In a recently published article, my co-author and I investigate supply network topology and robustness against disruptions. In this post I provide details of the study that couldn't be published due to the word limit constraints in the journal.
Research Motivation
Supply
disruptions have been an important managerial consideration for several years. Considerable
attention is now being given to this issue, especially after recent high
profile events such as the terror attack on the World Trade Center on September
11, 2001 and the disruption caused by hurricane Katrina. 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. In the case of Ford,
several assembly lines were stopped due to delayed deliveries from Canada and Mexico, resulting in a 13% decrease
in Ford’s outputs during the fourth quarter of 2001 as compared to its
production plan. Meanwhile, Toyota also had to halt its production as the
supplies from one of its key supplier could not be delivered due to the
supplier’s inability to receive a key component (steering sensors) that were
expected to arrive from Germany.
Firms
constantly face supply disruptions that adversely affect their performance. The
delayed deliveries of microprocessor chips to Ericsson and the consequential
$400 million losses incurred by the company due to a fire that affected the
semiconductor plant of its key supplier is an often cited example of the costly
implications of supply chain disruptions. In their recent news brief, Cadbury Schweppes reported
that their market share of candy is expected to be adversely affected due to the
disruption of production at one of their main candy facility in Sheffield, U.K.
caused by floods in June. In July 2007, 70% of Japan's
auto production was temporarily paralyzed for a week due to the disruptions in
the supply of piston ring costing $1.50 a piece. The disruption was 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. Toyota Motor Corp. had to halt production for
about one and a half days at all 12 of its domestic plants, causing a loss of
output of at least 25,000 vehicles, with 60% of these earmarked for exports.
Honda Motor closed a plant that produces the popular Civic and Fit models for a
day, resulting in the loss of 2,000 vehicles. Nissan Motor Co. halted
operations on several production lines at all four of its plants for almost two
days. Mitsubishi Motors Corp., Mazda Motor Corp., Suzuki Motors Corp. and Fuji
Heavy Industries Ltd., all had to stop or slow down their production for a day
or two.
Several
supply networks exhibit incredible robustness in the presence of disruptions
while others fail to survive random failures or targeted attacks. Supply chain practices such as redundancy and
flexibility play an important role in determining the resilience and robustness
of a supply network against disruption. Yet, the growing understanding of the
importance of network characteristics in determining the error tolerance of the
world wide web , Internet, and metabolic networks raises the question: Are resilience and robustness of supply
networks encoded in their topologies? Firms such as American Airlines, McDonald’s Corp, Limited Brands and Ace
Harware Corp., have characteristically different supply networks, which make their levels of resilience and robustness to random failures and
targeted attacks to be considerably different. While
the resilience of a supply network is its ability to come back to normalcy
after disruption, the robustness of a supply network focuses on the ability of
the network to withstand disruptions and continue normal mode of operations as
much as possible. It can be argued that the inherent robustness of the supply
network lends a significant contribution to the resilience of a supply network.
In this study we focus on the robustness of a supply network and examine whether the topology of a supply
network explain its robustness in the presence of random failures and targeted
attacks.
Research Design
We study this
system by building a multi-agent simulation model. The use of multi-agent simulation fits within the complex adaptive
systems (CAS) perspective of analyzing organizational issues. CAS are
characterized by macro-level emergent and adaptive properties that are not
exhibited by the individual agents at the micro-level. Several tenets underpin supply networks as
complex adaptive systems. The foremost
is the adaptive nature of supply networks, since they
continually evolve in dynamic environments.
Secondly, as CAS, supply networks exhibit self-reinforcing positive and
negative feedbacks that invoke path dependencies. Emerging phenomena originating in one part of
the network, in effect, propagate forward and backwards throughout the network
driving strategic decisions. Multi-agent simulation provides an ideal approach
to examine various issues underlying the research objectives of this
study. Using this approach we are able
to capture the complexities and dynamics associated with network topologies and
examine the evolutionary nature of choices made by firms within these supply
networks. The multi-agent simulation method enables an examination of patterns
emerging at the network level due to the micro level decisions made by
individual supply chain agents. It also allows an investigation of the impact
of failure of a node (representing a supply chain entity) on the overall
behavior of the supply network. We adopt the agent-based modeling framework
and generate networks by using the underlying principles of random networks and
scale-free networks. Some domain constraints related to supply networks are
considered in the agent-based model to eliminate networks that are impractical
and lack conceptual validity. We use the NetLogo modeling platform for developing the agent-based model. The details regarding the
agent-based model and the experimental design are presented in the following
sub-sections.
