The Impact of Digital Twins on Local Industry Symbiosis Networks in Light of the Uncertainty Caused by the Public Crisis

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The Impact of Digital Twins on Local

Industry Symbiosis Networks in Light of the Uncertainty Caused by the Public Crisis

Ziyue Chen, Norwegian University of Science and Technology, Norway Lizhen Huang, Norwegian Univeristy of Science and Technology, Norway

ABSTRACT

Digitaltwinsprovideasolutionforinformation-sharingbetweenenterprises,therebyalleviating

uncertaintiesinthesupplychain.InlightofthepubliccrisiscausedbyCOVID-19,theauthorssuggest

asignalgamemodelforatwo-stagesupplychainwithtwosuppliersandtwomanufacturers.Based

onthemodel,theimpactofthedigitaltwinplatformontheprofitsofthelocalindustrialsymbiosis

networkisanalyzed.Theresultsshowthattheuncertaintyofsupplyanddemandcausedbythe

publiccrisishasledtofluctuationsinprofitsandprofitvolatility.Underthisinfluence,suppliers

arewillingtoparticipateininformationsharingonthedigitaltwinplatform,butmanufacturersare

lesswillingtoparticipate.Moreover,applicationofthedigitaltwinplatformininformationsharing

isconducivetomaintainingandpromotingthesmoothoperationoftheindustrialchainunderthese

conditionsofuncertainty.

KeywoRDS

Digital Twin, Game Theory Model, Industrial Symbiosis Network, Information Sharing, Uncertainty

INTRoDUCTIoN

Theindustrialsymbiosis(IS)networkreferstothelong-termcooperativesymbiosisformedbythe

transferandexchangeofmaterial,energy,knowledge,andhumanandtechnologicalresourcesbetween

companieswithinaregion.Thenetworkaimstoobtainbothenvironmentalandcompetitivebenefits

(Wang,Mishima,&Adachi,2021).Theenterprise-levelISnetworkandhybridnetwork,includingIS

andtraditionalmodesofmanufacturing,arenewerendeavoursinNorway.However,COVID-19has

causedeconomicturmoilworldwidesincethebeginningof2020.Exceptforsomebasicindustries

(i.e.,medical,publicsecurity,foodretailing,etc.),mostindustrieshavesufferedasevereshock.Thus,

NorwayisexperiencinghasitshighestunemploymentratesinceWorldWarII.

COVID-19hasbroughtuncertaintytothemanufacturingindustryandproductionprocessdue

touncertainsupplies,transportationdisruption,andindeterminatedemand(Shrivastava,Ernst,&

Krishnamoorthy,2019).Inaddition,manycompaniesontheISnetworkhavenotestablishedafixed

modeofinformationcommunicationandtransaction.WhendealingwithshockslikeCOVID-19,

difficultiesininformationsharingandcommunicationleadtogreaterchallengesthanfacedby

companiesinthetraditionalsupplychain.First,thematerialsupplyishighlyuncertain.Itisimpossible

toorderrecycledmaterialsorpredicttheiroutputbecauserecycledmaterialsarenotamainstream

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productofthesuppliers.Theoutputofrecycledmaterialsdependsontheoutputofmainstreamproducts

(Liao&Li,2016).GreaterinstabilityofmainstreamproductsupplychainsduringCOVID-19makes

theirsupplyonthesymbiosisnetworkmoreunstable.Second,thecostsandenvironmentalimpactsof

productionplansbasedonrenewablematerialsmustbeevaluated.Availabilityofrecycledmaterials

islowandqualityisunstable.Comparedwithtraditionalmethodslikelandfillsandincineration,the

renewableremanufacturingprocessesmayleadtounexpectedlyhighproductioncosts,whichcause

moreenvironmentalpollution(Prosman&Sacchi,2018).However,duringCOVID-19,communication

betweencompanieswasrestrictedandcouldnotbeassessedinduetime.

Tosolvethisuncertainchallenge,moreinformationsharingbetweenenterprisesonthenetwork

isnecessary(Chan,Liu,&Szeto,2017;Kiiletal.,2019).DigitalTwins(DT),asanimportant

technologyfortherealizationofIndustry4.0,cancombinetheInternetofthings(IoT),artificial

intelligence(AI),machinelearning,andsoftwareanalysiswithspatialnetworkdiagramstocreate

real-timedigitalsimulationmodels.Thesemodelsareupdatedandchangedasthephysicalcopy

changes(Zhangetal.,2019).Asanemergingsolutionfordataintegrationandreal-timeprocessing

torealizeintelligentproduction,theDTplatformshavetheadvantagesofreal-timedatatransmission,

dataanalysis,andinformationvisualization(Qi&Tao,2018).Thisprovidesapotentialsolution

forinformationcommunicationofenterprisesonthecurrentISnetwork.However,thereislimited

researchontheimpactoftheDTplatformontheISnetworks.

