Disruption and Strategic Outsourcing to the Competitor in

DOI: 10.4018/IJORIS.2019010101

International Journal of Operations Research and Information SystemsVolume 10 • Issue 1 • January-March 2019

Copyright©2019,IGIGlobal.CopyingordistributinginprintorelectronicformswithoutwrittenpermissionofIGIGlobalisprohibited.

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Disruption and Strategic Outsourcing to the Competitor in the Common MarketZhaoqiong Qin, University of Central Oklahoma, Edmond, USA

ABSTRACT

Therearecircumstancesthatonefirmwilloutsource(purchase)productstoitscompetitorinthecommonmarketwhenexperiencinganunexpectedsupplydisruption.Suchstrategiestohedgeagainsttheunexpectedsupplydisruptioncommonlysuffersfromthehigherwholesalepricechargedbyitscompetitoralthoughithelpsmaintainitspresenceonthemarket.Itscompetitoralsoisconcernedaboutencroachmenttoselltheproductstothefirmasarivalinthecommonmarket.Mathematicalmodelsareformulatedtomaximizeeachparty’sprofitinbothcasesofoutsourcingandnotoutsourcingunderdecentralizationandcentralization.Theresultsshowthatbothpartiesbenefitfromthestrategyofoutsourcingatthetimeofdisruption.Moreinterestingly,theresultsalsoshowthatthecompetitor’scentralizeddecision-makingispreferred.

KeywORDSCentral Decision Making, Outsourcing, Supply Chain, Supply Disruption

INTRODUCTION

Withtheincreaseofoffshoring,globalizationanddemanduncertainty,supplyshortageanddisruptionriskhavebecomethepressing issues insupplychains.Thesekindsof issueshavebecomemoreseverefollowingexternalfactors(forinstance,naturaldisasters),orinternalfactors(e.g.,machinebreakdowns).The typical examples are automotivemanufacturers afterMarch11,2011TohokuearthquakeofftheeasterncoastofJapan–Over400partsinToyotawereinimmediateshortageandproductioncapacitywasreducedfor6monthsfollowingthedisaster(Tabuchi,2011).Moreover,arecentexplosionattheproductionplantofEvonik,abigsupplierofaspecialtyresinforautopartsinGermany, ledtosignificant inventoryshortfalls(BennettandHromadko,2012).Similarly, thefloodinginThailandhurtthesupplyofdiskdrivesandrelatedcomponentsfromIntel(Clark,2012b).SamsungmitigatedthesupplyshortagethroughoutsourcingtheGalaxyS4’sprocessortoitsrivalchipmakerQualcomminseveralcountrieswhenitcouldn’tproduceenoughofitsownExynos5Octaprocessor(Nguyen,2013).Clearly,outsourcingproductstocompetitorscanmitigatethesupplyshortageanddisruptionrisk.

Outsourcingproductstocompetitorsisinfashioninmanyindustries.Forexample,FordProbeisproducedbyMazdaMotorCo.andthencompetesagainstMX-6inthesportscarmarket;ZenithElectronics builds laptop PCs for Hewlett-Packard; and Lockheed produces parts for Boeing’s

Thisarticle,originallypublishedunderIGIGlobal’scopyrightonJanuary1,2019willproceedwithpublicationasanOpenAccessarticlestartingonFebruary2,2021inthegoldOpenAccessjournal,InternationalJournalofOperationsResearchandInformationSystems(con-vertedtogoldOpenAccessJanuary1,2021),andwillbedistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.org/licenses/by/4.0/)whichpermitsunrestricteduse,distribution,andproductioninanymedium,providedtheauthorof

theoriginalworkandoriginalpublicationsourceareproperlycredited.


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commercial aircraft (Spiegel, 1993). Apparently, these outsourcing strategies directly affect theprofitsofthesourcingcompaniesandtheircompetitors.Whencompaniesfacethesupplyshortageanddisruptionrisk,whether theywouldoutsourceproducts to theircompetitorsandcompetitorswouldprovideproductstohelphedgeagainstthedisruptionorshortageshouldbeevaluated.Sofarpreviousresearchhasshedlittlelightonthestrategiesofoutsourcingtocompetitorsinthecommonmarkettohedgeagainstthesupplyshortageordisruptionrisk.Weaimtofillthisgapintheliterature.

