2. Experimental Results and Discussion The threshold tests consist of 4 business scenarios pervasively existing in supply chains (We present the Layout of SCRS of Scenario One in Figure 5 3 ) and each scenario includes 20

experiments. The final experimental results are summarized in Figure 6.

The statistics of regression analysis manifest that there is a strong correlation between Δ* and ρ(Г). The simulation results confirm the inference derived from the analytical model that *

*

Δ is equal to ρ(Г).Through extensive experiments, it is able to reach a conclusion thatΔ the threshold value of recovery rate is highly correlated with ρ(Г) and their correlation is approaching nearly 1, and this provides strong supporting evidence to bolster the argument

3

Considering the limit on length of the article, we only present the layout of SCRN of Scenario One. If the audience is interested in the other three scenarios, please contact the authors. 24

thatΔ*=ρ(Г), which has been shown theoretically. The topological experiments in all contain 10 experiments. They contrast Δ* of SCRS in scale-free with the one in random graph. Table 2 makes a brief summary of the experimental results.

The information shown in Table 2 supports the fact that Δ* in a scale-free network is always smaller than the one in a random graph. It implies that the minimal threshold value of the recovery rate reduces when SCRS transform towards a more organized and regular network. Figure 7 plots the fault rate of random graph and scale-free network in the 10 experiments when Δ=0.7. It is shown that the curve of random graph is strictly dominating the whole curve of scale-free. It manifests that under the same situation, less risks will be triggered in scale-free than in random graph. Surprisingly, the difference is greater than we expect. The fault rate in scale-free network is 5% less than the one in random graph on average. Moreover in terms of the speed of recovery scale-free network is 25% faster than random graph. In a word, the scale-free is a more preferable topological structure than the random graph for supply chain risk management.

In sum, the model of SCRN offers an understanding of risk with causal relationships. There are multiple factors that impose effect on triggering probability of risk node. In different industry and different economic environment, factors are varied, and thus risk types and causal relationships are also changed.

It will lead to different topological structure of the

SCRN. Nonetheless in general, the risk nodes in SCRN are still triggered in small probability.

25

Even though the antecedent nodes are infected and risk nodes are triggered in conditional probability, the triggering probability is still small in most of cases. In very few nodes, we have to admit, there could be some cases that probability is not small enough. However, taking the perspective of a system, the assumption we made for equation (3) in Section 3.3 holds. In order to show such simplification does not hurt the accuracy of the model, we have conducted simulation to further verify. The simulation contains two parts. The first part named “threshold tests” has confirmed that Δ* is equal to ρ(Г) by simulating the process of SCRS from chaos to normality. The second part named “topological tests” has verified Δ*of a scale-free network is actually smaller than Δ* of a random graph system through. In order to make the two networks comparable, the topological data is generated by computer algorithm given the same nodes and links, and the probability data is given the same value. Although such settings are not practical, they are necessary for comparing Δ* under two types of topological structure. While the topological structure is evolving from random graph to scale free, Δ* is becoming smaller. It implies that the minimal requirement for recovery rate from chaos to normality is lower during this change. As the partnership can make the risk system evolve towards a more organized network (from random graph to scale-free in terms of topological structure), it can reduce the threshold value of required recovery rate, and speed up the recovery process for a risk node. The reason behind would be that the partnership helps reduce the probability of risk to be triggered when supply chains begin to recover. Under partnerships, though the conditional probability is much higher than its marginal probability, most of the nodes are triggered by their marginal probability rather than the conditional probability during the recovery process due to the

26

effect of topological structure. Given that, partnerships do make positive influence on supply chain risk management.

5. Conclusions Supply chains are going globally. The on-going trend of focusing more upon core competencies and keeping engaging in offshore outsource has caused dramatic growth of the interdependency among supply chain companies. Together with such a development, more and more companies are interested in cooperative relationships and are intentionally forming strategic partnerships. In traditional explanations, partnerships are for achieving advantages in competition (in RBV) and cost (in TCT), which can lead to supreme supply chain performance. Despite that the benefits it brings to operations have been widely recognized (Fynes et al. 2005; Lee 2002; Robson et al. 2008), its role in supply chain risk management is seldom explored in the literature. This study uses modeling approach to shed light on this field. The model proposed conceptualizes correlated risks into a supply chain risk network, capable to reflect the ripple effect resulted from partnerships. It can be applied in practice to assist managers in analyzing supply chain risks inside or outside the company. More importantly, it through linking resilience with the shape of risk distribution in the network innovatively reveals the impacts of partnerships made on supply chain risk management. Figure 8 below in a graphical manner presents a theoretical summary derived from this study.

