Analyzing the Resilience of Complex Supply Network Topologies Against Random and Targeted ...

12 Pages·2011·1.85 MB·English

28 IEEESYSTEMSJOURNAL,VOL.5,NO.1,MARCH2011
Analyzing the Resilience of Complex
Supply Network Topologies Against
Random and Targeted Disruptions
KangZhao,Member,IEEE, Akhil Kumar,Member,IEEE, TerryP. Harrison,and JohnYen,Fellow,IEEE
Abstract—In this paper, we study the resilience of supply net- tics network the corresponding entities might be supply units
works against disruptions and provide insights to supply chain and battalions. Since entities may take different forms in var-
managers on how to construct a resilient supply network from
iousapplicationdomains,werefer to themsimplyasnodesin
the perspective of complex network topologies. Our goal is to
anetwork.Manyresearchershavesuggestedthatsupplychains
study how different network topologies, which are created from
different growth models, affect the network’s resilience against shouldbeconsideredassupplynetworks[1],andthattheanal-
both random and targeted disruptions. Of particular interest ysisanddesignofsupplychainsshouldincorporatetheconcepts
are situations where the type of disruption is unknown. Using a ofcomplexsystems,especiallydynamiccomplexnetworks[2].
militarylogisticnetworkasacasestudy,weproposenewnetwork
Meanwhile,supplynetworks,especiallylargeorglobalones,
resiliencemetricsthatreflecttheheterogeneousroles(e.g.,supply,
often face disruptions, such as natural disasters, economic re-
relay,anddemand)ofnodesinsupplynetworks.Wealsopresent
a hybrid and tunable network growth model called Degree and cessions, unexpected accidents, or terrorist attacks. A disrup-
Locality-based Attachment (DLA), in which new nodes make tionmayinitiallyattackordisableonlyoneorfewnodesinthe
connections based on both degree and locality. Using computer system, but its impact may propagate further, sometimes even
simulations,wecomparetheresilienceofseveralsupplynetwork
withamplifications[3],amonginterconnectednodes.Suchdis-
topologies that are generated with different growth models. The
ruptions will thus affect the normal operations of many other
resultsshowthatthenewresiliencemetricscancaptureimportant
resilience requirements for supply networks very well. We also nodes. Occasionally, failures in a small portion of the system
found that the supply network topology generated by the DLA maycausethecatastrophicfailureofthewholesystem[4].Such
model provides balanced resilience against both random and eventsmayseriouslydisruptordelaytheflowofpeople,goods,
targeteddisruptions.
informationandfunds,andthusleadtohighercostsorreduced
IndexTerms—Complexnetwork,growthmodel,randomdisrup- sales[5].Asupplynetwork’sresilienceagainstdisruptionslies
tion,targeteddisruption,resilience,supplynetworktopology. initsabilitytomaintainoperationsandconnectednessunderthe
lossofsomestructuresorfunctions[6].Therefore,buildingre-
silientsupplynetworkshashighpriority,andithasattractedthe
I. INTRODUCTION
attentionofmanagers,shareholders,andresearchers[7].
Traditionalresearchonsupplychaindisruptionsoftenadopts
O UR daily life relies on the operations of supply chains, theriskmanagementperspectiveandfocusesonstrategiesand
which distribute goods and services, such as groceries, technologies to identify, assess, and mitigate risks and prob-
waterandelectricity,fromsupplierstoconsumers.Withglobal- lems caused by disruptions [5], [7]. Previous research [8] has
izationandthedevelopmentoftechnology,structuresofsupply revealedthatthetopologyofasupplynetworkhasgreatimpact
chainsareconstantlyevolvingandbecomingmorecomplex,as onitsresilience.Inotherwords,thewayindividualnodesareor-
newentitiesjointhesystemandnewconnectionsformbetween ganizedandconnected,andtheresultingnetworkstructure,e.g.,
them. As a result, today’s supply chain systems are shifting random,hierarchical,etc.,willaffectthesupplynetwork’sper-
away from the “chain” structure. Instead, they often feature a formancewhendisruptionsoccur.However,wefoundlittlere-
networkofinteractingentities,suchasmanufacturers,distribu- searchfollowingthisdirection.Inthispaper,weadoptthecom-
tors,andretailersinadistributionnetwork.Inamilitarylogis- plex-networkviewofsupplychainsandstudytheresilienceof
supplynetworksfromatopologicalperspective.Assumingthe
homogeneousrolesofnodes,theexistingliteratureofnetwork
ManuscriptreceivedMarch28,2010;revisedAugust31,2010;acceptedAu-
gust31,2010.DateofpublicationJanuary17,2011;dateofcurrentversion attachment strategies is often limited in application as the re-
February18,2011.TheworkofK.ZhaowassupportedbytheNetworkSci- silience of a supply network is measured inappropriately. By
enceExplorationResearchGrantfromPennStateUniversity.TheworkofA.
contrast,becausewetakeintoconsiderationtheheterogeneous
KumarwassupportedinpartbytheSmealCollegeofBusiness,PennStateUni-
versity. roles of nodes when evaluating supply network resilience, our
K.ZhaoandJ.YenarewiththeCollegeofInformationSciencesandTech- heuristic strategy is more general and effective than those de-
nology,ThePennsylvaniaStateUniversity,UniversityPark,PA16802USA
scribedinextantliterature.
(e-mail:[email protected];[email protected]).
A.KumarandT.P.HarrisonarewiththeDepartmentofSupplyChainand Theremainderofthepaperisorganizedasfollows.Wefirst
InformationSystems,SmealCollegeofBusiness,ThePennsylvaniaStateUni- briefly review related research. Using a military logistic net-
versity,UniversityPark,PA16802USA(e-mail:[email protected];thar-
workasacasestudy,weproposeanewtaxonomyofresilience
[email protected]).
