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Analysis of stochastic disruptions to support design of capacitated engineered networks

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Title:
Analysis of stochastic disruptions to support design of capacitated engineered networks
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Uribe-Sanchez, Andres F.
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Enterprise networks
Lean
Capacity disruptions
Countermeasure policies
Pandemic influenza
Dissertations, Academic -- Industrial Systems -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Abstract:
ABSTRACT: This work is a compilation of four manuscripts, three of which are published and one is in the second round of review, all in refereed journals. All four manuscripts focus on analysis of stochastic disruptions to support design of capacitated engineered networks. The work is motivated by limited ability to mitigate elevated risk exposure of large-scale capacitated enterprise networks functioning in lean environments. Such inability to sustain enterprise capacity in the face of disruptions of various origins has been causing multi-billion enterprise forfeitures and hefty insurance premiums. At the same time, decision support methodologies for reliable design of dynamic capacitated networks have been largely unavailable. This work is organized as follows. Paper 1 presents a methodology to analyze capacitated healthcare supply chains using a framework of forward flow-matching networks with multiple points of delivery. Special emphasis is given to developing stochastic models for capturing capacity trajectories at the points of delivery. Paper 2 focuses on assuring capacity availability for a critical vertex exposed to random stepwise capacity disruptions with exponentially distributed interarrival times and uniformly distributed magnitudes. We explore two countermeasure policies for a risk-neutral decision maker who seeks to maximize the long-run average reward. We present an extensive numerical analysis as well as a sensitivity study on the fluctuations of some system parameter values. Paper 3 extends the capacity assurance analysis for critical vertices by considering stepwise partial system capacity loss accumulating over time. We examine implementation of a countermeasure policy, aimed at reducing the disruption rate, for a risk-neutral decision maker who seeks to maximize long-run average return. We explore how the policy of maintaining the optimal disruption rate is affected by a number of system parameters. Finally, Paper 4 presents a dynamic predictive methodology for mitigation of cross-regional pandemic outbreaks which can be used to estimate workforce capacity loss for critical vertices due to such societal disasters.
Thesis:
Dissertation (PHD)--University of South Florida, 2010.
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ABSTRACT: This work is a compilation of four manuscripts, three of which are published and one is in the second round of review, all in refereed journals. All four manuscripts focus on analysis of stochastic disruptions to support design of capacitated engineered networks. The work is motivated by limited ability to mitigate elevated risk exposure of large-scale capacitated enterprise networks functioning in lean environments. Such inability to sustain enterprise capacity in the face of disruptions of various origins has been causing multi-billion enterprise forfeitures and hefty insurance premiums. At the same time, decision support methodologies for reliable design of dynamic capacitated networks have been largely unavailable. This work is organized as follows. Paper 1 presents a methodology to analyze capacitated healthcare supply chains using a framework of forward flow-matching networks with multiple points of delivery. Special emphasis is given to developing stochastic models for capturing capacity trajectories at the points of delivery. Paper 2 focuses on assuring capacity availability for a critical vertex exposed to random stepwise capacity disruptions with exponentially distributed interarrival times and uniformly distributed magnitudes. We explore two countermeasure policies for a risk-neutral decision maker who seeks to maximize the long-run average reward. We present an extensive numerical analysis as well as a sensitivity study on the fluctuations of some system parameter values. Paper 3 extends the capacity assurance analysis for critical vertices by considering stepwise partial system capacity loss accumulating over time. We examine implementation of a countermeasure policy, aimed at reducing the disruption rate, for a risk-neutral decision maker who seeks to maximize long-run average return. We explore how the policy of maintaining the optimal disruption rate is affected by a number of system parameters. Finally, Paper 4 presents a dynamic predictive methodology for mitigation of cross-regional pandemic outbreaks which can be used to estimate workforce capacity loss for critical vertices due to such societal disasters.
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AnalysisofStochasticDisruptionstoSupport DesignofCapacitatedEngineeredNetworks by AndresFernandoUribe-Sanchez Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofIndustrialandManagementSystemsEngineering CollegeofEngineering UniversityofSouthFlorida MajorProfessor:AlexSavachkin,Ph.D. TapasK.Das,Ph.D. JoseZayas-Castro,Ph.D. AlexVolinsky,Ph.D. YunchengYou,Ph.D. DateofApproval October19,2010 Keywords:enterprisenetworks,lean,capacitydisruptions, countermeasurepolicies,pandemicinuenza Copyright c 2010,AndresFernandoUribe-Sanchez

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DEDICATION Tomyfather,FernandoUribe.

