# Supply network topology and robustness against disruptions – an investigation using multi-agent model

Abstract: In this study we examine the relationship between supply network's topology and its robustness in the presence of random failures and targeted attacks. The agent-based model developed in this paper uses the basic framework and parameters in the experimental game presented in Sterman [1989, Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making context. Management Science, 35 (3), 321–339] for modelling adaptive managerial decision making in an inventory management context. The study extends the linear supply chain context to a complex supply network and undertakes a rigorous examination of robustness of these supply networks that are characterised by distinct network characteristics. We theorise that network characteristics such as average path length, clustering coefficient, size of the largest connected component in the network and the maximum distance between nodes in the largest connected component are related to the robustness of supply networks, and test the research h...

## Summary (3 min read)

### Introduction

- In recent times, supply disruptions are receiving considerable managerial attention due to their adverse impact on organizational performance.
- The increased interest in supply chain disruptions is also evident in research studies.
- The authors paper fits within this multiagent based approach.
- It has been observed that several supply networks exhibit incredible robustness in the presence of disruptions while others fail to survive random failures or targeted attacks.
- Further details on the analytical and empirical developments in the random graphs and scale-free network theory are presented in Albert and Barabasi (2000) and Dorogovtsev and Mendes (2002).

### Average path length

- The average path length presents an approach to characterize the spread of a network by calculating the average distance between any pair of nodes.
- For a network with N nodes, it is likely that not all nodes will have the same number of edges (also referred as node degree).
- The spread of the node degrees is characterized in terms of the distribution function P(k).
- The degree distribution of most random networks can be approximated by binomial distribution (with Poisson distribution being a more appropriate approximation for very large number of nodes).

### Clustering coefficient

- Clustering coefficient capture the small-world nature inherent in several real-world networks.
- In a random network the probability that nearest neighbors of a node are connected is equal to the probability that two nodes in the network are connected.
- In the event of disruptions it could result in high level of vulnerability due to the high levels of dependency among the nodes.
- Further, as the size of the largest connected component increase the maximum distance between any two nodes in the component increase.
- Drawing on this reasoning the authors hypothesize: H3: In the presence of disruptions, the robustness of supply network is positively associated with the size of its largest connected component.

### Research Design

- The use of agent-based simulation model in supply chain context is gaining research interest (e.g. Moyaux, et al., 2007).
- The approach enables us to capture the complexities and dynamics associated with network topologies and examine the evolutionary nature of choices made by firms within these supply networks.

### Agent-Based Model

- The authors model extends the experimental game presented in Sterman (1989) by allowing for more complex network topologies.
- The results obtained from the agent-based model provide a satisfactory replication of the results in Sterman (1989).
- Since in a network setup each supply chain entity (i.e. factory, distributors, warehouses, and retailers) can supply to more than one demand source, the authors had to add some extra rules that are not present in the basic experimental game setup presented in Sterman (1989).
- Two supply chain entities that are directly connected to each other are at a distance of one.
- In the random network topology each new node is connected to one randomly chosen existing node where all existing nodes have equal probability of being chosen.

### Experimental Design

- The development of the simulation model and the analysis of the data gathered from simulation runs follow the systematic approach suggested in literature (Kelton, 1997; Sargent, 1998; Nance and Sargent, 2002; Law, 2004).
- The overall experimental design and parameters used for the study are reported in table 1.
- The authors ran the agent based simulation model for 105 time ticks; each time tick corresponds to a week.
- The authors collect data from twenty replications of each scenario of the simulation model, and use the average of the weekly data obtained from these 20 replications for analysis.

### Results and Discussion

- The authors examine the robustness of individual topologies by undertaking paired sample t-test for each network topology considered in the study.
- In total 24 paired sample t-tests (for each disruption scenario explained in the experimental design) were conducted for each topology.
- Robustness of a network topology against disruptions is gauged by a non significant difference in the mean for the performance measures as reported by the paired sample t-test (i.e. p-value > 0.05).
- Initially, the authors undertake the binomial logistics regression analysis for the entire sample of network topologies considered in this study.
- The authors use the topology type (categorical variable denoting scale-free and random network) as a control variable.

### Overall Sample

- The results of the binomial logistics regression analysis for the overall sample are presented in table 3. [Table 3 about here].
- All other hypothesized relationships are strongly supported (p<0.05).
- The results in table 3 also show that scale-free networks are relatively more robust from the inventory perspective, however, when viewed from the backorders and total cost perspectives, random networks are more robust.
- The results present a compelling evidence of the association between network characteristics and robustness of supply networks.
- While the maximum distance between nodes in the largest connected component is not significantly associated with inventory and total cost based robustness measures, a unit increase in this variable increases robustness from backorders perspective by almost 5 times.