DigitalObjectIdentifier10.1109/JSYST.2010.2100192 metrics for supply networks. Following that, a new network
1932-8184/$26.00©2010IEEE
ZHAOetal.:ANALYZINGTHERESILIENCEOFCOMPLEXSUPPLYNETWORKTOPOLOGIES 29
growthmodelisintroduced.Throughcomputersimulations,the
resilience of the supply network topology generated with the
newgrowthmodelisevaluatedandcomparedwiththetopolo-
giesofothernetworks.Finally,thepaperwillgiveaconclusion
anddiscussfutureresearchdirections.
II. RELATEDWORK
The literature contains ways to evaluate and optimize the
resilience of networks [9]–[11]. However, these network opti- Fig.1. Ahierarchicalmilitarysupplychain.
mizationproblemsaregenerallyNP-hard[12].Asaresult,when
the network is complex and evolving, finding the optimal net- workgrowthmodelsrevealsdistributedstrategiesandheuristics
work configuration is computationally expensive. While tech- thatunderliemanyreal-worldnetworks.
niques, such as simulated annealing [13], genetic algorithms Network growth models study the evolution of complex
[14], and heuristic procedure [15], have been used in the de- networks by specifying how new nodes connect with existing
sign of supply chain and distribution networks, this stream of onesthroughaprocessof“attachment”.Asnewnodesentera
workfocusesmainlyonlocationoffacilities,capacityplanning network, the network topology emerges from the distributed
andminimizingtransportationcosts,insteadoftheresilienceof attachment decisions of individual nodes. Different growth
supplynetworkswhensomenodesfailtooperate.Mostofthe models follow different attachment rules and lead to different
relatedworkonresiliencyalsodoesnotconsiderthetwingoals network topologies. For instance, the random-attachment
ofmaintainingresilienceunderrandomfailuresandtargetedat- modelrandomlyconnectstwopairofnodeswithapre-defined
tacks. probability and generates an ER random network [28]. The
Moreover, the optimization-based approaches are generally growthmodelsareoftensimple,yettheycanproducecomplex
centralizedinnature,becauseasupplynetworkmanagerisre- network topologies [29]. For example, in the preferential-at-
quired to have complete knowledge and control of the whole tachment model [26], the probability that a new node attaches
networktooptimizeit.However,itisoftendifficulttomeetthis toanexistingnodeisproportionaltotheexistingnode’sdegree.
requirementintherealworld.Researchershavefoundthatthe This leads to the well-known scale-free topology that can ex-
structureofasupplynetworkoftenemergesfromthedistributed plainmanyreal-worldnetworks,suchastheInternet.Itisalso
decisionsofindividualnodes,regardlessofthecentralizedna- one of the key underlying principles that guides the evolution
ture of the design [16], because some heuristic strategies are ofsupplynetworks[30].
oftenusedwhenanodedecideswhichnodestoconnectto.Fur- Specifically,whentheresilienceofcomplexnetworksagainst
ther,amanageronlyknowsandcontrolsthenetworkofitscor- errorsandattackswasanalyzed,itwasfoundthatscale-freenet-
porationororganization,butthesupplynetworkatamacrolevel works offer high tolerance against random failures. However,
consists of networks from different corporations or organiza- networks with scale-free topologies are vulnerable to disrup-
tions.Corporations’ororganizations’optimizationoftheirown tionsthat targetthemost connectednodes[31].Thadakamalla
networks may not necessarily lead to a globally resilient net- et al. introduced the topological perspective into the study of
work.Therefore,managers’awarenessofhownetworkdesign supplynetworkresilience[8].Itwasarguedthattraditionalhier-
strategies at the micro level affect the resilience of the whole archicalsupplychains,inwhichanedgecanonlyexistbetween
supplynetworkatthemacrolevelisalsoimportant. twounitsofdifferenttypes,arevulnerabletodisruptions.Amil-
At the outset, we also distinguish our work from that in the itarylogisticnetwork,consistingofbattalions,forwardsupport
areaofsocialnetworktheory.Socialnetworktheoryviewsthe battalions(FSB)andmainsupportbattalions(MSB)wasused
attributes of individuals as less important than their relation- asanexample.InthehierarchicalsupplynetworkinFig.1,the
shipsandtieswithotheractorswithinthenetwork.Ithasbeen failure of a single FSB disconnects about 30% of the battal-
usefulforexplainingmanyreal-worldphenomena,butitleaves ionsfromsupplies.Therefore,theauthorsproposedanewnet-
lessroom for individual agency,so muchofit restswithinthe workgrowthmodel(henceforthreferredtoasthe
structure of the network(s) that they are part of. Some sample model) that extends the hierarchical model by allowing edges
referencesinthisareaare[17]–[19]. betweennodesofthesametype.However,itstillarbitrarilycre-
Complexnetworksaredefinedasnetworkswhose“structure atesmoreedgesforsupportunitsthanforbattalions.Thesupply
is irregular, complex and dynamically evolving in time” [20]. networkgeneratedbythismodeliscalledtheHierarchy net-
They are ubiquitous in nature and society and have drawn the work. Computer simulations showed that Hierarchy supply
attentionofresearchersfromdifferentdisciplines.Examplesin- networks have satisfactory resilience against disruptions. Our
clude social networks [21], co-authorship networks [22], bio- studywillextendthisresearchfurther.
logical networks [23], interorganizational networks [24], etc.
Researchhasrevealedtopologiesofmanyreal-worldnetworks
III. PROPOSEDAPPROACH
[25],[26].Forexample,somesupplynetworkshavescale-free
topologies[27],whichfeaturefewhigh-degreehubnodesand Inthissection,wefirstpresentataxonomyofresiliencemet-
power-law degree distributions. The research on complex net- ricsforsupplynetworks.Thenewmetricsreflecttheheteroge-
30 IEEESYSTEMSJOURNAL,VOL.5,NO.1,MARCH2011
TABLEI ofthemilitarysupplynetwork,thesupplyavailabilityrateisthe
SOMEGENERICMETRICSFORNETWORKRESILIENCE percentageofbattalionsthathaveaccesstoMSBs.