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ACKNOWLEDGEMENTS IwouldliketothankDr.AlexSavachkin,myfriend,advisorandmentor.Without hissupport,thisdoctoraldissertationandrewardingresearchexperiencecouldnothave beenpossible.Notonlybecausehisresearchinterestswerethereasontostartmydoctoral studies,butbecausehiswisdom,hardwork,workethic,andtruthfulfriendshiphavebeen asourceofinspiration. IwanttothankDr.TapasK.Dasforhisfriendship,mentoringandencouragement duringthepastyears.IamprofoundlythankfultoDr.JoseZayas-Castro,foreverything hehasdoneformeandbecausehealwaysbelievedinmyprofessionalpotential.Thanks areduetomyclosestfriendsandgraduateclassmatesattheUniversityofSouthFlorida. Ialsowouldliketothanktheothermembersofmycommittee,Dr.AlexVolinskyandDr. YunchengYou,fortheircontributionoftimeandintellectualenergyinthisendeavor. Thisachievementcouldnotbepossiblewithoutmyfamily:Gladicilla,Anita,Mauro, Mapis,Paty,Hugo,Natis,Andrea,So,andPipe.Iwanttothankthemfortheirlove, supportandencouragementthroughoutmylife.TheyprovidedthestrengthIneededto continue.ThankstoGodandtomyfather,becausetheyhavebeenalwaysnexttome. Lastandbynomeanstheleast,Ihavebeenluckytohavethesupport,encouragement, faith,andlovefrommybestfriendandrock,DaynaLee.Thissuccessisalsoyours.

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TABLEOFCONTENTS ABSTRACT ii INTRODUCTION1 CONCLUSIONS7 APPENDIXA:COPYRIGHTAPPROVALS10 APPENDIXB:PUBLICATION1:ANALYSISOFHEALTHCARESUPPLY CHAINSYSTEMSEXPOSEDTORANDOMCAPACITYDISRUPTIONS15 APPENDIXC:PUBLICATION2:TWOCOUNTERMEASURESTRATEGIES TOMITIGATERANDOMDISRUPTIONSINCAPACITATEDSYSTEMS36 APPENDIXD:PUBLICATION3:ANOPTIMALCOUNTERMEASURE POLICYTOMITIGATERANDOMCAPACITYDISRUPTIONS INAPRODUCTIONSYSTEM54 APPENDIXE:PUBLICATION4:APREDICTIVEDECISIONAID METHODOLOGYFORDYNAMICMITIGATIONOFINFLUENZA PANDEMICS69 ABOUTTHEAUTHOREndPage i

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ABSTRACT Thisworkisacompilationoffourmanuscripts,threeofwhicharepublishedandoneis inthesecondroundofreview,allinrefereedjournals.Allfourmanuscriptsfocusonanalysis ofstochasticdisruptionstosupportdesignofcapacitatedengineerednetworks.Thework ismotivatedbylimitedabilitytomitigateelevatedriskexposureoflarge-scalecapacitated enterprisenetworksfunctioninginleanenvironments.Suchinabilitytosustainenterprise capacityinthefaceofdisruptionsofvariousoriginshasbeencausingmulti-billionenterprise forfeituresandheftyinsurancepremiums.Atthesametime,decisionsupportmethodologies forreliabledesignofdynamiccapacitatednetworkshavebeenlargelyunavailable. Thisworkisorganizedasfollows. Paper1 presentsamethodologytoanalyzecapacitatedhealthcaresupplychainsusingaframeworkofforwardow-matchingnetworks withmultiplepointsofdelivery.Specialemphasisisgiventodevelopingstochasticmodels forcapturingcapacitytrajectoriesatthepointsofdelivery. Paper2 focusesonassuring capacityavailabilityforacriticalvertexexposedtorandomstepwisecapacitydisruptions withexponentiallydistributedinterarrivaltimesanduniformlydistributedmagnitudes.We exploretwocountermeasurepoliciesforarisk-neutraldecisionmakerwhoseekstomaximizethelong-runaveragereward.Wepresentanextensivenumericalanalysisaswellas asensitivitystudyontheuctuationsofsomesystemparametervalues. Paper3 extends thecapacityassuranceanalysisforcriticalverticesbyconsideringstepwisepartialsystem capacitylossaccumulatingovertime.Weexamineimplementationofacountermeasure policy,aimedatreducingthedisruptionrate,forarisk-neutraldecisionmakerwhoseeksto maximizelong-runaveragereturn.Weexplorehowthepolicyofmaintainingtheoptimal disruptionrateisaectedbyanumberofsystemparameters.Finally, Paper4 presentsa dynamicpredictivemethodologyformitigationofcross-regionalpandemicoutbreakswhich canbeusedtoestimateworkforcecapacitylossforcriticalverticesduetosuchsocietal disasters. ii

