Modeling and Analysis of Supply Chain Risk System under the Influence of Partners' Collaboration

Transcription

1 Modeling and Analysis of Suly Chain Risk System under the Influence of Partners' Collaboration Benamin P.-C. Yen, Bingcong Zeng School of Business, The University of Hong Kong, Hong Kong, China Abstract Confining the focus to individual enterrise, traditional risk management literature seems to echo inadequately in the context of collaborative suly chain, artially due to its exclusion of correlation of risks across comanies. In this study, we refine the notion of risk in suly chain and roose a model of suly chain risk system (SCRS) that consciously takes into account the correlation among risks resulting from artners collaboration. Through analytical inference we found that the level of collaboration contributes to the resilience of suly chain. It imlies that collaboration can ositively affect the toology of SCRS, thus benefiting suly chain oerations in terms of risk management. A simulation rogram has been develoed with aim to demonstrate the ractical feasibility of the roosed model. Imlemented in simulation, two sets of exeriments have been conducted for testing the model in actual business scenarios. The exerimental results rovide suorting evidence to consolidate the analytical findings. 1. Introduction The first decade of 21 st century has witnessed the dramatic growth of suly chain in which a consolidating linkage through a series of rocesses, from raw material rearation to manufacturing, transortation, storage, and eventually to delivery of services or roducts to the end consumers, ties u the arties involved with an interest chain so close that suly chain comanies are correlated in success and failure in some sense [1]. In such highly interactive business model, the relationshi among the arties is rather delicate. Desite conflicts surely existing, every now and then comanies in suly chain are inclined to collaborate with each other albeit it is for their own sake, e.g. for financial robustness, strategic advancement or oerational excellence [2]. As collaboration goes along, comanies may benefit from working with each other. They may seek to exand their collaboration both in breadth and in deth, and hence artnershi, a much more closed interorganizational relationshi, will be established, in which artners are coordinated to behave as a whole and they share not only their rofits but also the risks [3]. The imact of artnershi is tremendous. The literature has shown a great amount of evidence that it is a critical driving force towards an effective suly chain [4, 5]. While most of studies are focusing on the direct imact of artnershi uon the effectiveness and efficiency of the suly chain erformance, little attention is aid on the issues of suly chain risks emerging due to such intimate relationshi [6]. In fact, under artnershi the risk of an individual comany is not ust the risk of itself and it actually the risk of all the artners. For instance, if the ustream sulier broke down because of a strike occurring in worklace, it would robably eoardize the oerations of the manufacturer in the middle stream and further affect the sales of the retailers in the downstream. In other words, the risk of a comany is no longer limited within the boundary of enterrise. Partnershi has been exanding the scoe of risk management from the enterrise level to the suly chain level. Such a significant change uon risk management under the effect of artnershi, we believe, is truly worth to be investigated. Given the context of collaborative suly chain, risks among artners are linked with each other, which however is seldom considered in traditional risk management research. In attemt to echo the correlation of risks resulting from the effect of artnershi and to construct more accurate notion uon suly chain risks, this aer draws from the theories of system science and the literatures of risk management to roose a model of suly chain risk system (SCRS). SCRS organizes suly chain risks in a visual network according to their causal relationshis and reflects the artnershi effect delicately by the toological distribution of risk nodes and the chain influencing rocess. Through modeling and simulation, our analysis on SCRS reveals that the artners collaboration can significantly contribute to the resilience of suly chain. This offers a novel exlanation from the ersective of risk management for why nowadays increasing number of comanies is consciously engaged in artnershi in suly chain. The rest of this aer is organized as follows: section 2 is devoted to the literature review on suly chain risk management, with intention to identify the key issues as well as the research ga in the existing literature. In section 3, the roosed model of SCRS is resented and the imact of artnershi uon suly /11 $ IEEE 1