Considerthemilitarylogisticnetworkasanundirectedgraph
with nodeset and edgeset ,where de-
notes an edge between nodes . As shown in (1),
is also the union of two nonoverlapping subsets of battalions
(nodeset )andsupportunits(nodeset ).
(1)
Thenthesetofbattalionsthathaveaccesstosupportunitsin
neousroles(suchassupply,relayanddemand)ofdifferenttypes
thenetworkisdefinedby(2),where denotesapathbetween
of nodes in supply networks. We then introduce a new hybrid
nodes and .Thus isthesetofbattalionsthathaveac-
and tunable supply-network growth model to generate a new
cesstosupportunitsthroughthesupplynetwork.Consequently,
supplynetworktopology,andevaluatemultiplesupplynetwork
the supply availability for a military logistic network is de-
topologies’resilienceagainstdisruptionsusingthenewmetrics.
finedastheratiobetweenthecardinalitiesofsets and ,
asshown in (3):
A. NewResilienceMetrics
Incomplexnetworkresearch,theevaluationofresiliencefo- (2)
cusesonthelargestconnectedcomponent(LCC),inwhichthere (3)
isapathbetweenanypairofnodes.Existingresiliencemetrics
aregenerictopologicalmetrics,includingsizeoftheLCC,av- Second, the connectivity of the system is also important.
eragepathlengthintheLCC,andthemaximumpathlengthin Topological connectivity is often measured by the size of the
theLCC.TableIexplainsthesemetrics. LCC. In a supply network whose LCC contains all nodes,
Applying these generic metrics to the evaluation of supply a node can access any other node through the network. On
networkresilienceislargelybasedontheassumptionthatroles the contrary, if a supply network’s LCC contains, say, only
and functionsof nodesin a supply network are homogeneous. 40% of all nodes, the network may be partitioned into several
However, in real-world supply networks, different types of isolatedsubnetworks,which meansflowsof goodsorservices
nodesplaydifferentroles.Oftentimes,thenormalfunctioning are limited to within a smaller subnetwork. Here, we extend
of downstream nodes may depend on the operations of up- the metric of LCC and use size of the largest functional sub-
stream nodes. In addition, one of the fundamental purposes of network instead.For the military logistic network,a
a supply chain is to connect suppliers with consumers. This functional subnetwork is the set
typeof“Origin-Destination”connectionistheprerequisitefor ofallfunctionalsubnetworks)satisfiesthetworequirementsin
the flow of goods or services [32]. As a result, preserving this (4).ThustheLFSN isonewiththelargestsizein
typeofconnectionindisruptionsiscriticalformaintainingthe (5):
operationsofthewholesupplynetwork.
(4)
In the military logistic network in [8], support units, such
asFSBandMSB,playadifferentrolefromregularbattalions.
MSBs are supply providers and regular battalions are con-
sumers. FSBs act as distribution centers and forward supplies
(5)
to consumers. Battalions often cannot perform their duties
withoutsupplies.Therefore,anLCC,inwhichthereisnosup- Thedifferencebetweentheoldandthenewconnectivitymet-
portunit,orwherebattalionsarefarfromsupportunits,should ricsisthattheremustbeatleastonesupplynodeintheLFSN.
notbeconsideredresilientbecausethereisnoorlimitedsupply Asubnetworkofamilitarylogisticnetworkcannotfunctionand
flow in such a subnetwork. Similarly, the distance between maintaintheflowofsupplieswithoutasupportunitinit.When
battalions and their support units is generally more important nodes fail during disruptions, a supply network that features a
foraresilientsupplychainthanthedistanceamongbattalions. largerfunctionalsubnetworkcanmaintainahigherlevelofcon-
Therefore, the heterogeneous roles (as supply and demand nectivityandisconsideredmoreresilient.
nodes)ofdifferenttypesofnodesinasupplynetworkmustbe We also describe two metrics for accessibility of supplies.
consideredwhenevaluatingtheresilienceofasupplychain. Higher accessibility means that supplies are closer to con-
The proposed taxonomy consists of system- and topology- sumers, and they can receive them at lower cost or in lesser
level metrics. We will use the military logistic network as an time.Asmentionedearlier,fromtheperspectiveofsupplynet-
exampletoillustrateourmetrics. workresilience,thedistancebetweenapairofdemandnodesis
First,weintroduceavailabilityasacriticalresiliencemetric notasimportantasthatbetweenasupplyandademandnode.
for supply networks, because it shows whether nodes in the Consequently, we propose supply path length as the length of
supplynetworkcangetthesuppliesthattheyneedtomaintain the path between a demand and a supply node (denoted by
normal operations. At the topological level, availability is in- ).Thus,theaveragesupply-pathlengthintheLFSN
terpretedassupplyavailabilityrate,whichisthepercentageof is the average of the minimum supply-path lengths between
demandnodesthathaveaccesstosupplynodes.Inthecontext all pairs of supply and demand nodes in the LFSN [see (6)].
ZHAOetal.:ANALYZINGTHERESILIENCEOFCOMPLEXSUPPLYNETWORKTOPOLOGIES 31
TABLEII connect to existing high-degree nodes. Thus, they can access
TAXONOMYOFTHENEWRESILIENCEMETRICSFORSUPPLYNETWORKS other nodes efficiently and at lower cost. The random-attach-
mentmodelisastrategythatrandomlyselectsnodestoattach
a new node to. The Hierarchy [8] model allows connections
betweennodesatthesamelevelinthehierarchy.
WhileHierarchy usesad-hocattachmentrulesfordifferent
typesofnodes,weproposeamoregeneralmodelcalledDegree
andLocality-basedAttachment growthmodel,whichis
inspiredbylocality-basednetworkgrowthmodels[22].Inour
model, a node considers not only the connectedness, but also
thedistanceofacandidatenodewhenestablishingconnections.