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INTRODUCTION Leanmanufacturingphilosophyandassociatedbusinesspracticeshavebeenwidelyembracedanddeployedbyglobalenterprises.Thedesignofcapacitatedengineerednetworks isdrivenbyleanmanufacturingphilosophyandimplementationofglobaloutsourcing,reductionofinventories,consolidationofsuppliers,withthemainpurposeofimprovingoperationaleciency.AnexampleistheUSautomotiveindustry,wheresomeestimatesassert thattheshifttoJITschedulinghassavedcompaniesmorethan$1billionayearininventory costsalone. However,whileleanmanufacturinghassubstantiallyboostedoperationaleciency,such reductionismhasalsolefttheseenterprisesoperatinginanincreasinglyrisk-encumbered environment.Capacitydisruptionstriggeredbyforcesofnature,propertyandprocess relatedhazards,andhumaninterventions,haveshowntohaveaprofoundimpactonthe engineerednetworkrisk.Thefollowingexamplesdemonstratehowincreasedriskexposure andresultingcapacityimbalancecausemulti-billionenterpriseforfeituresandincreasing insurancepremiums. In1995,anearthquakehittheporttownofKobe,razedtotheground100,000buildings andshutdownJapan'slargestportforovertwoyears.In1999,anearthquakeinTaiwan displacedpowerlinestothesemiconductorfabricationfacilitiesresponsibleformorethan 50percentoftheworldwidesuppliesofcertaincomputercomponents,andshaved5percent oearningsformajorhardwaremanufacturersincludingDell,Apple,Hewlett-Packard, IBM,andCompaq.InSeptember2002,longshoremenontheUSWestCoastwerelocked outinalaborstrikefor11days,forcingtheshutdownof29ports.Withmorethan $300billionofdollarsingoodsshippedannuallythroughtheseports,thedisputecaused between$11and$22billioninlostsales,spoiledperishablesandunderutilizedcapacity. ThatDecember,apoliticalstrikeinVenezuelamadetransnationalbusinessesincluding GM,BP,Ford,GoodyearandProcter&Gamblehalttheirmanufacturingfortheduration 1