Inthisstudy,therearetwofirmsFirm1andFirm2todelivertheperfectsubstitutableproductstothecommonmarket.Firm1issteadywithenoughcapacitywhileFirm2mayexperienceunexpectedsupplydisruption.Whenthepotentialdisruptivefirmexperiencestheunexpectedsupplydisruption,itcanchooseeithertopurchasetheproductsfromFirm1tostillmaintainitspresenceonthemarketornottopurchaseandjusttobeabsentfromthemarket.Webuildmathematicalmodelstostudythesteadyfirm’sincentivestochooseitssupplychainstructure(centralizedordecentralized)andthepotentialdisruptivefirm’sstrategicoutsourcingdecisions(outsourcingornot)atthetimeofdisruption.We examine how the steady firm’s supply chain structure and the potential disruptive firm’soutsourcingstrategiesaffectbothfirms’performanceinthepresenceofthedisruptionriskλ .Basedonthefirms’performance,howshouldthesteadyfirmmakethedecisioninitssupplychainstructureandthepotentialdisruptivefirmmakethedecisioninoutsourcing?Specifically,weconsidertwocompetitors in the common market. They involve in the Cournot competition with perfectsubstitutability.Firm2facestheunexpectedsupplydisruptionriskwhileFirm1hasamplesteadysupply.Whensupplydisruptionoccurs,Firm1canchoosewhethertooutsourceproductsfromitscompetitor tobeat thesupplyshortagebasedon thesourcingagreementbetween themornot tooutsourceandbeabsentfromthemarket.Theobjectiveofthesetwocompetitorsistomaximizetheirownprofits.Wetrytoanswerthefollowingresearchquestions:1)WillitpurchasetheproductsfromFirm1whenFirm2experiencesthedisruption?2)HowwillFirm1makethedecisioninitssupplychainstructure,centralizeddecisionmakingbysellingitsproductstothemarketdirectlyonitsownordecentralizeddecisionmakingbysellingthroughanindependentretailer?

Ourresultsdeliverseveralinsights.First,wedemonstratethatbothcompetitorshaveincentivestocreateoutsourcingagreementsforthepotentialdisruptivefirm(Firm2)topurchasetheproductsfromthesteadyfirm(Firm1)intheeventofsupplydisruption.Thatistosay,outsourcingbenefitsnotonlythedisruptivepartybutalsoitscompetitorwhomitwillpurchaseproductsfromatthetimeofdisruption.Fromthedisruptiveparty’sstandpoint,thestrategicoutsourcingnotonlymaintainsitspresenceonthemarketintheeventofdisruptionbutalsoachievesahigherprofitcomparedtonotoutsourcingfromitscompetitor.FromitscompetitorFirm1’sstandpoint,thestrategicoutsourcingofFirm2intheeventofdisruptionoffersanopportunityforFirm1toachieveahigherprofit.Therefore,thestrategicoutsourcingtohedgeagainstthedisruptionriskcancreateawin-winsituation.Secondly,wefindthatFirm1willearnahigherprofitinthecentralizeddecisionmaking.Inotherwords,itispreferredforthesteadyfirmtodeliveritsproductstothemarketthroughacentralizedsupplychain.

Related LiteratureThestrategiestomanagetheriskofuncertainsupplyhavebeenextensivelyexploredintheexistingdisruptionmanagementliterature.AmongthetypicalexamplesareHuandKostamis(2014),TomlinandWang(2011),Tomlin(2009),FedergruenandYang(2008),Yangetal.(2009),Wadeckietal.(2012),YangandVolodymyr(2015),Ang,Iancu,andSwinney(2017)andDemirel,KapuscinskiandYu(2018).Whenweconsidertheissueofrisksinthesupplyuncertainty,ourworkisparticularlyrelatedtothemodelswithoutsourcingtothecompetitorswithcertainsupplyinthecommonmarkettohedgeagainsttheriskofuncertainsupply.

Traditionally thereare twogeneralapproaches tobuild themodelofuncertainsupply: therandomyieldmodel,assumingthattheoutputlevelisarandomfunctionoftheinputvariables(HenigandGerchak,1990;KouvelisandLi,2013;YangandVolodymyr,2015;Ang,Iancu,andSwinney,2017),andthetotalsupplydisruptionmodel,assumingthat it is the“all-or-nothing”


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form(Huetal.2013;Tomlin2006).Weadoptthetotaldisruptionmodelinwhichthesupplyisfullyfulfilled,ornothingisfulfilled.

Fromthecategoryofoutsourcing,Arya,MittendorfandSappington(2008)consideredthatthemonopolisticsupplierservedtheretailer’srivalinthecommonmarketwhiletheretailercaneithermaketheproductsinhouseoroutsourcetheproductsfromthemonopolisticsupplier.Theirresultsshowedthattheretailermaypayapremiumtooutsourceproductionfromacommonsupplierinordertoraiseitsrivals’costsonlywhenthesupplieristheleast-costproduceroftheproducts.Incontrasttotheirmodels,weconsiderbothfirmshavethesamemarginalcoststhroughtheirownchannels,amongwhichonefirmissteadywithenoughcapacitywhiletheotheronemayexperienceunexpectedsupplydisruption.Ourresultsshowthatintheeventofsupplydisruption,thedisruptivefirmwouldalwayspayapremiumtooutsourcetheproductsfromhercompetitorevenifhercompetitorisnottheleast-costproduceroftheproducts.

Fromthecategoryofdecentralization,Arya,MittendorfandYoon(2008)demonstratedthatthemanufacturercanbenefitfromhisdecentralizedcontrolofhisretailsupplychainwhenheprovidestheproductstohisrivalinthecommonmarket.Ourmodeldiffersfromtheirmodelinthatthesteadyfirmprovidestheproducttohisrivalwithpotentialsupplydisruptioninthecommonmarketonlywhenhisrivalexperiencesunexpecteddisruption.Ourresultsshowthat thesteadyfirmactuallybenefitsfromhiscentralizedcontrolofhisretailsupplychain.Thatis,thecentralizedcontrolofhisretailsupplychainispreferred.

