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Journal ArticleDOI

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

01 Mar 2011-International Journal of Production Research (Taylor & Francis Group)-Vol. 49, Iss: 5, pp 1391-1404

AbstractIn 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...

Topics: Average path length (61%), Network formation (61%), Supply network (60%), Robustness (computer science) (56%), Supply chain (56%)

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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1
SUPPLY NETWORK TOPOLOGY AND ROBUSTNESS AGAINST
DISRUPTIONS – AN INVESTIGATION USING MULTIAGENT MODEL
Anand Nair *
Department of Management Science
Moore School of Business
University of South Carolina
Columbia, SC - 29208, USA
Phone: (803) 777-2648
Fax: (803) 777-3064
E-mail: nair@moore.sc.edu
José M. Vidal
Department of Computer Science and Engineering
Swearingen Engineering Center
University of South Carolina
Columbia, SC - 29208, USA
Phone: (803) 777-0928
Fax: (803) 777-3767
E-mail: vidal@sc.edu
* Corresponding Author
(Forthcoming)
International Journal of Production Research

2
Supply Network Topology and Robustness against Disruptions – an
investigation using multiagent model
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) for modeling 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 characterized by distinct
network characteristics. We theorize 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 hypotheses using data from several simulation runs.
Simulations were carried out using twenty distinct network topologies where ten of these
topologies were generated using preferential attachment approach (based on the theory of scale-
free networks) and the remaining ten topologies were generated using random attachment
approach (using random graph theory as a foundation). These twenty supply networks were
subjected to random demand and their performances were evaluated by considering varying
probabilities of random failures of nodes and targeted attacks on nodes. We also consider the
severity of these disruptions by considering the downtime of the affected nodes. Using the data
collected from a series of simulation experiments, we test the research hypotheses by means of
binomial logistic regression analysis. The results point towards a significant association between
network characteristics and supply network robustness assessed using multiple performance
measures. We discuss the implications of the study and present directions for future research.
Keywords: Supply networks, Topology, Disruptions, Robustness, Scale-free Networks, Random
Networks, Agent-based model, Binomial Logistics Regression
Introduction
In recent times, supply disruptions are receiving considerable managerial attention due to
their adverse impact on organizational performance. Sheffi and Rice (2005) highlight the
supply chain implication of the terrorist attack on September 11, 2001 by giving the
examples of adverse effect on Ford’s and Toyota’s operations. Chozick (2007) report that
70% of Japan's auto production was temporarily paralyzed for a week due to the
disruptions in the supply of piston ring caused by a 6.8-magnitude earthquake that hit
central Japan thereby damaging Riken Corp.’s production plant, the supplier that makes
custom piston rings for most of the car makers in Japan.

3
The increased interest in supply chain disruptions is also evident in research
studies. For instance, studies have examined the financial implications of supply chain
disruptions (e.g., Hendricks & Singhal, 2003; 2005) and investigated risk mitigation and
contingency planning strategies in the presence of supply chain disruptions (e.g. Sodhi,
2005; Tomlin, 2006). There is also a growing research stream that examines disruption
and related supply chain issues by using a multiagent-based simulation framework (e.g.
Thadakamalla et al., 2004).
Our paper fits within this multiagent based approach. In this study we examine
how supply network topology is associated with its robustness in the event of disruptions.
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.
Sheffi and Rice (2005) provide examples of firms, whose supply networks are
characteristically distinct from each other, making their levels of resilience and
robustness to random failures and targeted attacks to be considerably different. 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 the largest connected component, and maximum distance
between two nodes in the largest connected component, on performance measured in
terms of inventory levels, backorders and total costs within a supply network.
Literature review and research hypotheses

4
Modeling of complex networks has focused on three main classes: (i) random graphs:
these variants of Erdős – Rényi model (Erdős and Rényi, 1959; Bollobás, 1985) are still
widely used in many fields and serve as a benchmark for many modeling and empirical
studies; (ii) small-world models: these models interpolate between the highly clustered
regular lattices and random graphs; and (iii) scale-free models (Barabási and Albert,
1999): these are motivated by the power-law degree distribution of the nodes in complex
networks as evident in several networks such as the World Wide Web (Albert et al.,
1999), the Internet (Faloutsos et al., 1999), or metabolic networks (Jeong et al., 2000).
When viewed from the perspective of robustness to failures, it is observed that random
networks and small-world networks have similar properties due to the similarity in their
degree distribution (Thadakamalla et al., 2004). Meanwhile, scale-free networks are
highly robust to random failures but are sensitive to targeted attacks. Thus, random
networks and scale-free networks present two characteristically distinct topologies, a
systematic examination of which can provide deeper insights regarding the association of
network characteristics with its robustness against disruptions.
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 emphasizing that supply
networks follow topologies commonly observed in complex adaptive systems (Surana et
al., 2005; Sun and Wu, 2005; Pathak et al., 2007; Wang et al., 2008; Bichou et al., 2007),
in this paper we consider random and scale-free network topologies for our research
investigation of robustness of supply networks.