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oftheconict.The2003outbreakofSARSinChinaandSingaporeforcedMotorolato closeseveralplants.Morerecently,the2005hurricaneKatrinadestroyedtheinfrastructure ofthestateofLouisiana.Inthesameyear,alaborstrikeinAsianaAirlinesresultedin over90percentofthecargoservicescanceled.Man-madedisasters,fromterroristattacks tocomputerviruses,arealsoontherise. Nowadays,aseeminglyminordisruptioninaleaninfrastructurecanhavethepotential toinitiateacascadingsequenceofcapacitylosses,threateninghumanlivesanddevastating largesectorsoftheeconomy.Asaresultoftheaboveevents,accordingtoarecentsurveyby A.M.BestCompany,Inc.of600executives,69percentofchiefnancialocers,treasurers andriskmanagersatGlobal1,000companiesinNorthAmericaandEuropeviewpropertyrelatedhazards{suchasresandexplosions{andsupplychaindisruptionsastheleading threatstotoprevenuesources. Historically,enterpriseshavelackedappropriatedecisionsupportmethodologiesand computationaltoolssuitableforaddressingriskincurredthroughcapacitydisruptions.In academia,traditionalresearcheortsonminimizingthecostofsupplychainoperations andthefocusonleveragingeconomiesofscaleoftenyieldresultsthatoverconcentrate resources.Suchoptimalsolutionscanbeverysensitivetosystemperturbations,initiated byinternalandexternaldisruptions.Theinabilitytorecognizethehiddencostsofsuch overconcentrationheightenstheriskofincreasedcostsandcapacityimbalance. Thetraditionalliteraturethatexplicitlymodeltheimpactofdisruptionshassofar beenfocusingprimarilyona local levelofissuesincludingscheduling,ordering,inventory management,andlotsizing.Theseworkshavemodeledlocalentitiesexposedto operational instabilitiesiniproductionrateandleadtimes,iisupplyrate,includingmachinefailures, iiipricesofresources,andivprocessqualityandyield. Oneofthemostcommontypesofdisruptionappearingintheliteratureisthatofsupply ratechanges.Importanteortsincludeimanagementofstochasticdemandsystems, wheretheproductsupplyisdisruptedforperiodsofrandomduration,iiclassiceconomic orderquantityEOQproblemwithsupplydisruptions,iiiorder-quantity/reorder-point inventorymodelswithtwosupplierssubjecttoindependentdisruptionstocomputethe 2

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exactformoftheaveragecostexpression,andivanalyticalmodelsforcomputingthe stationarydistributionoftheon-handinventoryinacontinuous-reviewinventorysystem withcompoundPoissondemand,Erlangdistributedleadtime,andlostsales,wherethe suppliercanassumeoneofthetwoavailable"andunavailable"statesatanypointin timeaccordingtoacontinuous-timeMarkovchain. Otherstudiesaddressbothsupplydisruptionsandrandomdemand.Someexamples areidynamicmodelsconcerningoptimalinventorypoliciesinthepresenceofmarket disruptions,whichareoftencharacterizedbyeventswithuncertainarrivaltime,severity andduration,iithecontinuous-reviewstochasticinventoryproblemwithrandomdemand andrandomlead-timewheresupplymaybedisruptedduetomachinebreakdowns,strikes orotherrandomlyoccurringevents,andiiitheinventory-controlmodelwhichincludes adetailedMarkovianmodeloftheresupplysystem.Anumberofeortswhichaddress supplyanddemandchangeshavebeendevelopedintheeldofoilstockpiling,astherehas beengraveconcernovertheoilsupplyfromtheMiddleEast. Modelingproductionratedisruptionsmachinefailureshasbeenlargelyaddressedby extendingclassicaleconomicmanufacturingquantityEMQmodels.Theseeortsinclude itheEMQmodelwhentheproductionprocessissubjecttoarandomdeteriorationfrom anin-controlstatetoanout-of-controlstate,iimodelsofdefect-generatingprocessin thesemiconductorwaferprobeprocesstodetermineanoptimallotsize,whichreducesthe averageprocessingtimeonacriticalresource,iiitheapproximationoftheEMQmodel withPoissonmachinebreakdownsandlowfailurerate,andivthestudyofanunreliable productionsystemwithconstantdemandandrandombreakdowns,withthefocusonthe eectsofmachinefailureandrepaironoptimallot-sizingdecisions.Otherstudiesderive someuniquepropertiesoftheirmodelcomparedtotheclassicalEMQmodel,underthe assumptionofexponentiallydistributedtimebetweenfailuresandinstantaneousrepairof themachine. Muchoftherecentliteraturefocusesonminimizingcostsofsupplychainoperations, whereasonlyasmallfractionoftheeortshavebeendedicatedtomodelingtheimpactof variousdisruptions,suchasthoseaectingdemandpatterns,supplierandproductionlead 3