Fromthecategoryofstrategiestomitigatetheriskofuncertainsupply,ChenandGuo(2014)investigatedtheincentivesforthefocalfirmoftwocompetitorstoadoptthedual-sourcingstrategyinthecaseofsupplyuncertainty:commonsupplierandalternativesupplier.Theyfoundthatthefocalfirm’sdual-sourcingstrategytohedgeagainstsupplydisruptionriskcancreateawin-winsituationthatleadstoincreaseretailpricesandexpectedprofitsforbothfirms.Ourmodeldiffersfromtheirs:ononehand,weassumethatweadoptthetotaldisruptionmodeltodescribethesupplyuncertaintywhiletheyadoptedthesimplerandomyieldmodel;ontheotherhand,intheirmodel,oneofthetwosuppliersiscommonforthetwocompetitorsandtheotheroneisalternativeonlyforthefocalfirm.Comparedtotheirmodel,ourmodelassumesthatoneoftwocompetitorshaveasteadysupplywhiletheotheronemayexperienceanunexpecteddisruptionwithrate λ .Thesteadycompetitorcanprovidetheproductstoitsrivalwhenitsrivalexperiencesthedisruption.Wefindthatthiskindofoutsourcingstrategytohedgeagainstthesupplydisruptionriskcanalsocreateawin-winsituationthatleadstoincreaseexpectedprofitsforbothcompetitors.

Tomitigatetheriskofsupplydisruption,YangandVolodymyr(2015)incorporatetheserviceofabetter-informedprocurementserviceprovider(PSP)intothestudy.TheyconcludethathiringaPSPcannotsolvetheproblemofanunreliablesupplybase.Ourstudyproposesadifferentstrategy-sourcingfromthereliablecompetitortomitigatetheriskofsupplydisruption.

Tosummarize,ourmodelis,tothebestofourknowledge,amongthefirsttoexplorethestrategyofoutsourcingtocompetitorsatthesameproductioncoststohedgeagainstdisruptivesupply,centralizedcontroltobenefitthefirmandthefirsttoconsiderhowoutsourcingtocompetitorstohedgeagainstsupplydisruptioncreatesawin-winsituationbyappropriatelywholesalepricecontracts.

ModelInourstudy,weconsidersupplychainmodelsconsistingoftwofirmssellingtheirproductsintheend consumer market. These two firms, labeled as Firm 1 and Firm 2, involve in the Cournotcompetition.Theydiffer intheirsupplyreliability.WhileFirm1hasreliablesupplyandenoughmanufacturing capacity, Firm 2 has the probability 1−λ to supply the expected quantity and

probabilityλ tosupplyzeroduetotheunexpecteddisruption.Weassumeλ ≤ 12

toindicatethat

Firm 2 will not involve in the competition if the supply disruption is significant. When supplydisruptionoccurs,Firm2caneitherpurchasetheproductsfromFirm1tocontinuetomaintainits


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presenceonthemarketornotpurchasefromFirm1andthenFirm1willmonopolythemarket.Inotherwords,Firm2canmakeachoicebetweenadoptinganoutsourcingstrategytoitsrivalFirm1tocontinuethebusinessandnotadoptingtheoutsourcingstrategytobeabsentfromthemarketwhensupplydisruptionoccurs.

Throughoutthestudy,weassumethat1)firmsareriskneutral;2)themarginalcoststoproducetheproductsinbothfirmsarethesame;and3)bothfirmshavethecommonknowledgeabouteachother’ssupplyrates.Eachfirmoptimallychoosesitsquantity,anticipatingitsrival’saction.Inthefollowingparagraphs,wedescribethesetwofirms’competitionindetail.

Tosimplifyourexposition,wealsoassumethattheproductsfrombothfirmsarehomogeneous.Consumerdemandisrepresentedbyalinear,downward-slopingdemandfunction p a q q= − −

1 2,

wherep istheretailpriceoftheproductsonthemarketandqiisthequantityoftheproductdelivered

byFirm i i( , )= 1 2 .Especially,ifFirm2experiencessupplydisruptionanddoesnotoutsourcetheproductsfromFirm1,thenq

20= .

Giventhismodelingframework,wefirststudythecasethatFirm1isacentraldecisionmakerandsellsitsproductsthroughitscentralizedsupplychaininSection3.1.Followingthis,westudythecasethatFirm1isadecentralizeddecisionmakerandsellsITsproductsthrougharetailerinitsdecentralizedsupplychain.MathematicalnotationsaresummarizedinTable1.