This model does not require special attachment rules for dif-
ferenttypesofnodesandmaybeappliedtoothertypesofcom-
plexnetworksingeneral.TheDLAgrowthmodelstartswitha
small number of disconnected nodes, say . We assume that
whenanewnodeentersthesystemitinitiatesedgestoconnect
Moreover,themaximumsupply-pathlengthintheLFSNisthe to existingnodes .Theattachmentrulesforanew
longest supply-path length between any supply and demand nodeareasfollows.
pair in the subnetwork [see (7)]. Naturally, shorter average Thefirstedgeconnectstoanode ofdegree withproba-
and maximum supply-path lengths mean better average- and bility where
worst-caseaccessibility:
(8)
The remaining edge(s) will connect to a node , which has a
(6) shortest distance of to the new node, with probability
where
(7) (9)
However,there isacaveatwhenusing thetwoaccessibility Equation(8)describesthedegree-basedattachmentpreference
metrics. In general, the comparison between the average and of the first edge of a new node, and is the customizable de-
maximumsupply-pathlengthsofdifferentsupplynetworks(or greepreferenceparameter.Giventhesame ,thenewnodewill
subnetworks) arefair andmeaningful only when thenetworks preferconnectingtoexistinghigherdegreenodes.When ,
areofsimilarsizes.WehavetotakethesizesoftheLFSNsinto the rule is similar to that of random networks, as every other
considerationbecausealargersupplynetworkwithmorenodes nodeinthenetworkhasthesameprobabilityofbeingconnected
willoftenhavelongeraveragepathsthananetworkwithsimilar withthenewnode.When ,theconnectionoccursbythe
topologybutfewernodes.Theexistenceofafewsupplynodes preferential-attachmentmodelofascale-freenetwork.Alarger
thatarefarawayfromsomedemandnodesmayincreasetheav- givesevenhigher tohigh-degreenodes.Therefore,as be-
erageandmaximumsupply-pathlengthinalargesubnetwork. comeslarger,itismorelikelythatthenewnodewillconnectto
WewillillustratethiswithourexperimentsinSectionIV. anexistingnodewithhigherconnectedness.Itisworthnoting
Itisalsopossibletocombinethesemetricsintoasingleob- that,attheverybeginningofthegrowthprocess,alltheexisting
jectivefunctioninordertocomparetheoverallperformanceof nodes are disconnected from each other, i.e., . In
differentsupplynetworksmoredirectly.However,wedecided thiscase,whenthefirstnewnodeentersthesystem,itwillran-
tousemultiplemetricsinsteadofasingleobjectivefunctionto domlychooseanexistingnodetoconnectto.
gainabetterunderstandingofasupplynetwork’sperformance Ontheotherhand,(9)givespreferencetolocalityfortheat-
from different perspectives. When the context in which a spe- tachment of a new node’s remaining edges if it is allowed to
cificsupplynetworkoperatesisknown,oneisinabetterposi- initiatemorethanoneconnection.Asthenodeisalreadycon-
tiontodetermineasingleobjectivefunction. nectedtothenetworkthroughthefirstedge,wecanthencalcu-
Table II summarizes our new metrics. We believe they can latetheshortestdistancesfromthisnodetoalltheothernodes.
more accurately measure supply network resilience, and are In (9), the non-negative integer distance and the customiz-
more systematic and realistic as compared to the metrics in able locality preference parameter constitute the attachment
previousworksuchas[8]. rule for the remaining edges of a new node. Given the same
, candidate nodes with smaller will have a higher proba-
B. NewHybridGrowthModel(DLA)
bility of being connected with new nodes. In other words, the
Asnotedearlier,thetopologyofacomplexnetworkdepends newnodeprefersnodesinitsneighborhoodoverdistantnodes.
onitsgrowthmodel.Inthecontextofsupplynetworks,growth When ,everyothernodeinthenetworkhasthesameprob-
models represent distributed connection strategies that a node abilityofbeingconnectedbythenewnodeasinarandomnet-
uses to decide which other nodes to connect to. For example, work.Alarger willreinforcetherelativeadvantageofnearby
inthepreferential-attachmentmodel[26],newnodespreferto nodes,whileasmaller willincreasethenewnode’schanceof
32 IEEESYSTEMSJOURNAL,VOL.5,NO.1,MARCH2011
Fig.2. AnexampleoftheDLAgrowthmodel.IDforthenewnodeisunder-
scored.
connecting to more distant nodes. Additionally, in the special
caseofasparsenetwork,wherenoexistingnodeisconnected
tothenewnodeviaanypath,anodeischosenrandomly.Lastly,
andforobviousreasons,multiplelinkstothesamenodearedis-
allowed.Also,becauseanewnodedoesnotneedtheexclusive
accesstoothernodeswhenestablishingconnections,deadlocks
willnothappeninourmodel.
Fig.2illustratesasimpleexamplefortheDLAgrowthmodel
with and .Inthisexample,eachnewnodewilles-
Fig.3. Cumulativedegreedistributionsforsupplynetworkswith1000nodes.
tablishtwoedges.Initially,thenetworkstartswiththreediscon-
nectednodes1,2,and3.Node4isthefirstnewnodethatenters
thesystemanditrandomlychoosestwonodestoconnectto,say, allsupportunitsbeforeanybattalionsaredeployed,arealsopos-
nodes1and2.Whennode5comesin,itsfirstedgewillprefer sibleandmayleadtodifferentsupplynetworktopologies.How-
existinghighdegreenodes,andthusnode4hasthehighestprob- ever,wechoosethisschemetoensureaconsistentcomparison
abilitytobechosen.Thesecondedgeofnode5willprefernodes with the previous work. We will then compare the resilience
that are close to it. Nodes 1 and 2 then have equal probability of supplynetworkswith Random,Scale-free,Hierarchy and
ofbeingchosen.Inthisexample,node5choosesnode4forthe DLA topologies. Each topology is generated with the corre-
firstedgeandnode1forthesecond.Similarly,node6connects sponding growth model and themilitarylogisticnetwork con-
tonodes4and2inStep4.Asmorenodesareadded,aDLAnet- figuration. For the DLA growth model, we use and
workwillemergefromthisattachmentprocess.Asnotedabove, .
the“hybrid”DLAismoregeneralthanHierarchy .Infact,the Fig.3illustratesthelog-logdegreedistributionsoffoursim-
Hierarchy modelisaspecialcaseoftheDLAgrowthmodel ulated1000-nodesnetworks.Ascale-freenetworkischaracter-
andcanberealizedwithasuitablechoiceofparameters.Inthe izedbythefamouspower-lawdistribution.Fig.4(a),4(b),and
nextsection,wewillevaluatetheresilienceofDLAnetworks, 4(c) show the snap shots of simulated small-scale supply net-
and compare it with other topologies using the new resilience workswithrandom,scale-freeandDLAtopologies(thelegend
metrics. is shown alongside). The DLA supply network features some
hub nodes and also some highly connected clusters, but con-
nectionstothehubsarenotasconcentratedasinthescale-free
IV. EXPERIMENTALRESULTS
network.