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times,prices,imperfectprocessquality,processyield,andotherfactors.However,sofar, onlyascantsubsetoftheliteraturehasattemptedtoanalyzesupplychain-widedisruptions, withmostoftheeortsfocusingonthefacilitylocationproblems. Atthispoint,wecansummarizethatresearcheortsaddressingthedisruptionofsupply arestillcomparativelynewandscant,andnoneoftheseattemptshaveaddressedtheissue ofstochasticcapacitydisruptionsindirectednetworks,inclosedform. Theworkpresentedinthisdissertationismotivatedbythelimitedabilitytomitigate elevatedriskexposureoflarge-scalecapacitatedenterprisenetworksfunctioninginleanenvironments.Suchinabilitytosustainenterprisecapacityinthefaceofdisruptionsofvarious originshasbeencausingmulti-billionenterpriseforfeituresandheftyinsurancepremiums. Atthesametime,decisionsupportmethodologiesforreliabledesignofdynamiccapacitatednetworkshavebeenlargelyunavailable.Thisdoctoraldissertationisacompilation offourmanuscripts,threeofwhicharepublishedandoneisinthesecondroundofreview, allinrefereedjournals.Allfourmanuscriptsfocusonanalysisofstochasticdisruptionsto supportdesignofcapacitatedengineerednetworks.Thisworkisorganizedasfollows. TherstmanuscriptisthepapertitledAnalysisofHealthcareSupplyChainSystems ExposedtoRandomCapacityDisruptions".Analversionofthisdocument,toappear inthespecialissueon HealthcareSystemsEngineering "inthe InternationalJournalof CollaborativeEnterprise byIndersciencePublisher,ispresentedintheAppendixB.1.IndersciencePublisherretainsthecopyrightofthismanuscript.Thewrittenauthorization fromthepublishertoincludethepaperinthisPh.D.dissertationisattachedinAppendix A.Inthispaper,wepresentanattempttocontributetodevelopmentofmathematicaltools formodelingandanalysisofriskinherentinhealthcaresupplychains,suchaspharmaceuticalandmedicalequipment/deviceenterprises.Ourunderlyingformulationleveragesthe analyticalconvenienceofformalismofcapacitatedfeed{forwardow{matchingnetworks FMNswithmultiplepointsofdeliveryPOD.Specialemphasisisgiventodeveloping stochasticmodelsforcapturingcapacitytrajectoriesatthepointsofdelivery. ThesecondmanuscriptistitledTwoCountermeasureStrategiestoMitigateRandom DisruptionsinCapacitatedSystems".Thispaperispublishedinthe JournalofSystems 4

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ScienceandSystemsEngineering ,volume19,number2,pages210-226,2010,bySpringer Publisher.AprintedversionispresentedintheAppendixB.2.SpringerPublisherretains thecopyrightofthismanuscript.Thewrittenauthorizationfromthepublishertoinclude thepaperinthisPh.D.dissertationisattachedinAppendixA.Inthisdocument,wefocus onassuringcapacityavailabilityforacriticalvertex.Weexaminerandomstepwisecapacitydisruptionswithexponentiallydistributedinterarrivaltimesanduniformlydistributed magnitudes.Weexploretwocountermeasurepoliciesforarisk-neutraldecisionmakerwho seekstomaximizethelong-runaveragereward.Aone-phasepolicyconsidersimplementationofcountermeasuresthroughouttheentiretyofadisruptioncycle.Theresultsofthis analysisformabasisforatwo-phasemodelwhichimplementscountermeasuresduringonly afractionofadisruptioncycle.Wepresentanextensivenumericalanalysisaswellasa sensitivitystudyontheuctuationsofsomesystemparametervalues. ThethirdmanuscriptistitledAnOptimalCountermeasurePolicytoMitigateRandom CapacityDisruptionsinaProductionSystem".Thispaperispublishedinthe International JournalofAgileSystemsandManagement ,volume3,number1/2,pages4-17-226,2008, byIndersciencePublisher.AprintedversionispresentedintheAppendixB.3.IndersciencePublisherretainsthecopyrightofthismanuscript.Thewrittenauthorizationfrom thepublishertoincludethepaperinthisPh.D.dissertationisattachedinAppendixA. Thisworkextendsthecapacityassuranceanalysisforcriticalvertices.Weinvestigatea manufacturingsystemexposedtounpredictedcapacitydisruptionswithexponentiallydistributedinteroccurrencetimesanduniformlydistributedmagnitudesofdisruptions.Each disruptionrendersastepwisepartialsystemcapacitylossaccumulatingovertimeuntilthe remainingcapacityreachesacertainlevel,uponwhichthesystemgraduallyrestoresthelost capacitytothetargetlevel.Weexamineimplementationofacountermeasurepolicy,aimed atreducingthedisruptionrate,forarisk-neutraldecisionmakerwhoseekstomaximize long-runaveragereturn.Weexplorehowthepolicyofmaintainingtheoptimaldisruption rateisaectedbyanumberofsystemparameters. ThenalmanuscriptistitledAPredictiveDecisionAidMethodologyforDynamicMitigationofInuenzaPandemics".Thisdocumentiscurrentlyinthesecondroundofreview 5