2 chain in terms of toological structure of SCRS is analyzed through analytical inference. The verification exeriments and the related results are disclosed in section 4. The main conclusions of the aer are summarized in section Managing risks in suly chain: maor issues in the literature Today, managing risks within the enterrise boundary is far from enough [7]. Comanies begin to notice that a number of risks imacting uon them may not exist in the comanies but come from their suly chain artners. Therefore, while continuously imroving ERM (enterrise risk management) within the comanies, they gradually ay more attention uon the risks in suly chain. Suly chain risk management (SCRM), comared to ERM, no doubt is a relatively new disciline. SCRM is more interested in the coordination and collaboration of rocesses and activities across functions within a network of comanies, with an intention to ensure that the suly chain is erforming effectively and efficiently as normal [8]. To coy with the uncertainty from the suly side and the demand side, ustream risk management and downstream risk management have emerged, forming two maor research areas in SCRM. Regarding ustream risk management, the main issues include suly network design, sulier relationshi management, sulier order allocation and contract management. Heler (1991) reorted that sulier relationshi in U.S. has exerienced a great shift from a common market transaction relationshi to a long-term cooerative artnershi in 1990s [9]. Dyer and Ouchi (1996) confirmed the similar situation haed in Jaan also [10]. Sekman and Davis (2004) ointed out that interdeendency resulting from artnershi is the main source of risks in the suly side, but it is not unmanageable [11]. Zsidisn (2003) rovided some useful suggestions to mitigate the ustream risks, including: 1) establishing buffer stock and enhancing inventory management; 2) avoiding single sourcing and using alternative sources of suly; 3) utilizing suly contracts to manage the fluctuation in sourcing rice; and 4) adoting quality initiatives to imlement comrehensive quality management [12]. Normally in suly chain, the suly caacity is fixed in most cases whereas the demand is changing all the time. Given that, comanies are required to aly various downstream risk management strategies to lower the robability of mismatch between the static constant suly and the dynamic uncertain demand. The literature is abundant in this area. Carr and Loveoy (2000) develoed a mathematical model to identify an otimal ortfolio of demand distributions [13], and Van Mieghem and Dada (2001) from an economic view made an indeth analysis on how to through dynamic ricing make an aroriate resonse to the unstable demand [14]. Regarding the henomena that comanies set different rice at different time, the literature exlained this as a strategy of risk mitigation. Pricing higher in eak seasons is actually to shift demand to off seasons rather than to gras high rofit margin from the customers [15]. It is found that the ricing mechanism is not only able to shift the demand across the time but also to shift the demand across the roducts. Chod and Rudi (2005) showed us a vivid case in which a higher rofit can be obtained through adoting differential ricing strategy to entice customers to shift the demand from one roduct to another [16]. In the context of suly chain, hysical exerimentations, suffering from technical and cost related limitations, are difficult to imlement in risk research [17]. Simulation is considered to be 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 adoted agent-based simulation to model suly chain dynamics and rovided a raid decision suorting tool for risk management [18]. Deleris and Erhun (2005) resented in their aer a Monte Carlo simulation with which different levels of risks in suly chain can be analyzed sohisticatedly [19]. Jain and Leong (2005) viewed suly chain as a comlex system and demonstrated the advantages of constructing suly chain simulations to stress test the system and investigate its erformance under risk situations [20]. After a brief literature review above, we are aware that the revious literature more or less has roensity to focus SCRM uon discrete sectors, mainly confined in either ustream or downstream risk management. Most of research is concentrating uon solely one area, and there are few studies that rovide an integrated view of the whole suly chain from risk management ersective. Furthermore, the correlation among the risks of the artners is few discussed in the literature. Such ga rovides a good research oortunity for our study. One of the goals of this research is to bridge this ga through investigating suly chain risks as a system and reflecting the correlation effect among the risks in suly chain. Considering the scale as well as the constraints of this study, simulation is chosen as the research methodology, for its fitness to SCRM studies suggested by the literature. 2