Asitisverydifficulttoconstructareal-worldsupplynetwork
Thenextstepistosimulatedisruptions.Theresearchoncom-
andgeneratedisruptionswithinittoevaluateitsresilience,we
plex network resilience often studies two types of disruptions
rely on computer simulations. In this section, we describe our
based on node removals: random and targeted disruptions.
methodforevaluatingandcomparingtheresilienceofdifferent
Random disruptions correspond to natural disasters (e.g.,
supply network topologies using simulation. The results from
earthquakes and hurricanes), accidents (e.g., fires and power
thesimulationofamilitarylogisticnetworkareillustratedand
outrage), and unexpected economic events (e.g., recessions
discussed.
and bankruptcy) in which every node has similar probabilities
of being disrupted.Wesimulate suchdisruptionsbyrandomly
A. SimulationSetup
choosing nodes and removing them from the network, so that
Weperformedadiscreteeventsimulationstudybasedonthe each node has the same probability of being removed. On the
method described in [33]. The main steps are: design a valid otherhand,intargeteddisruptions,“important”nodesaremore
conceptualmodel,developaprogramtosimulatethemodel,de- likely to fail than unimportant ones. Such failure might result
signandrunexperiments,andperformoutputdataanalysis.We from, for example, terrorist and military attacks, which are
simulatedthemilitarylogisticnetworkexamplein[8],soasto aimedatcriticalnodesinthesystem,suchasnetworkhubs,to
directlycompareHierarchy ,whichisdesignedformilitarylo- inflictmaximumdamage.
gisticnetworks,withothertopologies.Thenetworkisbasedon Among the many metrics to measure a node’s importance
areal-worldmilitarylogisticsystem.Itconsistsof1000nodes in a network, we choose the widely-used degree centrality in
and 1815 edges (the average degree is about 3.6). Battalions, line with previous research [8], [31]. In other words, we as-
FSB and MSB units enter the system following the ratio of sumethatthehigherthenodedegreeis,themoreimportantitis.
25:4:1,whichwasestimatedfromareal-worldmilitarylogistic Thereasonforpickingdegreeastheindicatorofimportanceis
system.Inotherwords,forevery25newly-deployedbattalions, thatitiseasierforattackerstofindthanothermetrics.High-de-
we added four FSBs and then one MSB into the supply net- gree nodes are often more visible because they are in contact
work.Inreality,otherdeploymentschemes,suchasdeploying with many other nodes [34]. Other centrality measures, such
ZHAOetal.:ANALYZINGTHERESILIENCEOFCOMPLEXSUPPLYNETWORKTOPOLOGIES 33
Fig.4. Simulated70-nodesupplynetworkswithvarioustopologies.(a)Randomsupplynetwork.(b)Scale-freesupplynetwork.(c)DLAsupplynetworkwith
.
as closeness, betweenness, and eigenvector centrality [35], re- thesize of their LFSN,it allows usto makea fair comparison
quireknowledgeofthenetworktopology,whichisusuallydif- ofaccessibilitynext.
ficult for attackers to obtain. To simulate targeted disruptions, Nevertheless, the accessibility metrics in Fig. 5(c) and (d)
we remove nodes in the order of decreasing node degree, and pointtowarddifferentconclusions.Ingeneral,whennodesare
updatethedegreesofallnodesaftereachremoval.Inaddition, removed, the accessibility of supplies worsen because the av-
edgesthatareconnectedtotheremovednodesarealsoremoved erageandmaximumsupply-pathlengthsintheLFSNincrease
inbothsimulationscenarios.Whilesimulatingdisruptionswith asmorenodesareremoved.Thisisintuitive,sincedisruptions
noderemovalshaslimitations(e.g.,itassumesthatdisruptions makeitincreasinglydifficultfordemandnodestoreceivesup-
will stop a node’s operation, while in the real world an entity plies. At the 60% node removal point, almost all supply-path
mayonly lose someof its capacitiesafter disruptions),agreat lengths reach their peak values and then start to fall. The de-
number of previous studies on complex network have shown creasesaremostlikelycausedbythefragmentationofthenet-
thatthissimpleandintuitiveapproachcanhelptorevealimpor- workandtheisolationof“hard-to-reach”demandnodes.
tantpropertiesonanetwork’sresilienceagainstdisruptions[8], Beforedisruptionshappen,thenetworkiswell-connected.A
[31]. demandnodemayhavemultiplesupplypathsavailable,leading
Inoursimulation,weremove50nodes(5%ofthetotalnodes) todifferentsupplynodes.Whensomenodesfail,supplycanstill
betweensuccessiveobservationstocorrespondtopreviousre- reach many demand nodes through alternative, albeit longer,
search [8] and to balance the simulation running time and the supply paths. The existence of those “hard-to-reach” demand
granularityoftheresults.Duringnoderemoval,wetrackthere- nodesthatarestillconnectedintheLFSNleadstotheincrease
siliencemetricsforeachnetworktopology.Intheend,wecom- in supply path length. However, the longer a demand node’s
parethenetworks’resilienceusingthemetrics.Toensureafair supply path is, the more this demand node depends on other
comparison, each network has the same number of nodes and nodestoreceivesupplies.Aseachnodehasthesameprobability
edges. On average, each new node initiates 1.8 new edges to to fail in random disruptions, the more dependent a demand
correspond with the military logistic network in [8]. Thus the nodeis,themorelikelyitistogetdisconnectedfromsupplies
totalnumberofedgeswillbearound1800andtheaveragede- whenadditionalnodesareremoved.Thusa“hard-to-reach”de-
greeis3.6edgespernode. mandnodehashigherprobablytobeisolatedfromtheLFSNas
morenodesareremoved.Aftermorethan60%ofnoderemoval,
many“hard-to-reach”demandnodesarenolongerintheLFSN.