Outcomes in the Equilibrium When Firm 1 is a Central Decision MakerIn thissubsection,weconsider thescenario thatFirm1 isacentraldecisionmakerandsells itsproductstothemarketthroughitscentralizedsupplychain.Figure1showsthesequencesofeventsinthisscenario.Asshowninthefigure,Firm1announcesthewholesalepriceperunitforFirm2topurchaseproductsfromhiminthecaseofsupplydisruption.Followingtheannouncement,Firm2decidestopurchasetohedgeagainstthesupplyuncertaintyornot.ThenbothFirm1andFirm2decidethequantitiesoftheproducttodelivertothecommonmarket,respectively.InthecontextofFirm2’sdecisionofpurchasingproductsfromFirm1whendisruptionoccurs,Firm2willdeliveritsownproductstothemarketwhenitssupplyissmoothwhileitwillpurchasetheproductfromFirm1whenitexperiencesthesupplydisruption.Finally,bothfirmsinvolveintheCournotcompetitionandthemarketclearsbasedonthequantitiesofproductsfrombothfirms.InthecontextofFirm2’sdecisionofnotpurchasingproductsfromFirm1,Firm2willnotprovidetheproducttothemarketwhenitexperiencesthesupplydisruptionandthenFirm1willmonopolythemarket.ThemarketclearsbasedonthequantitiesfromFirm1.However,bothfirmsinvolveintheCournotcompetitionwhenFirm2doesnotexperiencethesupplydisruptionandthemarketclearsbasedonthequantitiesofproductsfrombothfirms.

ToanalyzewhetherFirm2wouldpurchasetheproductsfromitsrivalFirm1ornotinthecaseofitssupplydisruption,wefirstobtaintheoutcomesthatfollowFirm2’sdecisionnottopurchasewhenitexperiencesthesupplydisruptioninSubsection3.1.1.ThenwederivetheoutcomesthatfollowFirm2’sdecisiontopurchasewhensupplydisruptionoccurs.WecharacterizetheequilibriumoutcomeswhenFirm1isacentralizeddecisionmakerinacentralizedsupplychain.

The Regime in Firm 2’s Decision of Not Purchasing From Firm 1 at the Time of its Supply DisruptionInthissubsection,weconsidertheregimethatitdoesnotpurchasetheproductsfromtherivalFirm1whenFirm2experiencessupplydisruption.

BasedonthesequencesoftheeventsinFigure1,followingFirm1’sannouncedwholesalepricew forFirm2topurchase,Firm2decidesnottopurchaseproductsinthecaseofsupplydisruption.Followingthat,bothfirmswilloptimallydecidethequantitiesoftheproducttodelivertothemarket,expectingtherival’srationalaction.Inotherwords,Firm1choosesitsoutputq f

1tomaximizeits


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Table 1. Modeling notation

Variable/parameterDescription

a :Marketsize

c :Marginalproductioncost

λ :ProbabilitythatFirm2isdisruptedwithsupply“zero”

qif :QuantitydeliveredbyFirm i i( , )= 1 2 whenFirm1isacentraldecisionmakerandFirm2doesnotpurchase

productsfromFirm1tohedgeagainstdisruption

πif :Firm i i( , )= 1 2 ’sprofitwhenFirm1isacentraldecisionmakerandFirm2doesnotpurchaseproductsfrom

Firm1tohedgeagainstdisruption

qip :QuantitydeliveredbyFirm i i( , )= 1 2 whenFirm1isacentraldecisionmakerandFirm2purchasesproducts

fromFirm1tohedgeagainstdisruption

πip :Firm i i( , )= 1 2 ’sprofitwhenFirm1isacentraldecisionmakerandFirm2purchasesproductsfromFirm1to

hedgeagainstdisruption

w :WholesalepriceFirm1chargesFirm2whenFirm1isacentraldecisionmakerandFirm2purchasesproductsfromFirm1tohedgeagainstdisruption

qjdf :QuantitydeliveredbyFirm j j R( , )= 2 ’sretailerwhenFirm1isadecentralizeddecisionmakerandFirm2

doesnotpurchaseproductsfromFirm1tohedgeagainstdisruption

πidf :Firm i i( , )= 1 2 ’sprofitwhenFirm1isadecentralizeddecisionmakerandFirm2doesnotpurchaseproducts


πRdf :ProfitofFirm1’sretailerwhenFirm1isadecentralizeddecisionmakerandFirm2doesnotpurchaseproducts


wdf :WholesalepriceFirm1chargesitsretailerwhenFirm1isadecentralizeddecisionmakerandFirm2doesnot

purchaseproductsfromFirm1tohedgeagainstdisruption

qjdp :QuantitydeliveredbyFirm j j R( , )= 2 ’sretailerwhenFirm1isadecentralizeddecisionmakerandFirm2

purchasesproductsfromFirm1tohedgeagainstdisruption

πidp :Firm i i( , )= 1 2 ’sprofitwhenFirm1isadecentralizeddecisionmakerandFirm2purchasesproductsfrom


πRdp :ProfitofFirm1’sretailerwhenFirm1isadecentralizeddecisionmakerandFirm2purchasesproductsfrom


wdp :WholesalepriceFirm1chargesitsretailerandFirm2whenFirm1isadecentralizeddecisionmakerandFirm2

purchasesproductsfromFirm1tohedgeagainstdisruption


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profitgivenbothfirms’unitproductioncostc andFirm2’soutputq f2