3 3. Concetual develoment and model building 3.1. Modeling individual suly chain risk What is a risk? How to concetualize it? Those are the fundamental roblems every study of risk has to confront. Although countless answers subected to various ercetions are conferred by the literature, their essence is never out of the below four interretations, including viewing risk as hazard [21], as robability [22], as consequence [23], and as otential adversity or threat [24]. No matter hazard, robability or otential threat, they emhasized that risk should be uncertain, which will haen some time and will not haen other time. It is believed that there exists a law of robability governing its occurrence [25]. Once a risk occurs, it will result in some negative consequence, such as hazard or adversity. Most of the times, the reasons behind causing the risk are attracting eole s attention, and eole are unstoably trying every means to seek for the origin of the risk. But it at the end always turns out to be a tantalizing conundrum when traced back to the root of the reasons of the reasons. The origin seems like a black box unknown or too comlicated to be known for eole, thus scholars give it a name uncertainty. Although there used to be a eriod in which academia was confused by does uncertain roduce risk or risk begets uncertain?, nowadays scholars have reached a consensus that it is uncertainty that leads to risk [22]. The discussion above uncovers an imortant fact that risk is not a simle obect, in other words, it is a system made u of comonents [26]. Kalan (1997) roosed that risk can be exressed by a trilet with the combination of scenario, robability and consequence[27]. Inheriting the similar idea, we believe that risk at least comrises three essential arts: 1) the drivers that generate the risk; 2) an event with robability that signifies the occurrence of risk; and 3) the consequence brought by the risk. By taking into account the three essential comonents of risk and incororating the concetion of correlation among risks, we roose a model named Risk with Casual Relationshi (RCR) to deict an individual risk. It is visualized in Fig.1. Fig.1 A model of Risk with Causal Relationshi (RCR) The model RCR rovides an understanding of risk with causal relationshi. It ortrays the rocess of causation rather than giving a static definition of an individual risk. Keeing in line with traditional interretations of risk, RCR involves drivers, event and consequences in the concetion. It concetualizes risk as an event that occurs in robability, which is denoted as a circle in the middle (See Fig.1). However, an isolated circle itself cannot be called risk. It is qualified as a true risk only and only if it haens with reasons (those refer to drivers) and consequences (the consequences should be negative). Thereby, to identify a risk, we cannot make udgment sheer based on whether it is an event with robability only. Like a customer visiting a suermarket, nobody will treat it as a risk desite that it haens stochastically. A true risk is able to cause negative consequences. Moreover, the occurrence of such event requires drivers which are the antecedents that cause the risk. Aware of the correlation among the risks, we infer that the antecedents should not include ust the factors that lead to the risk event, and it is also ossible that some risks which haened antecedently would trigger a rile effect and drive other risk event to haen. Given that, drivers we roose can be factors or risks: Driver (D) = Factor (F) Risk (R) Factors in RCR mainly refer to the causes uncontrollable or immeasurable. They can be erceived abstractly, and it is difficult to confirm their occurrence with a secific indicator. The maor difference between a factor and a commencing risk lies in that a commencing risk haens in robability while a factor is similar to uncertainty that is nearly imossible to quantified, and even though it can be quantified to some extent, it nearly cannot be changed. A tyical examle for factor is olitical climate. Political climate or olitical situation is uncontrollable to suly chain comanies, and an unstable olitical situation is able to trigger a number of risks, e.g. a strike risk in the manufacturing site, which may cause serious disrution in suly chain. Nevertheless, comanies can do very little to olitical situation, and in most cases they have to accet the factor and adat to the situation. Consequences in RCR are referred to the negative result of a risk. They can be a direct harmful imact quantified financially or another consequent risks being triggered which may cause other bigger loss in the later time: Consequence (C) = Imact (I) Risk (R) Imacts in RCR are referred to the ultimate and secific loss resulting from the risk, which can be measured quantitatively. 3