### Random Networks

- The authors present the results of the binomial logistics regression analysis for the sub-sample comprising of random networks in table 5. [Table 5 about here].
- A unit increase in average path length substantially increases the odds of vulnerability from backorders and total cost perspectives.
- A unit increase in the maximum distance between nodes in the largest connected component was found to increase the odds of a robust supply network by 3.7 times, 14.1 times and 16.9 times when the robustness is evaluated from inventory, backorders and total cost perspectives respectively.
- There are a few limitations of this study that provide directions for future research.

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##### Citations

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6,328 citations

364 citations

### Cites background from "Supply network topology and robustn..."

...Another important observation in literature is a linkage of SC complexity and resilience (Blackhurst et al. 2005; Nair and Vidal 2011; Bode and Wagner 2015; Dubey et al. 2019a; Tan, Cai, and Zhang 2020)....

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...…and Sokolov 2013; Demirel et al. 2019) • Robustness – ability to withstand a disruption (or a series of disruptions) to maintain the planned performance (Nair and Vidal 2011; Simchi-Levi, Wang, and Wei 2018) • Resilience – ability to withstand a disruption (or a series of disruptions) and…...

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336 citations

### Additional excerpts

...…capability, velocity capability, visibility capability, & collaboration capability • Network-level analysis with emphasis on a focal firm • Singe case study (a firm with its three supply chains) Nair and Vidal (2011) • Disruption not formally defined • Disruption as random failure and targeted…...

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...Although some researchers have argued, for instance, that high-degree nodes (Craighead et al., 2007) and short average path length (Nair and Vidal, 2011) play critical roles in network disruption, our analysis shows that node failure and average walk length are not necessarily related with a…...

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...• No operational measures for resilience • Unclear level of analysis • Survey Table 1 (Continued) Referencesa Definition Level of definition and analysis Methods/nature of study Main findings Conceptual definition Operational measuresb Wagner and Neshat (2010) • Disruption as “the trigger that leads to the occurrence of risk” (p. 122) • Not operational measures for disruption discussed; but instead, supply chain vulnerability drivers categorized into demand side, supply side, and supply chain structure • Unclear level of definition • Empirical • Propose a SCVI (supply chain vulnerability index) metric that can be used to assess the vulnerability of supply chains and compare vulnerabilities of supply chains across industries • A related concept, “vulnerability” is discussed • No operational measures for resilience • Level of analysis: multiple & mixed (a firm, supply chain, industry, and entire economy) • Survey • Resilience not discussed Jüttner and Maklan (2011) • Disruptions “imply a certain level of turbulence [Hamel and Valikangas, 2003] and uncertainty in the supply chain [van der Vorst and Beulens, 2002]” (p. 247) • No operational measures for disruption • Network-level definition • Qualitative • Suggest that supply chain risk and knowledge management enhance resilience by improving flexibility, visibility, velocity and collaboration capabilities at the supply chain/network level • Resilience defined by flexibility, velocity, visibility, and collaboration capabilities (adapted from Ponomarov and Holcomb, 2009) • Resilience measured as flexibility capability, velocity capability, visibility capability, & collaboration capability • Network-level analysis with emphasis on a focal firm • Singe case study (a firm with its three supply chains) Nair and Vidal (2011) • Disruption not formally defined • Disruption as random failure and targeted attack on network nodes (firms) for their inventory levels, backorders, and total costs • Network-level definition • Analytical • Certain established network characteristics (such as average path length, clustering coefficient, size of the largest connected component) are associated with the robustness of supply networks (to random failures/targeted attacks on demand and uptime of nodes) • Resilience (robustness) not formally defined • Resilience (robustness) as multiple network attributes such as average path length, clustering coefficient, size of the largest connected component (LCC), and max. distance between nodes in the LCC • Firm-level analysis • Simulation (agent-based modeling) Zhao et al. (2011) • Disruptions “affect the normal operations” (p. 1) and are either random or targeted • No operational measures for disruption • Network-level definition • Analytical • Suggest centrality as a measure for a node’s importance....