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inthespecialissueon OptimizationinDisasterRelief "inthe ORSpectrum bySpringer Publisher.AnalversionofthisdocumentispresentedintheAppendixB.4.Springer Publisherretainsthecopyrightofthismanuscript.Thewrittenauthorizationfromthe publishertoincludethepaperinthisPh.D.dissertationisattachedinAppendixA.Inthis work,wepresentalarge-scalesimulation-basedoptimizationmethodologyfordeveloping dynamicpredictivemitigationstrategiesforanetworkofregionalpandemicoutbreaks.The methodologyconsidersmeasuresofmorbidity,mortality,andsocialdistancing,translated intothesocietalandeconomiccostsoflostproductivityandmedicalexpenses.Wepresent asensitivityanalysisforestimatingthemarginalimpactofchangesinthetotalbudget availabilityandvariabilityofsomecriticalmitigationparameters.Themethodologyisintendedtoassistpublichealthpolicymakers.Thiseortcanbeusedtoestimateworkforce capacitylossforcriticalverticesduetosuchsocietaldisasters. 6

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CONCLUSIONS Currentlarge-scalecapacitatedenterprisenetworkscanspanmultiplecontinentsand subsumehundredsofsuppliersandcustomers.Inaddition,astheseenterpriseshavebeen adoptingthephilosophyofleanmanufacturing,includingslimminginventorybuers,global outsourcing,andconsolidatingsupplierbase,suchreductionismhasalsoleftthemoperating inanincreasinglyrisk-encumberedenvironment.Oneofthemostprofoundriskfactorsis unpredicteddisruptionsinavailablecapacity,asmightbecausedbyanumberofcontrollable anduncontrollablefactors,includingnature,processhazards,andhumanactivity.Atthe sametime,ecientpredictiveanalyticsandcomputationaltoolssuitableforanalyzingthe impactofcapacitydisruptionsonnetworkriskhavebeenlargelyunavailable. Inthisdoctoraldissertation,motivatedbylimitedabilitytomitigateelevatedriskexposureoflarge-scalecapacitatedenterprisenetworksfunctioninginleanenvironments,we focusonanalysisofstochasticdisruptionstosupportdesignofcapacitatedengineerednetworks.Inwhatfollows,wesummarizethemaincontributionofeachmanuscript. Intherstmanuscript,wepresentanoriginalanalysisofhealthcaresupplychain systemsexhibitingconvergingassemblyandexposedtorandomcapacitydisruptions.The supplychainwasmodeledasafeed{forwardow{matchingnetworkwithmultiplepoints ofdelivery-amathematicalformalismparticularlyusefulforunderstandingchangesinthe aggregatenetworkcapacity,asmightbeimpactedbyunpredictedperturbations.Inour novelwork,wecapturedthetime-xedprobabilitylawontheavailableeectivenetwork capacity,inthepresenceofcapacitypropagationdelays,inclosedform.Wethenconstrued twomodelsofstochasticdynamicsoftheavailableeectivecapacityatthenetworklevel. Thesetrajectoriescanbeusedtomodelanumberofdisruptivescenarios. Ouranalysiswillcontributetounderstandingthedegreeofriskexposureandvulnerabilityofglobalhealthcaresupplychains.Moreover,ourstudycanbeusedtoprovidea substantivemeasureofthetrade-obetweenaleanstructureofthesupplychainandits 7