.Mathematically,itsprofitπ1f canbeformulatedasfollowsin(1):

π λ λ1 1 2 1 1 1

1f f f f f fa q q c q a q c q= − − − − + − −( )( ) ( ) (1)

InEquation(1),a q qf f− −1 2

representstheproduct’spricetoclearthequantityonthemarketbasedontheCournotModel(Qin,2013)whenbothfirmsdelivertheproductstothemarketaslongasFirm2hasnodisruption.Therefore a q q cf f− − −

1 2 represents thenetprofit perunit of the

product.a q cf− −1

representsthenetprofitperunitoftheproductwhenonlyFirm1deliverstheproductstothemarketunderthecasethatFirm2disruptsanddoesnotoutsourcetoFirm1.Therefore,thewholeequation(1)representstheexpectedprofitofFirm1.

Similarly,Firm2’sprofitπ2f asfollowsin(2):

π λ2 1 2 2

1f f f fa q q c q= −( ) − − −( ) (2)

Equation(2)showsthatFirm2obtainprofitsonlywhenFirm2hasnodisruption.Jointlysolving(1)and(2),theoptimalquantityq f

1* ofFirm1andq f

2* ofFirm2tomaximize

theirprofitsareasfollowsin(3)and(4),respectively:

Figure 1. Sequence of events when firm 1 is a central decision maker


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qa cf

1

1

3* ( )( )=

+ −+λλ

(3)

qa cf

2 3* =

−+λ

(4)

Bysubstituting(3)intotheexpressionof(1),and(4)into(2),bothfirms’profitscanbeobtainedasin(5)and(6),respectively:

π λλ1

2

2

13

f a c= +

−+

( ) (5)

π λλ2

2

13

f a c= −

−+

( ) (6)

The Regime of Firm 2’s Decision of Purchasing From Firm 1 at the Time of Firm 2’s Supply DisruptionInthissubsection,weconsiderthepurchasingregimethatFirm2purchasesproductsfromtherivalFirm1whenitexperiencesthesupplydisruptionwhileitdoesnotpurchaseproductswhenitssupplyissmooth.Inthiscase,bothfirmsalwaysinvolveintheCournotcompetition.Thatis,Firm2doesnotoutsourcetheproductsfromFirm1ifitssupplyissmoothanddeliverstheproductstothemarketsuccessfullywhileitwillpurchasetheproductsfromFirm1ifsupplydisruptionoccurstoFirm2.

AccordingtothesequenceoftheeventsinFigure1,followingFirm1’sannouncedwholesalepricew forFirm2topurchaseinthecaseofsupplydisruption,Firm2decidestopurchasewhensupplydisruptionoccurs.Followingthat,bothfirmswilloptimallydecidethequantitiesoftheproducttodelivertothemarket,expectingtherival’srationalaction.Letq p

1andqp

2representthequantities

ofFirm1andFirm2’sproductstothemarket,respectivelyintheregimeofpurchasing,thenFirm1’sprofitπ

1p canbeformulatedasfollowsin(7):

π λ1 1 2 1 2p p p p pa q q c q w c q= − − −( ) + −( ) (7)

andsimilarly,Firm2’sprofitπ2p isasfollowsin(8):

π λ λ2 1 2 2 2 2

1p p p p p pa q q q q c wq= − −( ) − − −( ) (8)

Jointlyperformingthemaximizationin(7)and(8),theoptimalquantitiesqp1* andqp

2* ofFirm

1andFirm2asafunctionofthewholesalepriceareasfollowsin(9)and(10),respectively:

qa c w cp

1 2* ( )=− + −λ (9)


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qa c w cp

2

2

3* ( )=− − −λ (10)

Tokeepqp2

0* ≥ ,itisnecessarythatw ca c

− ≤−2λ

.

Bysubstituting(9)intotheexpressionof(7)and(10)into(8),bothfirms’profitscanbeobtainedasin(11)and(12),respectively:

πλ λ

1

2 2 25 5

9p a c a c w c w c=

− + − − − −( ) ( )( ) ( ) (11)

πλ

2

22

3p a c w c=

− − −

( ) ( ) (12)

Equilibrium Analysis When Firm 1 is a Central Decision MakerInthissection,wecharacterizetheequilibriumoutcomeswhenFirm1isacentraldecisionmaker.

LEMMA 1:Inthebasesetting,Firm2willpurchasetheproductsfromitscompetitorFirm1tohedgeagainsttheunexpectedsupplydisruptionifandonlyif:

w c a c≤ + − −−+

( )

( )

1

2

3 1

2 3λλ

λ λ

Lemma1showsthatFirm2iswillingtopaythepremiumtobuytheproductfromitscompetitorFirm1inthecaseofitssupplydisruption.Thepremiumitwouldpayisrelatedtothemarketsize,marginalcostandhersupplydisruptionrate.