B. SimulationResultsforRandomDisruptions
Instead,theremainingdemandnodesintheLFSNarecloseto
Fig.5showstheresponsesofthefournetworktopologiesto supply nodes. Meanwhile, the supply network becomes very
randomdisruptions.Thehorizontalaxesdenotethepercentage fragmented. The LFSN only has fewer than 200 nodes (20%
ofnodesthatwereremoved,whiletheverticalaxesarevalues oftheoriginalsize).WebelievethesmallerLFSNandthedis-
of the topology-level supply network resilience metrics from appearanceof“hard-to-reach”demandnodesintheLFSNcon-
Table II. The graphs are not extended beyond the 80% mark tribute to the decrease in supply path length when more than
on the horizontal axis because they converge after this point. 60%nodesareremoved.
Fig.5(a)and(b)showthatforallthefournetworktopologies, In any case, the supply-path lengths of Hierarchy are the
supplyavailabilityrateandthesizeoftheLFSNdecreasealmost shortest,indicatingthattheHierarchy networkisabletopre-
linearly as nodes are removed from the network. In terms of serve good supply accessibility. Even when 40–50% of nodes
availabilityandconnectivity,theperformanceofrandom,scale- are removed, there is no dramatic increase in its supply-path
free and DLA networks is very close, while the resilience of length. On the other end of the spectrum, accessibility in the
Hierarchy isslightlyworsethanoftheotherthree,asindicated randomnetworkhasthemostseriousdegradation.TheDLAis
byitssteeperslope.The95%confidenceintervalsforthefour betterthantheRandomnetwork,butnotasgoodastheScale-
networks’availabilityinTableIIIconfirmourobservationthat freenetwork,onaccessibility.
Hierarchy fallsalittlebehindintermsofmaintainingsupply Consideringallresiliencemetrics,webelievetheHierarchy
availability. In addition, since the four networks are similar in supply network is generally the most resilient against random
34 IEEESYSTEMSJOURNAL,VOL.5,NO.1,MARCH2011
Fig.5. Thefournetworks’responsestorandomdisruptions.Eachdatapointistheaverageof20runs.(a)Supplyavailabilityrate.(b)SizeoftheLFSN.(c)
Averagesupply-pathlengthintheLFSN.(d)Maximumsupply-pathlengthintheLFSN.
TABLEIII graphs are not shown beyond the 45% mark on the horizontal
95% CONFIDENCEINTERVALS FOR SUPPLY AVAILAIBILITY axis because they converge after this point. As expected, re-
RATES(%)INRANDOMDISRUPTIONS
silience of all the supply networks suffers different levels of
deteriorationswhencomparedwiththecaseofrandomdisrup-
tions.
We first examine availability. Unlike the uniformly
near-linear decreases found for random disruptions, the four
supply networksshow significant differences on this metricin
targeted disruptions. In Fig. 6(a), all four networks have very
low supply availability when 45% of the nodes are removed,
while in random disruptions, availability of all networks is
around 40% at this point. Among the four networks, only
disruptions. The resilience of other three network topologies the random network and the DLA network can still maintain
againstrandomdisruptionscanberankedinadescendingorder near linear decreases.DLA’savailabilityisclosetothatofthe
asScale-free,DLA,andRandomnetworks. random network at the early stage of the disruption (from 0
to 15%), but drops faster than for the random network after
C. SimulationResultsforTargetedDisruptions
20% of nodes are removed. Meanwhile, the Scale-free and
Arguably,resilienceagainsttargeteddisruptionsismoreim- Hierarchy networksseesignificantdecayinavailabilityfrom
portant than against random disruptions, because military lo- the very beginning of targeted disruptions. For example, 10%
gisticnetworksoftenfacemoretargetedattacksthanrandomat- noderemovalintheHierarchy networkleadstoanear60%
tacksfromopponents.Also,targetedattacksaregenerallymore dropinavailability.When20%ofthenodesareremoved,only
damaging than random attacks. Fig. 6 shows the responses of 20% of the battalions can still get supplies in the scale-free
the four network topologies to targeted disruptions. Similar to and the Hierarchy supply networks. By comparison, the
Fig. 5, the horizontal axes denote the percentage of removed Random and theDLA networkscanstill maintaintheirsupply
nodes,andtheverticalaxesdisplaytheresiliencemetrics.The availability at 64% and 48% respectively. 95% confidence
ZHAOetal.:ANALYZINGTHERESILIENCEOFCOMPLEXSUPPLYNETWORKTOPOLOGIES 35
Fig.6. Thefournetworks’responsestotargeteddisruptions.Eachdatapointistheaverageof20runs.(a)Supplyavailabilityrate.(b)SizeoftheLFSN.(c)
Averagesupply-pathlengthintheLFSN.(d)Maximumsupply-pathlengthintheLFSN.