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robustnessandagility.Thestochasticmodelsofcapacitydisruptionsdiscussedinthispaper presentoneoftheinitialattemptstocharacterizesupplychaindynamicsviaaFMN-based formalism.Inthefuture,thesestochasticmodelsofcapacitydynamicswillbegeneralized tofeaturedierentrecoverymodesandincorporatedispositionofstrategicinventorybuers orcapacityback-ups.Thisstochasticanalyticswillthenbecombinedwiththedynamicsof demandatthepointsofdeliveryandcapacityexpenditures,todevelopfuturemethodologies,basedonthetenetsofutilitytheory,toprovidedecisionsupportfordesignofresilient healthcaresupplychainsystems. Thesecondmanuscriptfocusesonassuringcapacityavailabilityforacriticalvertexof alarge-scalecapacitatedenterprisenetwork.Wepresentedoneofinitialattemptstoll thevacuumintheexistingliteratureandtofocusondevelopmentofactivecountermeasure policiesformanagingleancapacitatedsystemsinthepresenceofrandomcapacitydisruptions.Thevertexunderconsiderationexperiencedstepwisepartialcapacitydisruptions withexponentiallydistributedinterarrivaltimesanduniformlydistributedmagnitudes,followedbyinstantaneousrecovery.Examplesofsuchcapacitydynamicsinclude:ishortage ofrepairpersonnelandperformancedegradationcausedbyfailingequipmentwithafull repairuponacompletefailure,iinon-self-announcingstepwisesystemfailures,andiii gradualequipmentphaseoutandmodernization. Thisworkexplorestwodierentcountermeasurepoliciesforarisk-neutraldecision maker,whoseekstomaximizethelong-runaveragereward.Theinitialmodelconsideredaone-phasepolicy,wherecountermeasureswereimplementedduringtheentiretyofa disruptioncycle.Theresultsofthismodelservedasabasistoanalyzeatwo-phasestrategy,wherecountermeasureswereactivatedduringonlyafractionofadisruptioncycle.For thelattermodel,weaimedtodeterminetheoptimalthresholdwhenthecountermeasures shouldbedisengaged.Thispaperprovidesoneoftheinitialattemptsforprovidingclosed formsolutionsforoptimalcountermeasurepoliciesformitigationofrandomdisruptionsin capacitatedsystems.Wehopethatourworkwillbefurthergeneralizedtoaddresssimilar questionsforcapacitatedsystemsevolvingundermorecomplexcapacitydynamics. 8

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Thethirdmanuscriptextendstheanalysisonassuringcapacityavailabilityforacritical vertexofalarge-scalecapacitatedenterprisenetwork.Weexaminedaproductionsystem experiencingperiodiccapacitydisruptions,eachofwhichisfollowedbyarandomrecoverydelayandaconstantlinearrateofrecovery.Thesystemmanager'sobjectivewasto implementacountermeasurestrategytoalleviatetherateofdisruptionswithadecreasing convexcostfunction.Wederivedanoptimallevelofdisruptionratethatmaximizesthe long-runaveragereward.Theresultsofcomparativestaticssuggestthatchoosingtomaintainalowerdisruptionrateisoptimal,ifthesystemprotabilityishigh.Weconcluded thathigherunitprotsandmaximumcapacitylevelsincreasethecostsofdisruptionsand hence,mustbebalancedbyappropriatecountermeasurestrategies.Sinceshorterexpected recoverydelayandfasterlinearrecoveryreducetheeconomiclossofdisruptions,theoptimal leveloflambdaisincreasinginbothparameters. Finally,thefourthmanuscriptpresentsadynamicpredictivemethodologyformitigationofcross-regionalpandemicoutbreakswhichcanbeusedtoestimateworkforcecapacity lossforcriticalverticesduetosuchsocietaldisasters.Thedecision-aidmethodologypresentedinthispaperincorporatesvaryingvirusepidemiologyandregion-specicpopulation dynamics.Themodelsupportsdevelopmentofmitigationstrategiesforanecient,progressiveallocationofalimitedresourcebudgetoveranetworkofregionaloutbreaks.The modelseekstodynamicallyminimizetheimpactofongoingoutbreaksandtheexpected impactofpotentialoutbreaks,spreadingfromtheongoingregions.Themethodologyconsidersmeasuresofmorbidity,mortality,andsocialdistancing,translatedintothesocietal andeconomiccostsoflostproductivityandmedicalexpenses. 9