Agent-Based Model
Our model
extends the basic Beer game pby allowing for more
complex network topologies. The Beer game has four players – factory,
distributor, wholesaler and retailer – linked in the form of a serial supply
chain. Using the agent based model framework, we model the stock and flow
structure of the system and the decision rule used by managers. Once
the validity of the results for the basic beer game structure was established
we extended it by supporting the existence of any number of distributors,
retailers, and customers. The model allows the network to evolve until a
specified number of nodes (i.e. factories, distributors, warehouses and
retailers) are created. During the evolution, we can specify the logic by which
the nodes attach to other nodes. We subject the network formation process with
certain conditions to ensure that the resulting network represents a supply
network. In particular, we consider a single factory who can supply to
warehouse, distributors or retailers depending upon the specific network
topology that is under consideration. The supplies to the factory are modeled
with a lead time without explicitly modeling the raw materials and component
suppliers. In our network considerations, the end customer demand is always
satisfied from a retail location. This condition is included in the model,
since otherwise in scale-free network it will make several nodes redundant as
the customer demand would link with those nodes that are already highly
connected.
Since
our factory, distributors, warehouses, and retailers can have more than one
player buying from them we had to add some extra rules that are not present in
the basic beer game. The players satisfy the orders they receive on a
first-come first-serve basis, regardless of the amount in the order. If an
order cannot be completely filled then the player fills as much of the order as
it can and fills the rest when it receives new inventory (in the case of
factory when it completes the manufacturing process). The quantity that a
factory, distributor or wholesaler is unable to fulfill is treated as
backorder. The shortages at the retail location are lost orders. Another
difference from the basic Beer game is in the initial conditions. In the
original Beer game all players start with the same inventory since each one
only has one customer. In our model the initial inventory of each player is
proportional to how many other players buy from it, so a player with 2
customers will start with an inventory that is twice as large as that of a
player who only has 1 other player that buys from him.
Two
players that are connected directly to each other, where one of them buys from
the other one, are said to be at a distance of 1. More generally, the distance
between any pair of players is the smallest number of edges which one would
need to traverse in the graph to go from one node to the other. The calculation
of these values is the classic max-flow problem in graph theory that can be
solved using Dijkstra’s algorithm. Our model implements Dijkstra to find the shortest path between all
pairs of nodes and then uses these values to determine the average path length
and the largest connected component.
Using
this framework, we generate supply network topologies. It has been observed
that complex networks are characterized by large degree of clustering. The complexity inherent in supply networks suggest that these networks too
would be characterized in terms of higher clustering coefficients than random
networks. While studies have begun to consider the scale-free nature of supply
networks, rigorous empirical validation of the
topological nature of supply networks is yet to be done. Therefore, for the
purpose of generalizability and in concert with other studies that examine
topological issues, we consider two types of network
topologies: (i) scale-free topology (in line with the complex nature of supply
networks) and (ii) random networks (these most widely studied network topology
are considered for comparison). With the overall framework and constraints
presented earlier, scale-free networks were generated by using the preferential
attachment logic and the random networks are
generated by following a random attachment of nodes. Within each topological
type, we randomly generate 10 network topologies for in-depth examination.
To
generate a new network we start with one node, the factory, and then create new
nodes one at a time connecting them to existing nodes. In the random topology
each new node is connected to one randomly chosen existing node where all
existing nodes have equal probability of being chosen. In the preferential
attachment topology we follow the standard algorithm 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. For example, if there are three nodes and they have 1, 2, 3 edges
respectively then each will chosen with probability 1/2, 2/6, 3/6,
respectively. We measure the network characteristics, i.e. average path length,
clustering coefficient, size of the largest connected component and maximum
distance between nodes in the largest connected component by using the standard
conceptual and mathematical definitions.The conceptual definitions are as follows:
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.
Clustering Coefficient: The clustering coefficient presents an approach
to evaluate the probability that two nodes are nearest neighbors of each other.
Size of the largest connect component: A connected, isolated subgraph or cluster of a
network is defined as its component. We measure the size of the largest component in a network. We also measure the maximum distance between nodes in the largest connected component.