TheauthorsofthisstudyanalysetheimpactoftheDT-basedverticalinformationsharingbetween

enterprisesinthelocalISnetworkunderapubliccrisisrepresentedbyCOVID-19.Itaimstoillustrate

theeconomicimpactoftheDTplatform’sinformation-sharingfunctionontheISsupplynetwork.

First,theauthorsestablishasignalgamemodelframeworktodescribeamixedISnetworkcomposed

oftwosuppliersandtwomanufacturers.Second,basedonthescenarioanalysis,theauthorsmodel

threescenariosinwhichtwomanufacturingcompaniesagreeordisagreetosharedemandinformation

withsuppliersthroughtheDTplatform.Basedonthesolutionofthemodels,theauthorscompare

theconsequencesofthesedecisionsanddiscovertheinfluenceoftheplatformontheamountand

stabilityofenterpriseprofits.

Themaincontributionsofthisarticlearereflectedinthreeaspects.First,regardingtheaspectof

content,currentresearchonISandtheDTisundergoingrapiddevelopment.Atpresent,thereislittle

researchonsolutionstotheinformationsharingofISenterprisesandapplicationoftheDTplatform

ininterenterpriseinformationsharing.ThispaperdemonstratestheroleoftheDTinformation-sharing

functionontheISnetworkbasedonthesignalgamemodel,enrichingtheresearchcontentoftheIS

fieldandtheDTinthecross-enterpriseapplicationfield.Second,regardingthemethod,thispaper

constructsanISnetworkgamemodeloftwosuppliersandtwomanufacturers.Itenrichesnotonly

theresearchrelatedtosuchmodels,butalsotheresearchintoISnetworks.Third,regardingthe

application,thispaperincreasestheunderstandingofitsapplicationincross-enterpriseinformation

sharingandpromotesthedigitaltransformationofISnetworks.

Thispaperisarrangedasfollows.Thesecondsection,theliteraturereview,discussescurrent

researchonissuesrelatedtoinformationsharinginIS,theapplicationoftheDTininformationsharing,

andtheenterprisegamemodelinthesupplychain.AsupplychainmodelforISisconstructedinthe

thirdsection,whichincludesfourcompaniesinthesupplychain,theirproductionrelationships,and

threetypesofinformationsharingmodelsamongthesecompanies.Thefourthsectionisareviewof

theresults.Basedonthereverseinductionmethod,theoutputs,prices,andprofitsofthecompanies

inequilibriumundertheinformationsharingmodesareobtained.Thefifthsectionprovidesa

comparativeanalysisoftheequilibriumsolutionsobtainedinthefourthsectionanddiscussesthe

parametersinthemodel.Thelastsectionistheconclusionandimplications.

Background

Theliteraturerelatedtothisarticleincludesthreetopics:(1)informationsharinginIS;(2)application

oftheDTtoinformationsharing;and(3)gamemodelsforenterprisesinthesupplychain.Thissection

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reviewstheexistingbodiesofliteratureonthesetopics.Foreachoftheresearchareas,theauthors

summarizefromtheaspectsofauthor,subject,andmethod(seeAppendixA).

Information Sharing in IS

The government promotes information sharing among companies in the symbiosis network

(D’Hauwers,vanderBank,&Montakhabi,2020).Still,informationsharingisamainchallengein

thedevelopmentofthecurrentISsystem(FlorenciodeSouzaetal.,2020;Shi&Chertow,2017).

Concernsfocusontheunwillingnessofcompaniestosharetheirinformationandtechnicalchallenges

ofbuildingtheplatform.

Alongwiththeframeworkoftechnicalsolutions,information-sharingtechnologyresearchfocuses

ontheidentificationandmatchingofISopportunitiesbasedonspecificcases(Maqbool,Mendez

Alva,&VanEetvelde,2019;Yazdanpanah,Yazan,&Zijm,2019;Yeoetal.,2019).Framework

technologysolutionsincludeasustainablecooperationparadigm(Xiang&Yuan,2019).Research

onidentifyingopportunitiesincludesblueprintsonenergyandmaterialinformationsharing(Cervo

etal.,2020),theopportunityidentificationmodel(Cervoetal.,2019),theenterprise-matchingmodel

(Ghali&Frayret,2019),andthedemand-matchingstrategy(Fraccascia&Yazan,2018).

ToimproveinformationsharingintheISsystem,itisnecessarytosolvetechnicalproblems

andincentivizethewillingnesstoshareinformationbetweenallcompaniesinthesymbiosisnetwork

(Lucianoetal.,2016).Suchcompanieslackconfidenceinthebenefitsofinformationsharing.