ConventionalwisdomadvisesthatFirm1wouldneversellitsproductstoitscompetitorFirm2inthecommonmarketinordertomonopolythemarketifFirm2experiencesdisruptionandcannotsupplyproducts.However,asProposition1reveals,thisviewfailstoconsiderhowthesaleofproductstoitscompetitorFirm2tohelpincreasehisprofit.

PROPOSITION 1: In thebase setting,Firm1will sell products to its competitorFirm2whoexperiencesthesupplydisruptionatthewholesaleprice:

w c a c= + − −−+

( )

( )

1

2

3 1

2 3λλ

λ λ (13)

Byinserting(13)into(11):

πλ λ

λ1

2

2

211 4

4 3p a c=

+ +

+−

( )( ) (14)


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Proposition1indicatesthatFirm1iswillingtosellitsproductstothecompetitorFirm2tohelphedgeagainstsupplyshortagewhenFirm2experiencessupplydisruption.SinceFirm1’sprofitexpressedin(14)ishigherthanthatin(5),itismotivatedbythehigherprofitachievedinthissale.

Byinserting(13)into(9)and(10),respectively,then:

q

a cp1

3 113

4*

( )

=

− −−+

λλ

(15)

q a cp2

1

3* ( )=

−+

−λλ

(16)

PROPOSITION 2:Seebelow:(i) Underpurchasing,Firm2’sretailoutputislowerandprofitisthesamecomparedtothe

profitearnedundernopurchasing,i.e.,q qp f2 2* *< ,andπ π

2 2p f= .

(ii)Underpurchasing,Firm1’sretailoutputislowerandprofitishighercomparedtotheprofitearnedundernopurchasing,i.e.,q qp f

1 1* *< ,andπ π

1 1p f> .

Inmoredetails,bothofFirm1andFirm2deliveralowerquantitytothemarketinthepurchasingregimethanintheno-purchasingregimebasedonthecomparisonbetween(3)and(15),(4)and(16),respectively,whichsoftensthecompetitioninthemarketandleadtoahighermarketpriceinthepurchasingregimethanintheno-purchasing.BypurchasingproductsfromthecompetitorFirm1,Firm2enjoysitspresencestillinthemarketwhenitgoesthrough“zero”supplydisruption.Inthiscase,Firm2’sprofitcomesfromtwoparts:1)theexpectedprofitfromitsowndeliveryofitsownproductswithoutdisruptionand2)theexpectedprofitofthedeliveryofproductspurchasedfromFirm1underdisruption.ComparedtonopurchasingwhenFirm2experiencesdisruption,theexpectedprofitfromitsowndeliveryisdecreased.However,theexpectedprofitfromtheproductspurchasedfromFirm1canoffsettheeffect.Therefore,Firm2’sprofitkeepsconstantunderbothpurchasingandnopurchasing1.

ItisalsoshownthatFirm1canearnahigherprofitifpurchasingexists(Firm1sellingproductstoFirm2tohelphedgeagainstdisruption).WhenFirm2purchasestheproductfromFirm1inthecaseofdisruption,Firm1’sprofitcomesfromtwopartsshownin(7):1)theprofitfromtheretailmarketpresentedbythefirsttermin(7);2)thewholesaleprofitfromFirm2presentedbythesecondtermin(7).Comparedto(7),Firm1’sprofitin(1)onlycomesfromtheretailmarketifFirm2choosesnottopurchaseintheeventofdisruption.Bycomparing(1)tothefirsttermin(7),itisknownthatFirm1willearnlessprofitfromtheretailmarketinthecontextofFirm2’spurchasing.However,thewholesaleprofitfromFirm2underFirm2’spurchasingwilloffsetthisnegativeeffectandfurtherincreasethetotalprofitofFirm1whenFirm2choosestopurchasefromFirm1tohedgeagainstthesupplydisruption.

Outcomes in the Equilibrium When the Firm 1 is a Decentralized Decision MakerInthissubsection,weconsiderthescenariothatFirm1isadecentralizeddecisionmakerandsellstheproductsthroughanindependentretailer R .Figure2showsthesequencesofeventswhenFirm1isadecentralizeddecisionmaker.Asshowninthefigure,Firm1willannouncethewholesalepriceperunittotheretailerandFirm2.Followingtheannouncement,Firm2willmakethedecisioninpurchasingtohedgeagainstherunexpectedsupplydisruptionornot.InthecontextofFirm2’sdecisionofpurchasingfromFirm1,boththeretailerandFirm2decidesthequantitiestodeliver


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tothemarket.WhenFirm2experiencesthesupplydisruption,itwillpurchasetheproductsfromFirm1andthendelivertothemarket.However,whenFirm2suppliestheproductssuccessfully,itwillnotpurchasetheproductsfromFirm1.Finally,boththeretailerandFirm2involveintheCournotcompetitionandthemarketclearsbasedonthequantitiesofproductsdeliveredbytheretailerandFirm2.InthecontextofFirm2’sdecisionofnotpurchasingfromFirm1,theretailerandFirm2willdecidethequantitiesofproductstodelivertothemarket.Thefinalstageisasfollows:Firm2willbeabsentfromthemarketwhenitexperiencesthesupplydisruptionandthentheretailerwillmonopolythemarket.Themarketclearsbasedonthequantityofproductsdeliveredbytheretailer.However,boththeretailerandFirm2involveintheCournotcompetitionwhenFirm2doesnotexperiencethesupplydisruptionandthemarketclearsbasedonthequantitiesdeliveredbybothparties.