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...…al., 2010; Wagner and Neshat, 2010), conceptual (e.g., Christopher and Peck, 2004; Kovács and Tatham, 2009; Tang, 2006), qualitative (e.g., Craighead et al., 2007; Jüttner et al., 2003; Sheffi and Rice, 2005), and simulation/modeling (e.g., Nair and Vidal, 2011; Wu et al., 2007; Zhao et al., 2011)....

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...This also conflicts some research on supply network resilience that argues for the association between the well-established network metrics and resilience (e.g., Nair and Vidal, 2011)....

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292 citations

### Cites background from "Supply network topology and robustn..."

...…this included an increased understanding of how control parameters influence dynamic behaviours and how nonlinearities impact the performance of the SC. 2.4 Complexity and reliability theory Nair and Vidal (2011) study SC robustness against disruptions using graph-theoretical topology analysis....

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278 citations

### Cites methods from "Supply network topology and robustn..."

...Using agent-based simulation, Nair and Vidal (2011) showed that longer average paths between supply chain nodes decrease a supply network’s robustness....

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##### References

30,921 citations

### "Supply network topology and robustn..." refers background or methods in this paper

...The average path length of scale-free networks examined by Barabasi and Albert (1999) increases approximately logarithmically with the number of nodes, N....

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...…average path length, clustering coefficient, size of the largest connected component and maximum distance between nodes in the largest connected component by using the definitions and conceptualisations in extant research (Barabasi and Albert 1999, Albert et al. 2000, Thadakamalla et al. 2004)....

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...With the overall framework and constraints presented earlier, scale-free networks were generated by using the preferential attachment logic (Barabási and Albert 1999), and the random networks are generated by following a random attachment of nodes....

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...The clustering coefficient of scale-free networks proposed by Barabasi and Albert (1999) are higher than that of the random networks and this difference increases as the number of nodes increase....

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...In the preferential attachment topology we follow the standard algorithm (Barabasi and Albert, 1999) and connect each new node to one existing node but now each node’s probability of being chosen is directly proportional to the number of edges that it has....

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7,724 citations

### "Supply network topology and robustn..." refers background in this paper

...Modelling of complex networks has focused on three main classes: (i) Random graphs: These variants of Erdo00 s–Rényi model (Erdo00 s and Rényi 1959, Bollobás 1985) are still widely used in many fields and serve as a benchmark for many modelling and empirical studies....

[...]

7,255 citations

### "Supply network topology and robustn..." refers background or methods in this paper

...…average path length, clustering coefficient, size of the largest connected component and maximum distance between nodes in the largest connected component by using the definitions and conceptualisations in extant research (Barabasi and Albert 1999, Albert et al. 2000, Thadakamalla et al. 2004)....

[...]

...Studies, such as Albert et al. (2000), have focused on random graphs and scale-free network topologies to discern the error and attack tolerances of these networks. Consistent with this stream of research and with literature emphasising that supply networks follow topologies commonly observed in complex adaptive systems (Sun and Wu 2005, Surana et al. 2005, Bichou et al. 2007, Pathak et al. 2007, Wang et al. 2008), we investigate the robustness of supply networks by considering random and scale-free network topologies. The theory of random networks has its origin in the use of probability methods in problems related to graph theory. Erdo s and Rényi (1959) define a random graph to be one in which N nodes are connected to n edges, chosen randomly from N(N 1)/2 possible edges....

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...…component within a network and the maximum distance between the nodes in the largest connected component, particularly in the context of robustness against random failures and targeted attacks (see, for example, Albert et al. 2000, Cohen et al. 2000, Moreno et al. 2002, Thadakamalla et al. 2004)....

[...]

...Studies, such as Albert et al. (2000), have focused on random graphs and scale-free network topologies to discern the error and attack tolerances of these networks....

[...]

...This study builds on the extant literature in statistical physics that examine the error and attack tolerance of complex networks (Albert et al. 2000, Thadakamalla et al. 2004), and consider the impact of supply network characteristics, such as average path length, clustering coefficient, size of…...

[...]

[...]

6,328 citations

### "Supply network topology and robustn..." refers background in this paper

...Erdo00 s and Rényi (1959) define a random graph to be one in which N nodes are connected to n edges, chosen randomly from N(N 1)/2 possible edges....

[...]

...Modelling of complex networks has focused on three main classes: (i) Random graphs: These variants of Erdo00 s–Rényi model (Erdo00 s and Rényi 1959, Bollobás 1985) are still widely used in many fields and serve as a benchmark for many modelling and empirical studies....

[...]