4 In a short summary, RCR defines risk as a stochastic event with causes and effects. The occurrence of such event requires drivers which can be some factors or commencing risks. When the drivers are active (or say the conditions to trigger the risk event are satisfied), it does not mean the risk will haen definitely but ust imlies that the robability of risk to occur is extremely high. Some risks may cause economical damage in a direct manner while others may result in tremendous harms indirectly through triggering other risks in a consequence Modeling suly chain risk system When we link u the risks according to their causal relationshis, those will constitute a great network with intensive connections among the items in it. Fig 2 illustrates a visualized icture of this network for us. with the key features of suly chain risks. The correlation of risks in suly chain is reflected fully in the casual relationshi both in RCR and in RCN. RCR rovides an aroriate temlate for suly chain risks modeling, and suly chain risks can easily be secified following the concetion of RCR. TABLE 1 shows a list of suly chain risks in the rocess of sourcing. It demonstrates a well fitness of alying RCR in the context of suly chain. Similarly, the suly chain risk system (SCRS) can be engendered by a secific alication of RCN in suly chain (Please see Fig. 3). TABLE 1 A List of Suly Chain Risks in the Process of Sourcing Risk Name Drivers Event Indicator Consequences Suly disrution risk [28, 29] Sulier commitment risk [28, 29] - Unstable olitical climate(f) - Payment delay (R) - Cometitor seducing sulier to um out of the contract (F) - Suly disrution risk (R) - Payment delay (R) Sulier terminates the suly Sulier terminates the suly contract - Damaging the trust in artnershi (I) - Manufacturing stoage risk (R) - Material inventory shortage risk (R) Fig.2 Risk Causality Network (RCN) Excluding the factor nodes as well as the imact nodes, the region inside the dash line comoses a risk causality network (RCN). RCN is constructed on the basis of a number of individual risks under the model of RCR. To secure the causality in between, we suggest that the risks involved be at the same level. U to secific alication, RCN can be aggregated to a more strategic level or be drilled down to a more oerational level. In fact, its organization is not arbitrary and there are 3 rules, we are aware of, governing the construction of RCN: 1. The initial risk node in RCN must be triggered solely by factor(s); 2. The RCN should end with the risk nodes that result in negative imacts only. 3. The causality among risks imlies the time sequence, and thereby the antecedent risk must haen before the triggered risk. The roerty of time sequence determines that the RCN must be an acyclic grah. Long lead time risk [12, 30] Material inventory shortage risk [12, 30] Payment delay [30, 31] Offshore rocurement risk [31] - Sulier transortation risk (R) - Offshore rocurement risk (R) - Long lead time risk (R) - Cash in short (F) - Problems with the accounting system (F) - Low cost of rocurement (F) Note: F: factor; R: risk; I: imact The lead time runs out of the safety range The material inventory level is lower than the safety stock level Late ay to the sulier Purchase the raw material from offshore suliers - Material inventory shortage risk (R) - Manufacturing stoage risk (R) Manufacturing stoage risk (R) - Suly disrution risk(r) - Damaging the trust in artnershi (I) - Long lead time risk (R) RCR and RCN are two fundamental concets that assist us in modeling risks in suly chain. Though conceived in a general level that ignored the alication context, they have been concetualized Fig.3 Suly Chain Risk System (SCRS) 4

5 In SCRS, risk nodes are connected according to their casual relationshi in a network structure. The initial nodes are normally triggered by some unredictable environmental factors. For examle, severe fluctuation in raw material rice may cause flawed co-forecasting risk in suly, and it may trigger inventory risk if the rice is so high that the manufacturer is not able to afford the high rice and thus have to shrink the imort quota of inventory. The shortage in inventory may cause some bigger roblem if it cannot be fixed aroriately, one such like manufacturing stoage that can result in aalling disrution of the whole suly chain. Actually the state of each suly chain risk node at a time is determined by two factors: its marginal robability and its correlation with other risk nodes. Given that, the state of SCRS can be resented in a form of a set with the time roerty: RS t = {, corr }.