Therefore,itisnecessarytodemonstratetheadvantagesofinformationsharingtosymbiosis

enterprises.

Application of DT to Information Sharing

Multipleenterprisesformadynamicenterprisealliance;therefore,developmentoftheISsystem

willencouragecompaniestohaveadeepercooperationwithinthesupplychain(Qi&Tao,2018).

Moreover,solvingproblemsrelatedtoinformationsharingisconducivetoreducinguncertaintiesin

productionforsymbioticenterprises.Atpresent,studiesmentionthatinformationsharingisamain

challengefacedbyISnetworkswithinthecontextofIndustry4.0(Cervoetal.,2020).However,

fewstudiesprovidegeneralinformation-sharingsolutionsfromenterprisepairingonISnetworks

regardinghowtoproducecooperationamongenterprises(Fraccascia&Yazan,2018).Byanalysing

thecompetitivebehaviourofupstreamanddownstreamcompaniesinthesupplychain,theDTcan

simulatecooperationbycompaniesatstrategic,tactical,andoperationallevels(Cavalcanteetal.,

2019;Haag&Simon,2019;Lutters,2018).Theseeffortswillenhancedecision-makingsupport

(Smith,2020).

CurrentDTapplicationsininformationsharingcanbedividedintotheDTforsupplychainsand

DTforworkshopsinfactories.Applicationsattheworkshoplevelarethebasisforapplicationsat

theindustrychainlevel.SomecompanieshaveappliedtheDTtotheproductionprocess(D’Angelo

&Chong,2018),strengtheningtheirconfidenceinthedevelopmentandapplicationoftheDTatthe

supplychainlevel.However,fewstudiesanalysetheapplicationoftheDTintheISnetwork.

Game Models for enterprises in the IS Network

Atpresent,gametheoryismainlyusedinresearchingISnetworkstosolveproblemsofenterprise

incomedistribution,resourceoptimizationallocation,andenterprisecooperationmodeinISindustrial

parks.TheincomedistributionamongISenterprisesincludesreducingwastedischargecostsand

totalpurchasingcostsandsharingprofitstocompensatefortechnologyconversioncosts(Tanetal.,

2016;Yazan,Yazdanpanah,&Fraccascia,2020).Forexample,Parlar,Sharafali,andGoh(2019)

introducedaframeworkforanalysingallocationsoftheconversioncostsofanISsystem.

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(2016)builtacross-enterprisewatercoolingnetworkbasedonmultiobjectiveLPandananalytic

hierarchyprocesstopromotecostsavings.

ThestrategiccooperationbetweenISenterprisespredictstheevolutionmechanismofthe

symbiosissystemintheindustrialpark(Luo,Wang,&Shi,2019).Forexample,ZareMehrjerdiand

Lotfi(2019),whodesignedaflexibleandsustainablesupplychainnetworkbasedonatwo-stage

mixedintegerLP,tookanautomobileassemblycompanyasacaseforthemodel.Similarly,Lotfi

etal.(2019)designedaclosed-loopsupplychaintoachieveenvironmental,economic,andsocial

optimizationthroughthelaunchingandoperatingofmaterialflows.Ramosetal.(2018)deviseda

multileaderfollowergame(MLFG)modelfordesigningautilitynetworkforanecologicalindustrial

park(EIP),whichwasverifiedinacasestudyofanecoindustrialparkinNorway.

Model

Model Framework and Decision-Making Process

Usingthetwo-stagesupplychainstructureofWu,Wang,andShang(2019),theauthorsconstructed

alocalindustrysymbiosisoligopolymarketcompetitionmodelconsistingoftwosuppliersandtwo

manufacturers.Inthisgamemodel,fourplayerswithasymmetricinformationparticipateinthesignal

game(seeFigure1).

InFigure1,thegameisdividedintothreesteps.

• Step 1:Manufacturerspredictfuturemarketdemandthroughindependentobservation.They

shareinformationbasedontheuseoftheDTplatformonthesupplynetwork.Marketdemand

isuncertain.

• Step 2:Thesupplieralsosetsthepriceofrawmaterial.Thetwosuppliersareheterogeneous.

Oneisasupplierofrecycledmaterials;theothersuppliesprimarymaterials.Manufacturers

donotconsidertheenvironmentalcosts;therefore,theyonlyfocusontheprice.Thesupplyis

uncertain,sothecompetitionbetweenthetwosuppliersisanexampleofBertrandcompetition

withsupplyuncertainty.

• Step 3:Themanufacturersetsthepurchasequantitiesatthesametime.Thetwomanufacturers

usedifferentrawmaterials.Theproductsarethesame.Therefore,thispaperusestheCournot

modelwithdemanduncertaintytodescribethecompetitionamongmanufacturers.