ToanalyzewhetherFirm2wouldpurchasetheproductsfromtherivalFirm1ornotwhensheexperiencessupplydisruption,we firstobtain theoutcomes that followFirm2’sdecisionnot topurchasewhensupplydisruptionoccurs.ThenwederivetheoutcomesthatfollowFirm2’sdecisiontopurchasewhensupplydisruptionoccurs.WecharacterizetheequilibriumoutcomeswhenFirm1isadecentralizeddecisionmakersellinghisproductsthrougharetailerinadecentralizedsupplychain.

The Regime in Firm 2’s Decision of Not Purchasing From Firm 1 at the Time of Supply DisruptionInthissubsection,weconsiderFirm2willnotpurchasetheproductsfromFirm1whenFirm2experiencessupplydisruption.BasedonthesequencesoftheeventsinFigure2,followingFirm1’sannouncedwholesaleprice,Firm2choosesnottopurchase.ThenboththeretailerandFirm2decidetheoptimalquantitiestodelivertothemarket,respectively.Inthiscontext,Firm1’sretailermonopoliesthemarketwhenFirm2experiencessupplydisruptionwhileboththeretailerandFirm

Figure 2. Sequence of events when firm 1 is a decentralized decision maker


11

2involveintheCournotcompetitionwhenFirm2smoothlydeliverstheproductstothemarket.Therefore,mathematically,theretailer’sprofitcanbeformulatedasfollowsin(17):

π λ λRdf

Rdf

df

df

Rdf

Rdf

df

Rdfa q q w q a q w q= − − − −( ) + − −( )( )1

2 (17)

Similarly,Firm2’sprofitcanbeformulatedasfollowsin(18):

π λ2 2 2

1df

Rdf

df

dfa q q c q= − − − −( )( ) (18)

Jointlysolving(17)and(18),theoptimalquantityoftheretailerandofFirm2tomaximizetheirownprofitsareasfollowsin(19)and(20),respectively:

qa w c

Rdf d

f* ( ) ( )=

+ − + −

+

1 2 1

3

λ λ

λ (19)

qa w c

df d

f

2

2

3* =

+ −

+λ (20)

Firm1’sprofitcanbeformulatedasfollowsin(21):

π1df

df

Rdfw c q= −( ) * (21)

Byinserting(19)into(21)andbasedonthefirst-ordercondition,theoptimalwholesalepriceannouncedbyFirm1w

df * isobtainedasfollows:

wa c

df * ( ) ( )=

+ + −1 3

4

λ λ (22)

Accordingly, theoptimalquantityof theretailerandFirm2areasfollowsin(23)and(24),respectively:

qa c

Rdf * ( )( )

( )=

+ −+

1

2 3

λλ

(23)

qa c

df2

5

4 3* ( )( )

( )=

+ −+λλ

(24)

Byinserting(22),(23)and(24)into(17),(18)and(21),theprofitsoftheretailer,Firm2andFirm1areasfollows,respectively:


12

πλλRd

f a c=

+ −

+

( ) ( )

( )

1

4 3

2 2

2 (25)

πλ λ

λ2

2 2

2

1 5

16 3df a c=

− + −

+

( )( ) ( )

( ) (26)

πλ

λ1

2 21

8 3df a c=

+ −+

( ) ( )

( ) (27)

The Regime in Firm 2’s Decision of Purchasing From Firm 1 at the Time of Supply DisruptionInthissubsection,weconsidertheregimethatFirm2purchasestheproductfromFirm1tohedgeagainstthesupplyshortagewhenFirm2experiencesthesupplydisruption.Inthiscase,boththeretailerandFirm2alwaysinvolvesintheCournotcompetitionregardlessofFirm2’spotentialsupplydisruption.

AccordingtothesequencesoftheeventsinFigure2,followingFirm1’sannouncedwholesaleprice,theretailerandFirm2decidesthequantitiesoftheproductstodelivertothemarket.Finally,bothoftheretailerandFirm2involveintheCournotCompetition.Letq

Rdp andq

dp2

representthequantitiesplannedbytheretailerandFirm2todelivertothemarket,respectively,thentheretailer’sprofitcanbeformulatedasfollowsin(28)andFirm2’sin(29):

πRdp

Rdp

dp

dp

Rdpa q q w q= − − −( )2

(28)

π λ λ2 2 2 2 2

1dp

Rdp

dp

dp

dp

dpdpa q q q cq w q= − −( ) − − −( ) (29)

Jointlyperformingthemaximizationof(28)and(29),theoptimalquantitiesoftheretailerandFirm2areasfollowsin(30)and(31):

qa c w c

Rdp d

p* ( )( )=− + − −λ 2

3 (30)

qa c w c

dp d

p

2

1 2

3* ( )( )=− + − −λ

(31)