(1) i i t Where RS t denotes the state of SCRS at time t, i is marginal robability of a risk node i, and corr i is the causal correlation between risk node i and. i measures how likely the individual risk would haen, and corr i not only reflects the relationshi between nodes but also determines the toological structure of SCRS. Both i and corr i can be obtained from the historical data stored in enterrise data warehouse. But if the data is unavailable in the database, it can be estimated or suggested by the exerts in the filed of SCRM. RS t would vary at different time t in terms of the layout structure or the risk likelihoods in SCRS. It can be influenced by lots of factors, such as economic climate, industrial ractices or artnershi (See Fig.3.). In this study, we would like to investigate how artnershi imacts on the toological structure of SCRS Measuring resilience of suly chain risk system Vulnerability is an oosite concet against resonsiveness and it is used to describe a suly chain in lack of robustness and resilience with resect to various risks that imoses negative imact uon suly chain [32, 33]. Robustness and resilience are two key concets in SCRM. To large extent, they indicate the erformance of risk management in suly chain. Robustness of suly chain is referred to the ability of suly chain to resist the imact of risk and retain the same stable situation as it had before the occurrence of risk [33]. Facing risk, a robust suly chain is able to coe with it so that the negative imact of risk will cause very little harm to the suly chain oeration. In contrary to robustness, resilience is referred to ability of suly chain to return to a new stable or desirable situation after the imact of risk [33]. A resilient suly chain is able to adat to the new change brought by risks very quickly and then oerate in a stable manner again. In this study, our interest is in measuring the resilience of suly chain using the model of SCRS. In the model of SCRS, risk node has two states: one is healthy, indicating that the risk is inactive and not triggered; the other is infected, indicating that the risk is active and has been triggered by some factors or other risks. At each time oint t, the healthy risk node is ossible to be infected, which is subected to its robability to be triggered. If its antecedent risk nodes are not infected, it will be triggered by its marginal robability; but if some of its antecedent risk nodes have be infected, it will be trigged by its conditional robability which will be much higher than its marginal robability. In case that some risk nodes have been infected already, the suly chain comanies concerned will take actions, trying their best to recover the risk nodes back to the healthy state. The attemt may succeed or fail, subected to the recovery rate which measures how likely a risk node can be restored from a chaos back to normality. Generally, the higher the recovery rate is, the more quickly the risk node is able to return to health. Given that, the recovery rate in SCRS can be a good indicator to measure the resilience of suly chain. In fact, the imrovement of the recovery rate comes at cost. It requires suly chain comanies to devote significant investment in risk analysis and the develoment of mitigation aroach. However, in reality few comanies are able to afford such huge investment in SCRM whereas they know that it is truly crucial for them to maintain an accetable level of the recovery rate otherwise the business may suffer huge loss. In SCRS, we are aware that there must exist a minimum threshold for the recovery rate. If the recovery rate fails to catch u with the threshold value, there will be a ersistent chaos in the suly chain in which the healthy risk nodes will be trigged by conditional robability rather than marginal robability. Under this circumstance, the chain effect of risk infection will continue and never die out because the recovery rate is too low to suress the sawning chaos. If this were the case, it would be a catastrohe to the whole suly chain. Below, we would like to use an analytical model based on SCRS to analyze the recovery rate and try to deduce the threshold value through mathematical inference. The model setting is as follows: There are n risk nodes in the SCRS. We define the robability i (t) by 5

6 which risk node i is triggered at time t, as a result of infection by its antecedent infected nodes at time (t- 1). Suose that =1,2,,k are the antecedent nodes of node i. Δ is the average recovery rate of the suly chain. Γ is the triggered rate matrix of n n, defined as below: 11 Γ = 21 n n2 1n 2n nn d = 1 21 n n2 1 n 2n nn Where i is the marginal robability of risk node i, and i is the conditional robability given that node is infected. i is ositively associated with corr i (See Formula(1).) It is said that given other condition unchanged, in case that the correlation between node i and is stronger, if node is infected, then the robability of node i to be triggered will be higher. i is the triggered rate of risk node i given that node is infected, therefore i = i i i i = If risk node i is not infected at time (t-1), then the robability of infection at time t is the sum of robabilities of being triggered by the k antecedent nodes. By