Partnerships are effective strategies for seeking stability. They can enable supply chain networks to exhibit long-term and responsive collaborative behaviors. Under it more process integration and coordination happen within and between partners. Those cause some risks

27

twisted and some other untwisted, but overall speaking the correlations among risks in supply chains are being strengthened. Moreover it is found that the risk profile is under changing also. Companies who collaborate as partners would like to engage in joint processes rather than working individually. They prefer to take advantage of partners’ strategic resource to enhance their own operations. The enterprise boundaries become blurred when more and more internal operations are being collaborative process. Under this circumstance a number of internal operational risks are transformed into or even merged to be collaboration risks. Those are reflected in supply chain risk system (SCRS) that the centricity of the system is greatly increased and collaboration risks as the center nodes have strong diffusion impact on the risk nodes nearby. It implies that when partnerships go deep, SCRS will evolve towards a more organized and centralized network in which its integration will be continually improving. A more integrated SCRS tends to be more responsive and hence it is able to help supply chains recover from chaos to normality more quickly. This study shows crucial fact that partnerships can significantly contribute to the resilience of supply chains and benefit supply chain risk management. This offers a novel view from a risk perspective to explain why an increasing number of supply chain companies are consciously engaged in partnerships nowadays. However, we have to say the improvement of resilience brought by partnerships comes at cost. Too close relationships may result in over interdependence among partners. The whole supply chain could be at danger of crash if one of the partners fails. It reminds us that as managers determine appropriate practices to manage supply chains, the partner selection, relationship investment and supply chain design, all of those should take into account risk issues. Furthermore, because of partnerships, supply

28

chain risks are inter-twisted tightly in a complicated but center-inclined network. Special attention needs to pay on the key nodes with high degree of connections. For their critical positions those nodes should be prioritized in risk management profile, and companies involved are strongly recommended to work together and take proactive approach to mitigate and control those risks. One of the practical implications of this study is that partnerships need to be implemented not only in operational collaboration but also in managing supply chain risks. It is understandable that managers intend to protect the operations within their profit scope and it seems true the best result would come if each member could take good care of its own risks. However, in reality such isolated risk management approach will increase and amplify the risks rather than reducing them. For instance, a strategic supplier who wants to limit its inventory risk exposure, he lowers the inventory level by holding less stock for his own benefit. But his action meanwhile may potentially increase the risk of shortages and disruptions through the whole chain. Essentially speaking, what he does is transferring the risks to other partners. It makes no contribution to reducing supply chain risks. Instead, it may increase the overall risk level and cause supply chains to become more vulnerable. In fact, no one link or party in supply chains can has the sufficient information to identify and manage risks comprehensively. To really tackle the risks, as Jüttner (2005) suggested, partners should expand their interests beyond their own companies and broaden their view to the whole chain. More importantly, they need to commit resources to cooperative supply chain risk management and the driving incentive comes from the belief that the benefits it brings will outweigh the costs it pays.

29

Today’s global supply chain normally contains hundreds of members, or even thousands. It is infeasible to get them all work together on risk management. A more realistic way is to let a small number of close partners cooperate first. Probably, the leading companies in supply chains could initiate the cooperative risk management with their key suppliers and customers to reduce local risks in SCRS. Over time it is expected that more companies will join the initiatives and the scope of cooperative risk management will continue to expand. With progress going further, different initiatives may grow and overlap, conferring a better coherent view of risks in supply chains. Theoretically there is an inevitable progression towards larger scope of cooperative risk management, since companies are continually pursuing better supply chain performance. In practice, cooperative risk management is still limited within close partners, and therefore the extent of cooperation in risk management is highly depended on the scope of partnerships. Future study will extend the analytical model to include more dynamics in different time stages. Constant recovery rate and static correlation among supply chain risks are assumed in the current model for keeping a certain degree of simplicity. In the future model, they would be allowed to dynamically vary with time proceeding. Future research may also focus on the study of investment required to mitigate and control the risks in SCRS given specific scenarios. For studying the risk control investment, it is critical to know the extent to which the correlations between risks in supply chains would differ subjected to the stage of the alliance and to the aspect of costs and benefits of the partnerships. How to adjust partnerships to optimize risk correlation in supply chain risk management? Then how to minimize the required investment in order to achieve an expected result? Those are significant questions to

30

investigate in the future. We feel we have only scratched the surface and it is hoped that our study could inspire researchers and practitioners, and help them form a new perception regarding the relationship between partnerships and supply chain risk management.

7. Appendix Lemma: Given the i th eigenvalue of S is in the form of i , S  i ,  (1   ) , the eigenvectors of S are the same as those of  . Proof: Let u i , be the eigenvector of  corresponding to eigenvalue i , . Then, by definition,

 u i , = i ,  u i , .

