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

TL;DR: In this article, the authors examined the relationship between supply network's topology and its robustness in the presence of random failures and targeted attacks, using 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.

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

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.

Figures

Table 5: Binary Logistics Regression Analysis Results (Random Networks) INVENTORY

Table 1: Experimental Design*

Table 2: Descriptive Statistics for the Overall Sample and the Sub-sample comprising of scale-free networks and random networks

Table 3: Binary Logistics Regression Analysis Results (Overall Sample) INVENTORY

Table 4: Binary Logistics Regression Analysis Results (Scale-free Networks) INVENTORY

Full text

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.

Frequently asked questions

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.