In
an agent based model all the facilities as well as the customers (modeled as a
random demand function that sets the value of demand at every time step as a
number between 0 and 8) are treated as agents. We set the number of agents to
30. To ensure comparability of these topologies we ensure that each topology
consists of 18 facilities comprising of one factory, twelve retail locations
that are directly facing the customer demand and five intermediaries acting as
distributors or warehouse. The choice of the scale (i.e. one factory, five
intermediaries and twelve retailers) is arbitrary and the model can be scaled
to higher and lower number of nodes. The specific network topologies considered
in the study are presented below.
Note: Square represents manufacturing plant, circle represent
distribution center/ warehouse and pentagon represents retail outlets that are
in direct contact with the customers
*The following ten network topologies were generated by using the algorithm for preferential attachment:
**The following ten network topologies represent random networks:
In
the event when a facility fails due to random failure of targeted attack, the
purchase orders and deliveries arriving to the facilities accumulate until the
facility becomes functional. Once the
facility is operational, the purchase orders and deliveries are attended to on
a first-come first-serve basis.
The
timing in our model is the same as in the original Beer game. The unit of
analysis is in weeks and all facilities take decisions on a weekly basis. Both
orders and deliveries have to spend one week in transit and the total
replenishment cycle (from order to receipt) is 4 weeks.
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. To ensure a close
correspondence to theory, we choose the parameter
values to be identical to the original beer game. The overall
experimental design and parameters used for the study are reported in table 1.
We ran the agent based simulation model for 105 time
ticks. These 105 time ticks correspond to 105 weeks, constituting 2
years of data of decision making and performance in a supply network context.
Twenty replications of simulation runs are used and we average the weekly data
obtained from these 20 replications. In total 25 experiments (with 20 replications
of each experiment) were conducted for each topology (i.e. a total of 500
experiments for the 20 network topologies considered in the study) using 3
instances of probability of random failures (0, 5%, 10%), 3 instances of
probability of targeted attacks (0, 5%, 10%) and 3 instances of severity of
disruptions measured in terms of the downtime of the affected facility (1
week, 2 weeks, 3 weeks).
We examine the
robustness of individual topologies by undertaking paired sample t-test for
each network topology considered in the study. The performance of a network in
the absence of both random failures and targeted attacks is used as the base
case. The performance of all twenty network topologies considered in this study
in the presence of varying degrees of random and targeted disruptions are
compared with the base case. 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). The topologies that exhibit significant difference of performance
(i.e. p-value ≤ 0.05) are considered as vulnerable.
As a next step, we utilize the information from the
paired t-test and categorize the topologies as robust (coded as 1) or
vulnerable (coded as 0). We use binomial logistics regression analysis to
examine the relationship between network characteristics, i.e. average path
length, clustering coefficient, size of the largest connected component within
the network and the maximum distance between nodes in the largest connected
component, and the robustness of supply network against disruptions. First, we
undertake the binomial logistics regression analysis for the entire sample of
network topologies considered in this study. We use the topology type
(categorical variable denoting scale-free or random network) as a control
variable. Subsequently, we split the sample into scale-free and random-networks
and investigate the hypothesized relationships in
these network topologies separately. For each topology, we use the data
collected from the 24 disruption scenarios based on the probability of random
failures, probability of targeted attacks and severity of the facility
shutdown.
Results
The
results for the overall sample present a compelling evidence of the association between network
characteristics and robustness of supply networks. We find that a unit increase
in average path length and clustering coefficient substantially increase the
odds of making the supply network vulnerable from the point of view of
inventory levels, backorders and total costs. For every
unit increase in the size of the largest connected component the odds of having
a robust supply network from the perspectives of inventory levels, backorders
and total costs increase by about 1.6 times, 3 times and 2.6 times
respectively. A unit increase in the maximum distance between nodes in the
largest connected component increases the odds of a robust supply network from
backorders and total cost perspective by a factor of 8.7 and 10.2,
respectively. The significant association of the categorical control variable
(1: Scale-free network; 2: Random network) also deserves some discussion. The
results show that a scale-free network is relatively more robust
from the inventory perspective, however, when viewed from the backorders and
total cost perspectives, the odds of a random network being robust than scale-free
networks are as high as 5.6 times and 2.9 times respectively.
We also conducted separate analyses for the data representing scale-free and random networks.