S=   (1  )I S u = u  (1 )u i ,

i ,

i ,

S u i , =  i , u i ,  (1   )u i , = [i,

 (1  )]ui,

Therefore, i , S  i ,  (1   ) , and the eigenvectors of S are the same as those of 

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TABLE 1 A List of Supply Chain Risks in the Process of Sourcing Risk Name Supply disruption risk (Dani 2009; Rowbottom 2004)

Drivers

Event Indicator

Consequences

- Unstable political climate(F)

Supplier terminates the

- Damaging the trust in

- Payment delay (R)

supply

partnership (I)

Supplier commitment

- Competitor seducing supplier

risk

to jump out of the contract (F)

Supplier terminates the

risk (R)

(Dani 2009;

- Supply disruption risk (R)

supply contract

- Material inventory

Rowbottom 2004)

- Payment delay (R)

shortage risk (R)

- Supplier transportation risk

- Material inventory

Long lead time risk (Blome and Henke 2009; Zsidisin 2003)

(R)

The lead time runs out

shortage risk (R)

- Offshore procurement risk

of the safety range

- Manufacturing stoppage

(R)

risk (R)

Material inventory shortage risk

The material inventory

- Long lead time risk (R)

level is lower than the

(Blome and Henke

safety stock level

2009; Zsidisin 2003) Payment delay (Blome and Henke 2009; Hallikas et al. 2004)

Manufacturing stoppage risk (R) - Supply disruption

- Cash in short (F) - Problems with the

Late pay to the supplier

accounting system (F)

risk(R) - Damaging the trust in partnership (I)

Offshore procurement risk (Hallikas et al.

- Manufacturing stoppage

Purchase the raw - Low cost of procurement (F)

2004)

material from offshore suppliers

Note: F: factor; R: risk; I: impact 37

- Long lead time risk (R)

TABLE 2 Type

Summary of Threshold Values of Recovery Rate in Topological Tests Exp.

1

2

3

4

5

Setting

N=10 L= 10

N= 10 L= 20

N= 20 L= 30

N= 30 L= 50

N= 50 L= 80

Random

*

0.2517

0.3759

0.3147

0.3272

0.2905

Scale-free Type

*

0.1045 7 N= 130 L= 210 0.3371

0.1042 8 N= 210 L= 340 0.4112

0.1051 9 N= 340 L= 550 0.3425

0.1057 10 N= 550 L=890 0.3413

0.1078

0.1093

0.1121

0.1163

Random

*

0.1058 6 N= 80 L= 130 0.3286

Scale-free

*

0.1066

Exp. Setting

Note: N: number of risk nodes; L: number of links

Drivers (Ds)

Risk (R)

Consequences (Cs)

FIGURE 1 Model of Risk with Causal Relationship (RCR)

Partnerships Factor (F)

Supply Chain Risk System (SCRS)

Risk (R)

Risk (R) Factor (F)

Factor (F)

Risk (R)

Risk (R)

Impact (I)

Economic Climate Impact (I)

Industrial Practices FIGURE 2 Supply Chain Risk System (SCRS)

38

FIGURE 3 Effect of Partnerships on Topological Structure of SCRS

FIGURE 4 Snapshot of SCRS Simulation Program

39

Scenario One: S-M-D 1. Flawed Co-Forecasting Risk in Supply (P) 2. Flawed Co-Forecasting Risk in Demand (P) 3. Supply Commitment Risk (S) 4. Sole Sourcing Risk (S) 5. Inventory Shortage Risk (S) 6. Material Quality Risk (S) 7. Manufacturing Stoppage Risk (M) 8. Finished Goods Shortage Risk (M) 9. Strike Risk (M) 10. Logistics Disruption Risk (D) 11. Late to Market Risk (D)

Manufacturer Source 4

Delivery

Make 5 7

11 8

3

10 6

Collaboration: Plan 1

2

Supplier

Distributor

Make

Delivery 8

7

Source

Delivery

5

11

11 10

9

Page 1

FIGURE 5 Layout of SCRS of scenario one in threshold tests

FIGURE 6 Regression Statistics in Threshold Tests

40

Comparison of Fault Ratio Given Delta=0.7 0.175

0.17

Fault Node Percentage

0.165

0.16

0.155

0.15

0.145

0

1

2

3

4

5

6

7

8

9

10

Experiments Y

Random

Scale-Free

FIGURE 7 Comparison of Fault Rate in Topological Tests

Risk Correlation

+ Integration of Supply Chain Risk System

Risk Transformation

+

Resilience of Supply Chains

+

FIGURE 8 Risk Perspective of Partnership Effects on Supply Chains

41

11