TABLEIV Clearly,theRandomandDLAsupplynetworksshowacon-
95% CONFIDENCEINTERVALS FOR SUPPLY AVAILAIBILITY siderableadvantageovertheScale-freeandHierarchy supply
RATE(%)INTARGTEDDISRUPTIONS
networksinavailabilityandconnectivitywhenfacingtargeted
disruptions.Whatabout accessibility?SimilartoFig.5(c)and
(d), the plots of average and maximum supply-path lengths in
Fig.6(c)and(d)arealsobell-shaped.Actually,Fig.6(c)and(d)
haveverysimilargraphs,exceptthattheyusedifferentvertical
axesscales.Intuitively,wewouldliketocomparevaluesofeach
network’ssupply-pathlengthsintheLFSN,butsuchacompar-
isonisnotrepresentativeiftheLFSNshavevarioussizes.While
this condition was satisfied in the results from random disrup-
intervals in Table IV further illustrate that the four networks’ tions, however, as shown in Fig. 6(b), the sizes of the LFSNs
availabilities are very different in targeted disruptions than in inthefournetworksdiffersignificantlyforthesamedisruption
randomdisruptions. rate (especially when the disruption rate lies between 0% and
Wealsoconsiderconnectivity.AsdemonstratedinFig.6(b), 25%). For example, when 15% of the nodes are attacked, the
the deterioration in resilience is even worse in terms of con- supply-pathlengthsintheLFSNoftheHierarchy networkare
nectivity.Eventherandomnetwork,thebestperformeronthis about 26% shorter than those of the DLA network. However,
metric,cannotmaintainalineardecrease.ThesizeofitsLFSN at the same point, the size of Hierarchy ’s LFSN turns out to
is only 8% of its original size when 30% of the nodes are re- beonly7%ofthesizeofDLAnetwork’sLFSN.Therefore,one
moved.WealsoobserveverypoorperformancefromtheHier- cannotconcludethatHierarchy hasbetteraccessibilitysince
archy network,whoseLFSNdropsto22%ofitsoriginalsize thislikelyadvantagemaybeduetothemuchsmallersizeofits
withonly10%nodesremoved. LFSN.
36 IEEESYSTEMSJOURNAL,VOL.5,NO.1,MARCH2011
Fig.7. Distributionsofshortestsupply-pathlengthinthefournetworks’largestfunctionalsubnetwork(15%targeteddisruption).
To better highlight the issue of accessibility comparison in the peaks. Therefore, we believe the random network has the
the 0% to 25% disruption range, we draw the distributions of bestaccessibilityfollowedbytheDLAnetwork.TheScale-free
the shortest supply-path lengths in the four networks’ LFSN andHierarchy networksshowsimilaraccessibility.
at the 15% disruption point in Fig. 7. The horizontal axis de- Overall,theRandomnetworkisthemostresilientagainsttar-
notes the shortest supply-path lengths from a battalion to its geteddisruptions,withDLAaclosesecond.Hierarchy isthe
nearestsupplyunit,andtheverticalaxisrepresentsthenumbers leastresilientagainsttargeteddisruptionsamongthefour,while
ofbattalionsthatcanaccessitsnearestsupplyunitwithagiven theScale-freenetworkisonlyslightlybetter.
shortestsupply-pathlengthintheLFSN.InHierarchy ’sLFSN
with45nodes,anearestsupplyunitisalwayswithinadistance
V. DISCUSSION
of1to3toabattalion.Meanwhile,inDLA’smuchlargersub-
networks, more battalions can access the nearest supply unit Scale-free supply networks are very vulnerable to targeted
within a distance of 1 or 2 than in Hierarchy . However, a disruptions.Thisislargelybecausetheiroperationsrelyheavily
numberofbattalionsarefarawayfromasupplyunit,withdis- on hub nodes, which have very high degrees and are removed
tance up to 7, thus contributing to DLA’s higher average and at early stages of targeted disruptions. Recall that scale-free
maximumsupply-pathlength.Yet,comparedwithHierarchy , networks’preferential-attachmentgrowthmodelcorrespondsto
DLA has far more battalions that can easily obtain supplies thestrategythatnodesfocusmainlyonefficiencyandcost.The
withinthesamedistanceasHierarchy can. resultssuggestifnodesmakeconnectiondecisionssolelybased
Fig.6(c)and(d)stillcontributetoouranalysis,becausethey onefficiencyandcost,theresultingnetworkmaybevulnerable
illustratetherateatwhichthesupply-pathlengthsincreaseinthe totargeteddisruptions.
LFSN,i.e.,howfasttheaccessibilitydeteriorateswhendisrup- Besides confirming previous research results, our study
tionsoccur.Althoughsupply-pathlengthsofscale-freeandHi- based on new resilience metrics also provides some new
erarchy startwithrelativelylowervalues,theyincreasefaster and surprising insights. For example, earlier work showed
thanofDLAandRandomnetworks.Thesupply-pathlengthsof that Hierarchy supply networks were reasonably resilient
Scale-freeandHierarchy networksalsoreachtheirpeaksvery against both random and targeted disruptions [8]. By our new
early. By the 10% point, the supply-path lengths have almost resiliencemetrics,theystillretainverygoodresilienceagainst
tripled.Ontheotherhand,thepeaksofDLAandRandomcome random disruptions. However, their resilience against targeted
at20%and25%pointsrespectively.Inotherwords,thesupply disruptions,whicharemorelikelythanrandomattacksinamil-
accessibility of the Scale-free and Hierarchy networks dete- itary environment, is very disappointing. They have the worst
rioratesfasterthanoftheDLAandtheRandomnetworks.We availability and connectivity among the four supply networks.
foundthatsupply-pathlengthsreachpeakvalueswhenanother Removalofonlyasmallpercentageofnodeswilldisastrously
round of node removal makes the size of LFSNs drop below fragment the network and disrupt its flows and operations.