definition, the robability that node i is not infected at (t-1) is [ 1 i ( t 1)], and then the robability of being triggered by antecedent nodes k is i ( t 1). So robability of being trigged from neighbors is [ 1 ( t 1)] ( t 1) i If node i is already infected at time (t-1), then the robability that it will remain infected at time t is the oint robability that it was triggered at time (t-1) and the robability that it does not recover. So the robability of non-recovery when already inflected is ( 1 Δ) ( t 1) Therefore, summing the two events yields the robability that node i is at the infected state at time t (including the case of being triggered and the case of remaining inflected ): k i (t) = [ 1 ( t 1)] ( t 1) + (1 Δ ) ( t 1) Where i=1,2,,n i i k i i i i Put it into matrix form, we can get P (t) = [ 1 i ( t 1)] ΓP( t 1) + (1 Δ) P( t 1) = {[ 1 i ( t 1)] Γ + (1 Δ) I} P( t 1) (2) Where i=1,2,,n, and (t) is a column vector T ( t), ( t),, n ( t)] [ 1 2 Formula (2) shows in an elegant form of dynamical system with Markova chain roerty. The state equation is ideal excet for the term [ 1 i ( t 1)], which does not fit nicely into the matrix formulation. Given that, we would like to assume i ( t 1) is rather small and such that 1 i ( t 1) 1. Then, P(t) [ Γ + (1 Δ) I ] P( t 1) (3) Under SCRS, the assumtion above is reasonable. Normally seaking, the robability that a risk haens is relatively very small. Even given that some antecedent risks have been triggered, the conditional robability will be much higher than the original marginal robability but it in most occasions is still very small. Given that, assuming i ( t 1) 0 may not lead to great accuracy loss in P (t), and formula (3) will be a good aroximation in calculating P (t). Let [ Γ + (1 Δ) I] be S, called the system matrix, we can obtain the first order difference equation: P (t) = S P( t 1)..(4) When P(0) is given P (t) = S t P(0) (5) We define ρ(s) as the largest nontrivial eigenvalue of system matrix S and ρ (Γ) as the largest nontrivial eigenvalue of triggered rate matrix Γ. ρ (S) and ρ(γ) can be shown to have the following relationshi 1 : (S) ( Γ) + (1 Δ (6) ρ = ρ ) Formula (5) and (6) convey a message that SCRS is a convergent system if ρ (S) <1, or equivalently, if Δ is at least larger than ρ (Γ). Suosing suly chain is in a chaos state P(0) at time t=0, with time asses by, if the recovery rate Δ > ρ (Γ), P(t) will converge and return to a stable or normal state that each risk node in SCRS is 1 Due to the sace limit, the roof is omitted. The readers can contact the authors for the detail of the roof if they are interested in it. 6

7 triggered by its marginal robability. The convergent seed reflects the resilience of suly chain, which is subected to the recovery rate Δ given ρ (Γ) unchanged. The SCRS can quickly return to normality if the recovery rate Δ is very high. But if Δ < ρ (Γ), the chaos will ersist in the suly chain, in which most of risk nodes in SCRS are triggered by its conditional robability. Hence, risk will haen by much higher chance, and accidental events will continuously break out anywhere in the suly chain, robably able to result in long-term disrution in oeration and tremendous loss in finance. To revent such disaster, Δ should at least maintain at the level of ρ (Γ), and Δ = ρ(γ) is the minimum threshold for the recovery rate. oint activities is named as collaboration risks, and the collaboration risks normally are the risk nodes with high degree of connections. Therefore, when artnershi goes dee, artners will collaborate more frequently and they may choose co-working in form of oint activities rather than working individually. Hence, that will result in more collaboration risks in suly chain. Such change reflected in SCRS in terms of toological structure is a rocess of transformation from random grah to scale-free network (See Fig.4) Suly chain resilience and artnershi The threshold value of the recovery rate Δ is equal to the largest nontrivial eigenvalue of triggered rate matrix Γ. It is associated with the toological structure of SCRS. The toological structure is concerned with the roblems such as how the risk nodes are distributed and in which atterns they are organized. In terms of the orderliness and regularity, there exist two tyical tyes of structures: random grah and scale-free network. Random grah is referred to the system in which its comonents are organized randomly, and there is no attern able to be recognized regarding its toological structure [34]. Scale-free network is referred to the system in which small ortion of its comonents are with high degree of connections with other comonents but most of its comonents are with low degree of connections with other comonents, and this regulation holds regardless the scale of the system [26, 34]. The rationale behind is that each time when a new node enter into the network, it will first choose the