5
The theory of random networks has its origin in the use of probability methods in
problems related to graph theory. Erdős 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. There are
n
NN
C
]2/)1([
possible graphs that can be formed with all graphs having
equal probability of being realized in the probability space. The theory of random graphs
concerns with an examination of this probability space as
N .
The scale-free networks were motivated from a mismatch between the clustering
coefficients found in real-world network and those predicted by random graphs. Also, it
has been observed that even for those networks for which P(k) (a distribution function
representing the probability that a randomly selected node has exactly k edges) has an
exponential tail, the degree distribution do not follow Poisson distribution as suggested in
random graphs theory. Barabási and Albert (1999) present the idea of scale-free network
by considering the power-law degree distribution that is observed in several real world
networks. The networks grow by continuous addition of new nodes. Instead of following
a random-attachment of nodes, these networks follow a preferential attachment logic
whereby new nodes join a node that is already highly connected (i.e. exhibit high degree).
Formally, the probability Π that a new node n will connect to a node i in the network
depends on the degree k
i
of node i:
=Π
j
j
i
i
k
k
k )(.
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). In the following subsections we present details
regarding network characteristics that are used for our research investigation.

Citations
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Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

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Journal ArticleDOI
Abstract: An intertwined supply network (ISN) is an entirety of interconnected supply chains (SC) which, in their integrity secure the provision of society and markets with goods and services. The ISNs are o...

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)....

    [...]

  • ...…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…...

    [...]


Journal ArticleDOI
TL;DR: This study conceptualizes supply network disruption and resilience by examining the structural relationships among entities in the network by comparing four fundamental supply network structures, and shows that node/arc-level disruptions do not necessarily lead to network- level disruptions, and demonstrates the importance of differentiating a nodes/arc disruption vs. a network disruption.
Abstract: Increasingly, scholars recognize the importance of understanding supply network disruptions. However, the literature still lacks a clear conceptualization of a network-level understanding of supply disruptions. Not having a network level understanding of supply disruptions prevents firms from fully mitigating the negative effects of a supply disruption. Graph theory helps to conceptualize a supply network and differentiate between disruptions at the node/arc level vs. network level. The structure of a supply network consists of a collection of nodes (facilities) and the connecting arcs (transportation). From this perspective, small events that disrupt a node or arc in the network can have major consequences for the network. A failure in a node or arc can potentially stop the flow of material across network. This study conceptualizes supply network disruption and resilience by examining the structural relationships among entities in the network. We compare four fundamental supply network structures to help understand supply network disruption and resilience. The analysis shows that node/arc-level disruptions do not necessarily lead to network-level disruptions, and demonstrates the importance of differentiating a node/arc disruption vs. a network disruption. The results also indicate that network structure significantly determines the likelihood of disruption. In general, different structural relationships among network entities have different levels of resilience. More specifically, resilience improves when the structural relationships in a network follow the power-law. This paper not only offers a new perspective of supply network disruption, but also suggests a useful analytical approach to assessing supply network structures for resilience.

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…...

    [...]

  • ...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…...

    [...]

  • ...• 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....

    [...]

  • ...…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)....

    [...]

  • ...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)....

    [...]


Journal ArticleDOI
TL;DR: The reasons and mitigation strategies for the ripple effect in the supply chain are observed and a ripple effect control framework that includes redundancy, flexibility and resilience analysis is presented.
Abstract: In this study, the ripple effect in the supply chain is analysed. Ripple effect describes the impact of a disruption propagation on supply chain performance and disruption-based scope of changes in...

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....

    [...]


Journal ArticleDOI
Abstract: A great deal of research has focused on supply chain risk management, but the question “Which supply chain characteristics increase the frequency of supply chain disruptions?” has not received much attention from empirical research. This is a relevant question, because firms seek stability in their operations, and therefore managers need to know how the structure of their supply chains affects the occurrence of disruptions. The present study addresses this issue with a specific focus on upstream supply chain (supply-side) disruptions. Drawing on the literature on supply chain complexity, we devise and test a model that predicts the frequency of supply chain disruptions based on a multi-dimensional conceptualization of upstream supply chain complexity. Not only do the empirical findings suggest that all of the three investigated complexity drivers – horizontal, vertical, and spatial complexity – increase the frequency of disruptions, but also that they interact and amplify each other's effects in a synergistic fashion.

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

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"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....

    [...]

  • ...…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…...

    [...]


Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

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....

    [...]


Frequently Asked Questions (1)
Q1. What are the contributions in "Supply network topology and robustness against disruptions – an investigation using multiagent model" ?

In this paper, the authors examined the impact of supply network characteristics, such as average path length, clustering coefficient, size of the largest connected component, and maximum distance between two nodes in the largest connecting component, on performance measured in terms of inventory levels, backorders and total costs within a supply network.