100, which is about 10% of their original sizes. For example, Hence, they are unsuitable against targeted disruptions which
intheHierarchy network,thesupply-pathlengthsreachpeak maywellariseinmilitarylogisticsystems.
values when 10% of nodes are removed and the LFSN has a The reason for the Hierarchy ’s vulnerability against tar-
size of 222. If an additional 50 nodes are removed, the LFSN geted disruptions lies in its growth model,which intentionally
retainsonly45nodes,whilethesupply-pathlengthsseesignifi- assigns more connections to support units. Therefore, support
cantdrops.WearguethatbythetimethesizeoftheLFSNfalls unitswillnaturallybecometopologicalhubsinthesupplynet-
below 10% of its original size, the network has already been work. When target disruptions strike, support units will have
decomposed into many isolated subnetworks, and the normal higher probabilities of being attacked. The failures of support
operations of the whole supply network have also been seri- units, which act as both functional hubs and topological hubs,
ously disrupted. Consequently, supply-path lengths after their will inevitably hurt the availability and connectivity. The im-
peak values are not as meaningful to consider as those before plication is that always assigning more connections to supply
ZHAOetal.:ANALYZINGTHERESILIENCEOFCOMPLEXSUPPLYNETWORKTOPOLOGIES 37
TABLEV
NUMERICALANALYSISFORSUPPLYAVAILABILITYRATE(10%TARGETEDNODEREMOVAL)
nodes may not be the best strategy to improve a supply net- likely to occur in practice. For random disruptions, the supply
work’sresilienceagainsttargeteddisruptions. availabilityratefallsbetween86%and89%andisonlyslightly
ThemeritofDLAsupplynetworksisthattheyshowgood,al- affectedbychangesin and .Ontheotherhand,fortargeted
thoughnotnecessarilythebest,resilienceagainstbothtypesof disruptionsavailabilityismuchmoresensitiveto and values.
disruptions.TheresilienceoftheDLAnetworkoftenliesinbe- SupplyavailabilityratesofDLAsupplynetworkswith10%tar-
tweenthatoftheRandomandtheScale-freenetworks.Specif- getednoderemovalaresummarizedinTableV.Eachvaluein
ically, in random disruptions, DLA is more resilient than the thetableistheaverageofresultsfrom100runs.
Randomsupplynetwork,whileintargeteddisruptionsitismore FromTableVweseethatas increases,theavailabilityde-
resilientthantheScale-freenetwork.Thus,itoffersabalanced cays. Meanwhile, given the same degree preference , higher
optionwhenonecannotpredicttheprobabilityofeithertypeof preferenceforlocality-basedattachment,i.e.,increasing ,will
disruption. generally lead to slightly lower availability. Some may notice
While previous research often improves resilience by intro- that when is high, has little impact on availability. This
ducing redundant capacities in manufacturing, transportation, may be explained by the very strong preference for high-de-
andstorage,etc,theapproachtakenbyDLAisslightlydifferent gree nodes. As a result, there emerge one or few “super hub”
becauseitdoesnotrequireanodeoredgetoreserveredundant nodes that are connected to almost all the other nodes. When
capacities. Instead, it changes the way that a supply network anewnodeentersthenetwork,itwillmostlikelyestablishthe
is constructed and consequently the network topology. Admit-
firstconnectionwitha“superhub”node.Thenmostoftheother
tedly,DLAisnotaclearlydominantmethod.Similartoredun-
nodeshavethesamedistanceof2tothisnewnode,sothepref-
dancy-basedapproaches,italsorequiresmoreinvestmenttoop-
erenceforlocalnodesbecomeslessimportant.Theresultsalso
erateandmaintainasupplynetwork.Thisisbecause,whenno
agree with our previous finding that random supply networks
disruptionoccurs,DLA’saccessibilityisnotasgoodasthatof
(i.e.,DLAwith and )havebetteravailabilitythan
Scale-freeandHierarchy ,whichimpliesthatitmaycostmore
scale-freeand DLAnetworkswith and intar-
todeliversuppliestodemandnodesinaDLAnetwork.
geteddisruptions.
DLA’sattachmentrulesalsoreflectthedistributednatureof
It should also be noted from our analysis that the impact of
supply network evolution. A new node entering a supply net-
localityonresilienceisweakerthanthatofdegree.Thiscanbe
work has only local information. Therefore, connecting with
attributed to the fact that on average each new node initiates
nearbynodesinitsneighborhoodismucheasierandlessexpen-
only1.8newedgesinourexperimentsinordertoensureafair
sive.Infact,theperformanceofDLAsuggeststhatwhennodes
comparisonwiththepreviouswork[8].IntheDLAmodel,the
considerbothefficiencyanddistancewhilemakingconnection
firstedgeattachmentisbasedondegree,whilesubsequentedge
decisions, the resulting supply network will have balanced re-
attachmentsarebasedonlocality.Thismeansthatattachments
silienceagainstbothtypesofdisruptions.ThusDLArepresents
basedonlocalityareabout20%fewerthanthosebasedonde-
a cost-effective strategy to build efficient yet resilient supply
gree.Webelievethatgivenmoreattachmentsbasedonlocality,
networks.
the impact of locality on availability might even be more pro-
Moreover,bytuningthedegreepreferenceparameter and
nounced.
thelocalitypreferenceparameter ,weareabletogeneratedif-
The numerical analysis shows that one can tune the DLA
ferentsupplynetworktopologies.Generally,alarger leadsto
model to generate supply network topologies with different
stronger preference for high degree nodes. Consequently, the
levels of resilience against different types of disruptions. This
resultingsupplynetworkwilldeviatefartherfromrandomness
customizability has important implications for the design and
andrelymoreheavilyonfew“superhub”nodesthathavevery
high-degrees. Larger means more local connections. The re- management of supply chains. As there is no single supply
sultingsupplynetworkwillfeaturemoreclustersandfewercon- networktopologythatdominatesallothersinbothrandomand
nections that bridge nodes that previously have long distance targeted disruptions, one needs to seek a balance or trade-off
between them. We conducted a simple numerical analysis to betweentheresilienceagainstrandomdisruptionsandtargeted
understand how the tuning of parameters and affects the disruptions. The DLA network growth model provides the
resultingDLAsupplynetwork’sresilience. opportunity for nodes to make connection decisions based on
Asanexample,weanalyzedtheeffectofchanging and on what type of supply network they are in and the balance of
supplyavailabilityrateswhen10%ofthenodesareremovedin possibledisruptionsthesupplynetworkwillface.Forinstance,
eachdisruptionscenario.Noderemovalhigherthanthisisnot a DLA model with lower is more appropriate for military