node with highest degree of connections to connect with, in other words, the node with higher degree of connections gets higher chance to be connected with, and the node with lower degree of connections gets lower chance to be connected with. Therefore, it will result in such scale-free system. With dramatic growth of artnershi in suly chain, comanies are inclined to closely collaborate with each other. They enoy being engaged in oint activities in which comanies cooerate together to accomlish certain oerations. Such oint activities may be associated with lots of other oerations, thus caable to influence the suly chain in a wide extent. If roblems haen in those activities, it may harm the suly chain greatly. In SCRS, the risk hidden in Fig 4 Effect of Partnershi on Toological Structure of SCRS A fact has been revealed by system science that scale-free network is a more organized system comared to random grah [34]. Given that, theoretically seaking, ρ(γ) of a scale-free network should be less than the one of random grah. Thus, Δ for scale-free network is less than the one for random grah. In other words, artnershi makes the SCRS evolve towards a more organized and regular system, and then lowers the minimum threshold Δ required for the recovery rate. Moreover, referred to formula (6) ρ (S) = ρ ( Γ) + (1 Δ), when ρ (Γ) decreases, ρ (S) will dro from 1 to 0 given that Δ > ρ (Γ). It imlies that the decrease of ρ (Γ) is able to seed u SCRS from chaos to normality. Thereby ρ(γ) is negatively associated with the resilience of suly chain. The effect of artnershi uon SCRS reflects in reducing ρ(γ) and making the system inclined towards a more organized structure. Hence, artners collaboration contributes to the resilience of suly chain. Through artnershi and collaboration, suly chain can recover from chaos or disrution more quickly. 4. Verification exeriments In the revious section, two conclusions have been drawn theoretically: 1. There exists a minimum threshold value Δ that revents the SCRS from ersistent chaos, and Δ = ρ (Γ) 2. Partnershi makes the SCRS more inclined to 7

8 evolve towards scare-free network, a more organized and regular system comared to random grah, and such imact benefits the resilience of suly chain by reducing ρ(γ) and lower Δ. These two findings are mainly relied on analytical inference in theory, and thus lack emirical evidence to manifest their correctness. Given that, in this aer, simulation is emloyed as the verification method to test the conclusions mentioned above. As a matter of fact, simulation is the only feasible choice under the rigorous research requirement of this study. First, it is too difficult to collect emirical data in the industry. Desite that risk management has been studied for more than 15 years, few comanies have the records of risk data in their database [35]. Moreover, the research target is on suly chain which involves multile comanies. Obtaining consistent historical data across comanies is extremely difficult. Furthermore, the key research scenario is fixed on a suly chain from chaos back to normality. It is only simulation that can construct such a secific scenario that the research interest is able to be satisfied Design of exeriments A simulation rogram has been develoed to imlement the attributes and behaviors of the model of SCRS. Fig.5 shows a snashot of this system. Fig 5 Snashoot of SCRS Simulation rogram With the hel of this simulation rogram, researchers can construct the scenarios they are really interested and conduct the exeriments following their research lan. In this aer, two set of exeriments are designed to test the conclusions drawn analytically using the model of SCRS. The first set of exeriments is named threshold tests, which are intended to verify that Δ = (Γ) through simulation. The exeriments involve 4 key stes: Ste1 is to construct a SCRS with reasonable setting. In this ste, a SCRS is built by alying a real scenario in business. The risk nodes and their casual relationshis are suggested by 4 exerts in the field of SCRM. The marginal robability and conditional robability, due to the need for large data, are generated using the comuter algorithm. Suggested by the literature, a small robability should below 0.3 [26]. Given that, for marginal robability, it is generated uniformly within the interval of (0, 0.2), and conditional robability is generated within the interval of (marginal robability, 0.3) since conditional robability must be larger than the marginal one. Under this network setting, we can obtain the value of ρ(γ) by calculating the largest eigenvalue of Γ matrix. According to Frobenis- Perron theorem, it is assured that a ositive value of ρ(γ) can be obtained because for a ositive square matrix there must be at least one ositive real eigenvalue. Ste2 is to record the normal state of SCRS. Through simulation, we are allowed to imitate the rocess in