Figure 1. Players and their connections

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Manufacturer

Demand Uncertainty of Manufacturers

Thetwomanufacturersinthisarticlearemanufacturerlandmanufacturerf.Eachmanufacturer

determinesitsownoutputbasedontheobservedmarketdemandandconditionofitscompetitors.

Then,themanufacturerordersrawmaterialsfromsuppliers.DuetoCOVID-19,marketdemand

isuncertain.Thisaffectsthemanufacturers’outputandamountofrawmaterialsorderedfromthe

supplier.

AccordingtoWuetal.(2019),thedemanduncertaintyinthispaperisdescribedbytherandom

variableθ,θ∼0,σ_θ²

 

.

Inaddition,theprivatedemandsignalobservedbythemanufacturerfromthemarketisX.The

observationerrorisε,ε∈( ,0+∞).ForX:

1. Xistheunbiasedestimateofθ,whichmeansthatE X

( )

θ ⁼θ.Thisillustratesthatthemarket

demandestimatedbythetwomanufacturersisnotsystematicallybiased.

2. X_landX_fareindependentofeachother.Namely,EθX X_l, _f α α_lX_l α_fX_f

 

 = ₀+ + .α₀,α_l,

andα_fare constants. This means that the two manufacturers observe market conditions

independentlywithoutsharinginformation.

3. X_landX_fhavethesamedistribution.Thismeansthatthereisnodifferenceinthetechnical

levelofobtainingmarketinformationbetweenthetwomanufacturers.Neithermanufacturerhas

astrongerabilitytoobtainmoreinformationormoreaccurateinformation.

Production Competition Between Manufacturers: Cournot Model

Accordingtothemodelframeworksection,productioncompetitionbetweenthetwomanufacturers

isdescribedusingtheCournotmodel.Themarketinversedemandfunctionis:

P= + −a ^θ

(

Q_l +Q_f

)

^. ⁽¹⁾

whereQisthemanufacturers’output.landfrepresentthetwomanufacturersinthesamemarket

position.

Themanufacturers’productionfunctionis:Q = ⋅A q.(2)

InEquation(2),qisthequantityofrawmaterialspurchasedbythemanufacturersfromthe

suppliers.Aisaconstant.A=1.

Themanufacturers’onlyvariableunitcost,w w, ∈

{

w w_l, _f

}

,isdeterminedbythequantityand

priceoftherawmaterialspurchasedbythemanufacturerfromthetwosuppliers.Therefore,the

manufacturers’profitfunctionsare: Π

Π^l_f ^l_f ^l_f q P A w

q P A w

= ⋅ −







( )

( ).(3)

Supplier

Supply Uncertainty from Suppliers

Thetwosuppliersinthemodelaresuppliertandsupplierr.Suppliertisasupplierbasedontraditional

production(asupplierofrawmaterialsbasedonfirst-timeproduction).Supplierrisarawmaterial

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duringCOVID-19,trafficblockadesandtransportationinterruptionscausedbyworkers’sickleave

ledtoshort-termsupplyshortages.Inthemodel,supplyuncertaintyisdescribedbythequantity

fluctuationofthesupply,Y,Y ∈

(

^{0 1}^, ^_^∼^_^{µ σ}^, _Y²^_.Thefluctuationcoefficientreferstotheratioofthe

actualquantityofrawmaterialsprovidedbythesuppliertothequantityofrawmaterialsorderedby

themanufacturer.ThefluctuationcoefficientsofthetwosuppliersY_tandY_rareindependentof

eachother.

Theactualquantityofrawmaterialsobtainedbyamanufactureristheproductoftheorder

quantityqandthefluctuationcoefficientY.Whenmanufacturerlordersrawmaterialswiththe

quantityofq_tlfromsuppliert,theamountofrawmaterialsactuallyobtainedbythemanufactureris

Y q_{t tl}.

Thesupplyuncertaintyisδ_Y,δ σ µ

Y

= Y .Whenδ_Yincreases,theuncertaintyinthesupplyof

rawmaterialsfromsuppliersbecomeslarger.

Price Competition Between Suppliers: Bertrand Model

Accordingtothemodelframeworksection,theBertrandmodelisintroducedtodescribethepricing

competitionbetweentwosuppliers.

Theprofitfunctionofthetwosuppliersis:

π π

t t t t lt ft

r r r t lr fr

w c Y q q w c Y q q

=

(

−

) (

⁺

)

=

(

−

) (

⁺

)





 . (4)

InEquation(4),w_tandw_raretheunitpriceofrawmaterialsfromtwosuppliers.c_tandc_r arethecostsofthetwosuppliers.Thetotalunitcostsofthetwosuppliersarethesame.Thecost

structures,includingtransportationandproductioncosts,aredifferent.