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APPENDIXA COPYRIGHTAPPROVALS 10

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APPENDIXB: PUBLICATION1:ANALYSISOFHEALTHCARESUPPLYCHAIN SYSTEMSEXPOSEDTORANDOMCAPACITYDISRUPTIONS Inthisappendix,wepresentthenalversionofthemanuscriptAnalysisofHealthcare SupplyChainSystemsExposedtoRandomCapacityDisruptions"toappearinthespecial issueonHealthcareSystemsEngineering"intheInternationalJournalofCollaborative EnterprisebyIndersciencePublisher.Theco-author,Dr.AlexSavachkin,authorizedto includethisdocumentinmydissertation.IndersciencePublisherretainsthecopyrightof thismanuscript.Thewrittenauthorizationfromthepublishertoincludethepaperinmy Ph.D.dissertationisattachedinAppendixA. 15

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APPENDIXC: PUBLICATION2:TWOCOUNTERMEASURESTRATEGIESTO MITIGATERANDOMDISRUPTIONSINCAPACITATEDSYSTEMS Inthisappendix,wepresentthenalversionofthemanuscriptTwoCountermeasure StrategiestoMitigateRandomDisruptionsinCapacitatedSystems"publishedintheJournalofSystemsScienceandSystemsEngineering,volume19,number2,pages210-226,2010, bySpringerPublisher.Theco-authors,Dr.NiyaziBakirandDr.AlexSavachkin,authorizedtoincludethisdocumentinmydissertation.SpringerPublisherretainsthecopyright ofthismanuscript.Thewrittenauthorizationfromthepublishertoincludethepaperin myPh.D.dissertationisattachedinAppendixA. 36

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APPENDIXD: PUBLICATION3:ANOPTIMALCOUNTERMEASUREPOLICYTO MITIGATERANDOMCAPACITYDISRUPTIONSINAPRODUCTION SYSTEM Inthisappendix,wepresentthenalversionofthemanuscriptAnOptimalCountermeasurePolicytoMitigateRandomCapacityDisruptionsinaProductionSystem"publishedintheInternationalJournalofAgileSystemsandManagement,volume3,number 1/2,pages4-17-226,2008,byIndersciencePublisher.Theco-authors,Dr.AlexSavachkin andDr.NiyaziBakir,authorizedtoincludethisdocumentinmydissertation.Inderscience Publisherretainsthecopyrightofthismanuscript.Thewrittenauthorizationfromthe publishertoincludethepaperinmyPh.D.dissertationisattachedinAppendixA. 54

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APPENDIXE: PUBLICATION4:APREDICTIVEDECISIONAIDMETHODOLOGY FORDYNAMICMITIGATIONOFINFLUENZAPANDEMICS Inthisappendix,wepresenttheversionofthemanuscriptAPredictiveDecisionAid MethodologyforDynamicMitigationofInuenzaPandemics"currentlyinthesecondround ofreviewinthespecialissueonOptimizationinDisasterRelief"intheORSpectrumby SpringerPublisher.Theco-authors,Dr.AlexSavachkin,AlfredoSantana,DianaPrieto, andDr.TapasDas,authorizedtoincludethisdocumentinmydissertation.Springer Publisherretainsthecopyrightofthismanuscript.Thewrittenauthorizationfromthe publishertoincludethepaperinmyPh.D.dissertationisattachedinAppendixA. 69

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ABOUTTHEAUTHOR AndresUribe-SanchezreceivedhisB.S.inIndustrialEngineeringwithemphasison OperationsResearchandFinancefromtheUniversityofLosAndes,Bogota,Colombiain 2003.In2006,hereceivedhisM.S.inManagementSystemsattheUniversityofPuerto RicoatMayagez.HereceivedhisPh.D.inIndustrialEngineeringfromtheUniversity ofSouthFloridain2010.InApril2010,hewasawardedtheDistinguishedGraduate AchievementAwardfromtheUniversityofSouthFlorida.Hisareasofresearchinterest includeengineeringriskanalysis,supportofhealthcareenterprisecapacitymanagement, anddecisionsupportformitigationoflarge-scalepublichealthdisasters.