which the SCRS is oerating in a normal state. During the rocess, the rogram would record down the number of the triggered nodes at each time t and store the data into a database. For each time t, it is called a run. For each exeriment, the rocess would be simulated for 2000 runs in order to cature a comrehensive data of normal state of SCRS. Ste3 is to simulate the rocess of SCRS from chaos to normality and obtain Δ in this recovery rocess. In this ste the first task is to simulate the chaos state of SCRS. The chaos state is referred to a situation in which the risk network is overwhelming by risk events and nearly all risk nodes are triggered by conditional robability. Then in a chaos state, by assigning different recovery rates, we would find out the minimum one that is able to recover the SCRS from chaos to normality. To udge whether the SCRS has already returned to normality, we comare the current state with the normal state that has been obtained in ste 2. By using two-samle T test, if the P-values of T statistic and F statistic both exceed 0.05, we can confirm that the SCRS has returned from chaos to normality. Ste4 is to examine the correlation between Δ and ρ (Γ). In this ste we would like to check the relationshi between Δ and ρ (Γ), and see if they are strongly correlated as redicted in the analytical model. The second set of exeriments is named toological exeriments. They are through simulation to test whether Δ of a scale-free network is actually ρ 8

9 lower than Δ of a random grah system. The most difficult art in these exeriments is to generate the SCRS with toological structure of scale-free or random grah. For scale-free network, Barabasi- Albert (BA) aroach is chosen as the network generating algorism while for random grah, Erdos- Renyi (ER) aroach is used to construct the network. To make these two tyes of network comarable, the simulation rogram by default generates the same amount risk nodes with constant marginal robability of 0.1 and constant conditional robability of 0.15, and the same amount of links within the SCRS also. TABLE 2 Summary of Threshold of Recovery Rate in Toological Tests 4.2. Exerimental results and discussion The thresholds tests consist of 4 business scenarios ervasively existing in suly chain and each scenario includes 20 exeriments. The final exerimental results are summarized in Fig.6: Fig 6 Regression Statistics in Threshold Tests The statics of regression analysis manifest that there is a strong correlation between Δ and ρ (Γ). The simulation results confirm the inference derived from the analytical model that Δ is equal to ρ (Γ).Through extensive exeriments, it is able to reach a conclusion that Δ the threshold value of recovery rate is highly correlated with ρ(γ) and their correlation is aroaching nearly 1, and this rovides strong suorting evidence to bolster the argument that Δ = (Γ), which has been shown theoretically. ρ The toological exeriments in all contain 10 exeriments. They are contrasting Δ of SCRS in scale-free and random grah. TABLE 2 briefly shows the summary of the exerimental results. Note: N: number of risk nodes; L: number of links TABLE2 uncovers a fact that Δ of a scale-free network is always smaller than the one of a random grah. It indicates that the threshold of the recovery rate reduces when the SCRS evolves towards a more organized and regular network. The effect of artnershi will make suly chain more inclined to transform from random grah to scale-free. Such change in toological structure can significantly contribute to the resilience of suly chain. It can reduce the minimum threshold required to revent chaos from ersisting in suly chain, and it also can seed u the recovery rocess for a risk node from chaos to normality. In a word, artnershi does make ositive influence on the management of suly chain risks. 5. Conclusions Suly chain risk management is a rincile comonent in the body of suly chain management research. Previous studies mostly focusing on secific tye of risk aid little attention uon the internal correlation existing among the risks in suly chain. This study re-concetualizes suly chain risks into a general form and rooses a model through which risks can be integrated into a suly chain risk system (SCRS) caable to reflect not only the mutual correlation but also the causal relationshi among them. Through modeling and simulation, it is revealed that the artnershi can significantly contribute to the resilience of suly chain and benefit the risk management in suly chain. This offers a novel view from the ersective of risk management to exlain why more and more suly chain comanies are consciously engaged in artnershi nowadays. It is hoed that this study would insire ractitioners and hel them to form a new ercetion regarding the relationshi between artnershi and suly chain risk management. 9

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