Structure of Information Sharing Between Manufacturers and Suppliers

Accordingtothemodelstructureinthemodelframeworksection,thecurrentmarkethasfourplayers,

twomanufacturersandtwosuppliers.Eachmanufacturermakesanindependentdecisionwhetherto

sharethemarketsignalsithasobtainedfromitssuppliersthroughtheDTplatform.Fourinformation- sharingscenariosbetweensuppliersandmanufacturersareobtainedfromthisinformation.Inthe

followingfigures,thedirectionofthearrowisthedirectionoftheinformationflow.

Scenario 1: No DT for Either Manufacturer

Inscenario1,thetwomanufacturersdonotusetheDTplatformforinformationsharing.Therefore,

thesupplierscannotobtainmarketdemandsignals.Therelationshipbetweenthemanufacturersand

suppliersisshowninFigure2.

InFigure2,eachenterpriseisanisolatedislandregardingitsinformation.

Scenario 2: DT for One Manufacturer

Inscenario2,onemanufacturerinthemarketsharestheobservedmarketdemandsignalswithtwo

suppliersthroughtheDTplatform.Theothermanufacturerdoesnotshareinformation.Therearetwo

manufacturersinthemarket;therefore,thesituationsintheinformation-sharingstructurebetween

manufacturersandsuppliersaresimilar.SeeFigure3.

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InFigure3,manufacturerlhasaninformationexchangewithtwosuppliers.Manufacturerfdoes

notshareinformationwiththetwosuppliers.AccordingtoFigure4,manufacturerfhasaninformation

exchangewiththetwosuppliers;manufacturerlsharesnoinformationwiththetwosuppliers.

Scenario 3: DT for Both Manufacturers

Inscenario3,twomanufacturersinthemarketusetheDTplatform.Bothmanufacturersalsoshare

theirobservedmarketdemandsignalswiththeirsuppliers.Figure5showstherelationshipbetween

themanufacturersandsuppliers.

Results of the Model

Basedontheuncertaintymentionedinthisresearch,thissectionconductsascenarioanalysisofthe

differentinformation-sharingdecisions.ItalsodiscussestheimpactoftheDTplatformonsolving

theuncertaintyimpactofthelocalsupplyend-of-lifeproductsorcoproductionchain.

Figure 2. Supply chain information exchange structure without DT

Figure 3. Supply chain information exchange structure of enterprise l using DT

Figure 4. Supply chain information exchange structure of one enterprise f using DT

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Scenario 1: No DT for either Manufacturer

InFigure2,whenthetwomanufacturersdonotshareinformation,theprofitfunctionsofthetwo

suppliersare:

E E w c Y q q E E w c Y q

t t t t lt ft

r r r r lr

π π

 

 = ^_

(

−

) (

⁺

)

^_

 

 = ^_

(

−

) (

⁺⁺^qfr

)

^_

. (5)

Theprofitfunctionsofthetwomanufacturersare:

EΠ_l X X_l, _f E a( Y q_{t lt} Y q_{t ft} Y q_{r lr} Y q_{r fr})(Y q_{t lt} Y q_{r lr})

 

 = ^_ + −θ − − − + −−

(

+

)

^_

 

= + − −

Y w q Y w q X X

E X X E a Y q Y

t t lt r r lr l f

f l f t lt

,

, (

Π ^_ θ _{tt ft}q −Y q_{r lr}−Y q_{r fr}⁾⁽Y q_{t ft} +Y q_{r fr}⁾−

(

Y w q_t _{t ft} +Y w q_r _{r fr}

)

X X_l^, _f^_^.

(6) Accordingtothetwogamestagesinthemodelframeworksection,thesuppliersfirstconduct

apricegametodeterminethepriceofrawmaterials.Subsequently,themanufacturersconducta

productiongametodeterminethequantityofrawmaterialstobeorderedfromthesuppliers.According

tothebackwardinduction,aftersolvingtheoptimalorderquantityofthetwomanufacturers,the

optimalsupplypriceofthetwosuppliersissolved(seeAppendixB).Therefore,theauthorscan

obtaintherawmaterialpriceswithouttheDTplatform.

w w a c

t NN

r

NN Y Y

Y

* = * = +

(

+

)

+

δ δ

δ

2 2

2

1

2 1 . (7)

InEquation(7),δ_Yisthesupplyuncertaintycausedbysupplyshock.aisthemarketsizeandc

istheunitcostofthesuppliers.