For scale-free networks we find that the average path length, clustering coefficient and size
of the largest connected component are significantly associated with deterioration
of inventory levels in the presence of disruptions. We do not find support for the association of maximum distance between
nodes in the largest connected component with deterioration in inventory levels
in the presence of disruptions. All network characteristics considered in this study are significantly
associated with robustness of supply networks evaluated from the perspective of
deterioration in backorders in the presence of disruptions. We do not
find evidence for the association of average path length and
maximum distance between nodes in the largest connected component with deterioration
of total costs in the supply network in the presence of disruptions. However,
clustering coefficient and the size of the largest connected component were
significantly associated with robustness from total cost perspective.
The results suggest that a unit increase in clustering coefficient substantially increase the
odds of making the supply network vulnerable. A unit increase in average path
length also substantially increase the odds of making the supply network
vulnerable from the point of view of inventory levels and backorders. As the size of the largest connected component of scale-free
networks increase by one unit the robustness of the network from inventories,
backorders and total costs perspectives increase by almost 2, 2.7 and 5 times,
respectively. 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.
For random networks the results indicate weak
association of clustering coefficient and maximum distance between nodes in the
largest connected component with robustness of supply networks in terms of
inventory levels. The results do not support an association of
average path length and size of the largest connected component with robustness
in terms of inventory levels. Relationships for robustness,
measured in terms of backorders and total costs, were supported. We
find that similar to scale-free networks, a unit increase in clustering
coefficient substantially increases the odds of vulnerability of random
networks against random failures and targeted attacks. A unit increase in
average path length substantially increases the odds of vulnerability from
backorders and total cost perspectives. A unit increase in
the size of the largest connected component increases supply network
robustness, viewed from backorders and total cost perspectives, by a factor of
3.2 and 2.1 times, respectively. 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.
Managerial Implications
The results of
this study present important managerial guidelines to build a robust supply
network. Along with redundancy and flexibility, we highlight the role played by
supply network topology in characterizing its robustness. The findings motivate
a reassessment of supply chain structure from a topological perspective with an
explicit consideration of network characteristics. Instead of relying on security professionals,
business continuity planners and insurance professionals, risk management and
business continuity should be a part of the strategic initiatives of a firm.
From a supply chain context, network design forms an important strategic
consideration. Our study sheds light on the salient aspects of network design
that play an important role in building a robust supply network.
Based
on the findings from this study we emphasize that long average path lengths
between nodes in a supply network are detrimental for its robustness against
disruptions. Shorter average distances between nodes in the network allow
faster propagation of products and information and thus aid in enhancing the
responsiveness of supply network in the event of disruption. A clustered form
of supply network has been widely adopted by several firms due to its advantages
in terms of consolidation, efficiency and quick response. The significant
association of the size of the largest connected component with robustness of
supply networks provides motivation for formation of large sub-structures in
the supply network. However, the results also suggest careful examination of
the nature of connection between nodes in these clusters as well as in the
overall supply network. Specifically, a negative association between clustering
coefficient and robustness of supply networks suggest a caution against forming
cliquish structures. Managers ought to give due cognizance to this issue and
carefully balance the advantages of a clustered configuration of facilities in
the supply network with the potential disadvantages in the presence of
disruptions. Finally, the reach of a facility in the largest sub-structure
plays a positive role in enhancing the robustness of a supply network.
For firms that are in the process of creating a
supply network, it is useful to take these factors into account. At the same
time for supply networks that are evolving in a complex fashion it is important to constantly keep track of the overall network in light
of its basic characteristics. A topological perspective when combined with the aspects
of flexibility and redundancy can greatly enhance the robustness of supply
networks. By presenting the association of individual network characteristics
with robustness of supply networks, we present an
approach towards a carefully nuanced supply network design.
The
study’s findings motivate the need for an evaluation of supply network
robustness from multiple outcome metrics. It is evident from the results that
even though a topology is robust when viewed from the inventory perspective it
could be vulnerable when examined from the perspectives of backorders and/or
total cost. Likewise, a network that is robust from the perspectives of
backorders could be vulnerable when evaluated from the perspectives of
inventory and total costs. It is therefore important to give consideration to
various performance metrics to get a better understanding of the robustness of
the supply network.
Source: Nair, A. and Vidal, J. M.
(2011). Supply Network Topology and Robustness against Disruptions: An
investigation using Multiagent Model. International
Journal of Production Research, Special Issue: “Multi‐agent and Holonic Techniques for Manufacturing Systems:
Technologies and Applications,”
49(5), 1391-1404.