Theorderquantitiesofthetwomanufacturersfromthetwosuppliersare:

q q a c

lt NN

lr

NN Y

Y Y Y

* *

( )( ) ( )(

= =

(

−

) (

⁺

)

+ + +

+ +

δ

µ δ δ µ δ ε

2

2 2 2

1

3 2 2 1

1

2 2 3))

( )( ) ( )(

* *

X

q q a c

l

ft NN

fr

NN Y

Y Y Y

= =

(

−

) (

⁺

)

+ + +

+ δ

µ δ δ µ δ

2

2 2 2

1

3 2 2 1

1 2 22ε+3













 )X_f

. (8)

Figure 5. Supply chain information exchange structure with DT

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InEquation(8),µisthemeanvalueoftheexternalimpactofthemacro-environmentonthe

productionquantityofthesuppliers.X_listheunbiasedestimateofthemarketdemandsignalobserved

bysupplierl.X_fistheunbiasedestimateofthemarketdemandsignalobservedbysupplierf.εis

theerrorofthesignalobservedbythesuppliers.

Thesuppliers’profitsinequilibriumare:

π π δ δ

δ δ

t NN

r

NN Y Y

Y Y

* * ( )(a c)

( )( )

= = + −

+ +

2 1

3 2 2 1

2 2 2

2 2 2 . (9)

Themanufacturers’profitsinequilibriumare:

Π_l^NN Π^NN_f ^Y

Y Y Y

* * ( ) (a c)

( )( )

( )

= = + − (

+ + + +

2 1

9 2 2 1

2 1

2 2 2

2 2

δ

δ δ

σ ε

δ

θ

+

+2 3)( +2ε)² . (10)

Scenario 2: DT for one Manufacturer

InFigure3,whenonemanufacturersharesinformationontheDTplatform,theprofitfunctionsof

thetwosuppliersare:

E X E w c Y q q X

E X E w c

t l t t t lt ft l

r l r r

π π

 

 = ^_

(

−

) (

⁺

)

^_

 

 = ^_

(

−

))

^{Y q}r

(

lr ⁺^qfr

)

^Xl^_

. (11)

Theprofitfunctionsofthetwomanufacturersare:

 

 = ^_ + −θ − − − + −−

(

+

)

^_

 

= + − −

Y w q Y w q X X

E X X E a Y q Y

f l f t lt

,

, (

(

Y w q_t _{t ft} +Y w q_r _{r fr}

)

X X_l^, _f^_^.

obtaintherawmaterialpriceswithjustonemanufacturerapplyingtheDTplatform.

w w a c

t X

DN r

DN Y Y

Y

Y Y

l

* *

( )( )

= = +

(

+

)

+ +

δ δ

δ

δ ε

2 2

2

2 2

1

2 1 2 1 1 . (13)

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InEquation(13),δ_Yisthesupplyuncertaintycausedbythesupplyshock.aisthemarketsize;

cistheunitcostofthesuppliers.εistheerrorofthesignalobservedbythesuppliers.

q q a c

lt DN

lr

DN Y

Y Y

* *

( )( ) ( )

= =

(

−

) (

⁺

)

+ + + +

+ δ

µ δ δ

δ µ δ

2

2 2

1

3 2 2 1

1

3 2 (( )( )

( )(

* *

2 1 1

1

3 2 2 1

2 2

δ ε

δ

µ δ δ

Y

l

ft DN

fr

DN Y

Y Y

X

q q a c

+ +

= =

(

−

) (

⁺

)

+ + ))

( )( ) ( )

( )( )( )( )

+ + + − +

+ + + + +

2 1 2 3 2 1

6 2 2 1 1 2

1 2

2 2

δ ε δ

µ δ δ ε ε

Y Y

Xl

µµ δ(_Y₂ )(ε )X^f

2 2

+ +















.

(14) InEquation(14),µisthemeanvalueoftheexternalimpactofthemacro-environmentonthe

bysupplierl.X_fistheunbiasedestimateofthemarketdemandsignalobservedbysupplierf.

Thesuppliers’profitsinequilibriumare:

π π δ δ

δ δ

δ δ

t DN

r

DN Y Y

Y Y

* * ( )(a c)

( )( )

( )

= = + −

+ + + +

2 1

3 2 2 1

2 1

2 2 2

2 2 σσ

δ δ ε

θ 2

2 2 2

3(_Y +2 2)( _Y +1) ( +1). (15) Themanufacturers’profitsinequilibriumare:

Π_l^DN ^Y

Y Y

* ( ) (a c)

( )( )

( )

= + − (

+ + + +

+

2 1

9 2 2 1

2 1

9 2

2 2 2

2

δ

δ δ

δ σ

δ

θ

))( ) ( )

( ) ( )

( )( )

* (

2 1 1

2 1

9 2 2 1

2

2 2

2 2 2

δ ε

δ

δ δ

δ ^Y

f

DN Y

Y Y

a c

+ +

= + −

+ + +

Π ^Y^Y

Y Y Y

2 2 2

2 2

1

9 2 2 1 1

2

4 2 1 2

+

+ + + +

+ + +



 )

( )( ) ( ) ( )( )( )

σ

δ δ ε

σ ε

δ ε ε

θ θ











, (16)

whereσ_θ²isthevarianceofdemandfluctuations,illustratingthedemanduncertainty.

Themarketpositionsofthetwosuppliersaresymmetrical.Therefore,theequilibriumsolution

basedonFigure4is:

w w a c

t X

ND r

ND Y Y

Y

Y Y

f

* *

( )( )

= = +

(

+

)

+ +

δ δ

δ

δ ε

2 2

2

2 2

1

2 1 2 1 1 . (17)

q q a c

lt ND

lr

ND Y

Y Y

* * Y

( )( )

= =

(

−

) (

⁺

)

+ δ + + + + −

µ δ δ

δ ε

2

2 2

1 2

3 2 2 1

2 1 2 33 2 1

6 2 2 1 1 2

1

2 2 2

2

2 2 2

( )

( )( )( )( ) ( )( )

δ

µ δ δ ε ε µ δ ε

Y

Y Y

f

Y

X Xl

q

+

+ + + + +

+ +

fft ND

fr

ND Y

Y Y

q a c

* *

( )( ) ( )

= =

(

−

) (

⁺

)

+ + + +

+ δ

µ δ δ

δ µ δ

2

2 2

1

3 2 2 1

1

3 2 ((2δ_Y² 1)(ε 1)X^f

+ +















.

(18)

(11)

π π δ δ

δ δ

δ δ

t ND

r

ND Y Y

Y Y

* * ( )(a c)

( )( )

( )

= = + −

+ + + +

2 1

3 2 2 1

2 1

2 2 2

2 2 σσ

δ δ ε

θ 2

2 2 2

3(_Y +2 2)( _Y +1) ( +1). (19)

Π_l^ND ^Y

Y Y

* ( ) (a c)

( )( )

( )

= + − (

+ + + +

+

2 1

9 2 2 1

2 1

9 2

2 2 2

2

δ

δ δ

δ σ

δ

θ

))( ) ( ) ( )( )( )

( ) (

*

2 1 1

2

4 2 1 2

2 1

2 2

δ ε

σ ε

δ ε ε

δ

θ

Y Y

f

ND Y a

+ + +

= + −

Π cc

Y Y

Y

Y Y

)

( )( )

( )

( )( ) ( )

2

2 2 2

9 2 2 1

2 1

9 2 2 1 1

δ δ

δ σ

δ δ ε

θ

+ + + +

+ + +















. (20)

Scenario 3: DT for Both Manufacturers

InFigure5,whenbothmanufacturersshareinformationontheDTplatform,theprofitfunctionsof

thetwosuppliersare:

E X X E w c Y q q X X E X X

t l f t t t lt ft l f

r l f

π π

, ,

,

 

 = ^_

(

−

) (

⁺

)

^_

 

 =^{E w}^_

(

r−^{c Y q}r

)

r

(

lr ⁺^qfr

)

^{X X}l, f^_. (21) Theprofitfunctionsofthetwomanufacturersare:

 

 = ^_ + −θ − − − + −−

(

+

)

^_

 

= + − −

Y w q Y w q X X

E X X E a Y q Y

f l f t lt

,

, (

(

Y w q_t _{t ft} +Y w q_r _{r fr}

)

X X_l^, _f^_^.

obtaintherawmaterialpricesfromtheDTplatform.

w w a c

X X

t DD

r

DD Y Y

Y

Y Y

l f

* *

( )( )

= = +

(

+

)

+ +

(

+

)

δ δ

δ

δ ε

2 2

2

2 2

1

2 1 2 1 2 . (23)

InEquation(23),δ_Yisthesupplyuncertaintycausedbythesupplyshock.aisthemarketsize;

cistheunitcostofthesuppliers.εistheerrorofthesignalobservedbythesuppliers.

( )

(12)

InEquation(24),µisthemeanvalueoftheexternalimpactofthemacro-environmentonthe

bysupplierl.X_fistheunbiasedestimateofthemarketdemandsignalobservedbysupplierf.

Thesuppliers’profitinequilibriumare:

π π δ δ

δ δ

δ δ

t DD

r

DD Y Y

Y Y

* * ( )(a c)

( )( )

( )

= = + −

+ + + +

2 1

3 2 2 1

4 1

2 2 2

2 2 σσ

δ δ ε

θ 2

2 2 2

3(_Y +2 2)( _Y +1) ( +2). (25) whereσ_θ²isthevarianceofdemandfluctuations,illustratingthedemanduncertainty.

Themanufacturers’profitinequilibriumare:

Π_l^DD Π_f^DD ^Y

Y Y

a c Y

* * ( ) ( )

( )( )

( )

= = + −

+ + + +

2 1

9 2 2 1

4 1

9

2 2 2

δ

δ δ

δ σ_θ

((δ_Y² +2 2)( δ_Y² +1) (² ε+2). (26)

Discussion

Intheprevioussection,theauthorsobtainedtheequilibriumofthepurchaseunitprice,purchase

quantity,andprofitsoftwosuppliersandtwomanufacturersunderdifferentinformation-sharing

conditions.Thesensitivityandrationalityofthemodelarealsodiscussed(seeAppendixF).Profitis

themainconcernofenterprises.Therefore,inthissection,theauthorsexplainhowtheprofitsofeach

enterpriseandthetotalprofitofthesupplychainareaffectedbytheinformation-sharingmechanism.

Profits of Suppliers Under the Three Modes of Information Sharing

Theauthorswillfirstcomparetheprofitsofthetwosuppliersinthethreescenarios.Next,theywill

comparetheprofitvariationratesundertheshocks.Theprofitsarecomparedbycalculatingthe

differencesbetweenEquation(9),Equation(15),Equation(19),andEquation(25),asisshownin

Equation(27).

π_t^NN^* =π_r^NN^* <π_t^DN^* =π_r^DN^* =π_t^ND^* =π_r^ND^* <π_t^DD^* =π_r^DD^*. (27)

(13)

Topic Author Subject Method

InformationSharing

inIS

Cervoetal.(2019) Identify,evaluate,andpromotesymbioticcooperation Engineeringandproject

management-orientedsupport

(EPOS)methodology Cervoetal.(2020)* Blueprintforindustrialsymbiosis Casestudy D’Hauwersetal.

(2020) Government’sroleinsharingeconomyinformation Casestudy FlorenciodeSouzaet

al.(2020) Diagnosethepresenceofindustrialsymbiosispracticesin

fivedomains Circulareconomymodelling

Fraccascia&Yazan

(2018)* Impactofanonlineinformation-sharingplatformonan

industrialsymbiosisnetwork Agent-basedmodelandcasestudy

Ghali&Frayret

(2019) Frameworkfortheinitiationofindustrialsynergies SocialsemanticWeb Lucianoetal.(2016) Potentialmethodimprovementofregionalindustrialsymbiosis Interview,meeting,andcasestudy Maqbooletal.(2019) Evaluationofinformationtechnologydevelopmentin

EuropeanIS Contentanálisis

Shi&Chertow

(2017) Organizationalboundarychangeofanindustrialsymbiosis

company Casestudy

Xiang&Yuan(2019) Demandandcollaboration-drivenmodelofsmartindustrial

parks SWOTanalysisandcasestudy

Yazdanpanahetal.

(2019) Decisionsupportforindustrialsymbiosisopportunities Industrialsymbiosisopportunity

filteringmethod

Yeoetal.(2019) Toolstopromoteindustrialsymbiosis Review

ApplicationofDTto

InformationSharing

Cavalcanteetal.

(2019) Supplierperformanceriskunderuncertainty Machinelearningandsimulation Cervoetal.(2020)* Blueprintforindustrialsymbiosis Casestudy

D’Angelo&Chong

(2018) Logisticsforcompanies Discreteeventsimulationmodel

Fraccascia&Yazan

(2018)*

Impactofanonlineinformation-sharingplatformonthe

environmentandeconomicbenefitsofanindustrialsymbiosis

network Agent-basedmodelandcasestudy

Haag&Simon

(2019) Materialandinformationflowforhorizontalandvertical

integration Web-basedmodels

Lutters(2018) Productionenvironmentplatformforstakeholders Resourcesandprocessesmodel Qi&Tao(2018) Applicationcomparisonofbigdataanddigitaltwinsin

manufacturing Review

Smith(2020) ValueofAItofutureagriculture Review

GameModelsfor

EnterprisesintheIS

Network

Leongetal.(2016) Modellingofcoolingandcoolingwaternetworksbetween

factories Multi-objectivelinearprogramming

Lotfietal.(2019) Decisionoptimizationinaflexibleclosed-loopsupplychain Two-stage,mixedintegerlinear

programming

Luoetal.(2019) Industrialsymbiosisstrategyofane-commerceindustrialpark Dynamicevolutiongamemodel Parlaretal.(2019) Resourceoptimizationontheindustrialsymbiosisnetwork Optimalcontrolandcooperative

gamemodel Ramosetal.(2018) Optimizationofpublicutilityresourcesintheecoindustrial

park Multileader-followergamemodel

Tanetal.(2016) Processintegration(PI)toolsinindustrialecology(IE)

applications Cooperativegamemodel

Yazanetal.(2020) Strategiestoshareadditionalcostsofoperatingindustrial

symbiosis Noncooperativegame-theoretical

model ZareMehrjerdi&

Lotfi(2019) Designofaresilientandsustainablesupplychainnetwork Two-stage,mixedintegerlinear

programming

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