Byinserting(31)into(29),thenFirm2’sprofitisasin(32):

πλ

2

21 2

3dp d

pa c w c=

− + − −

( )( ) (32)

Similarly,Firm1’sprofitcanbeformulatedasfollowsin(33):


13

π λ1 2dp

dp

Rdp

dp

dpw c q w c q= − + −( ) ( )* * (33)

Byinserting(30)and(31)into(33),then:

πλ λ λ

1

21 2 1

3dp

dp d

p

w ca c w c

= −+ − + − − −

( )( )( ) ( )( )

(34)

Equilibrium Analysis When Firm 1 is a Decentralized Decision MakerInthissection,wecharacterizetheequilibriumoutcomeswhenFirm1isadecentralizeddecisionmaker.Thatis,Firm1sellsitsproductsthrougharetailerinadecentralizedsupplychaincompetingwithFirm2whoexperiencespotentialunexpectedsupplyriskinacommonmarket.Basedontheoutcomesfromthescenariosthat1)Firm2doesnotpurchasetheproductsfromFirm1atthetimeofFirm2experiencingsupplydisruptioninSubsection3.2.1;2)Firm2purchasestheproductsfromFirm1atthetimeofsupplydisruptioninSubsection3.2.2,whataretheequilibriumoutcomeswhenFirm1sellsitsproductsthrougharetailerinadecentralizedsupplychain?

Lemma2showsustheconditionthatFirm2purchasestheproductfromFirm1tohedgeagainstthesupplyshortagewhenitexperiencesthesupplydisruption.

LEMMA 2:When:

w c a cdp ≥ +

− + − ++ −

−

+

3 1 5 4 3

4 3 1 2

λ λ λλ λ

( ) ( )

( )( )( )

Firm 2 will purchase the product from Firm 1 at the time of its supply disruption, wherex x+ = max( , )0 .

Lemma2isconsistentwithFirm2’sprofitexpressedin(32)whichisincreasinginthewholesalepricechargedbyFirm1.Thehigherthewholesalepriceis,thelowerthequantityfortheretailertodelivertothemarketis,whichmitigatesthecompetition,sothehighernotonlythemarginprofitearnedbyFirm2,butalsothequantityoftheproductsdeliveredbyFirm2.Therefore,theprofitearnedbyFirm2inthe“purchasing”regimewillbehigherthanthatinthe“no-purchasing”regimewhenthewholesalepriceisbeyondathreshold.

NowwhatistheoptimalwholesalepriceforFirm1toannounce?Proposition3showstheanswer.

PROPOSITION 3:Inthebasesetting,Firm1willhelpFirm2tohedgeagainstthesupplydisruptionbysellingproductstoFirm2atthetimeofFirm2experiencingsupplydisruption:(i)theoptimalwholesalepriceannouncedbyFirm1is:

w c a cdp* ( )

( )( )= +

+

+ −−

1

4 1 2

λλ λ

(35)

(ii)Firm1’sprofitisasfollowsin(36):

πλ

λ λ1

2

2

21

24 1dp a c=

+

+ −−

( )

( )( ) (36)


14

Proposition3indicatestheoptimalwholesalepricethatFirm1chargestosellitsproductstotheretaileranditscompetitorFirm2tohelphedgeagainstsupplyshortagewhenFirm2experiencessupplydisruption.At thiswholesaleprice,Firm1’sprofitexpressed in (36) in the“purchasing”regimeishigherthanthatin(27)inthe“no-purchasing”regimeandFirm2alsoachievesahigherprofitinthe“purchasing”regime.Thisisa“win-win”game.

Accordingly,byinserting(35)into(30)and(31),respectively,then:

q a cRdp *

( )( )=

+ −

+ −−

2 5 5

12 1

2

2

λ λλ λ

(37)

and:

q a cdp2

2

2

5 2 5

12 1*

( )( )=

+ −

+ −−

λ λλ λ

(38)

Proposition4makesacomparisonofthequantitiesdeliveredtothemarketandwholesalepriceannouncedbyFirm1betweentheregimeof“nopurchasing”andregime“purchasing”.

PROPOSITION 4:UnderFirm1’sdecentralizeddecisionmaking:(i) w w

df

dp* *< ;

(ii) q qRdp

Rdf* *< ;

(iii)When0 18 129 11

20 5. .≈

−≤ ≤λ ,q q

dp

df

2 2* *≤ whilewhen0 129 11

20 18< <

−≈λ . ,

q qdp

df

2 2* *> .

Proposition4showsthati)thewholesalepricechargedinthe“purchasing”ishigherthaninthe“no-purchasing”.ThisistheresultofFirm1toinduceFirm2topurchaseatthetimeofdisruptiontoobtain ahigherprofit, asweexplained in i)ofProposition3; ii) the retailerdelivers a lowerquantityoftheproductstothemarketinthe“purchasing”regime.Asexpressedin(30),thequantitydeliveredbytheretailerisdecreasinginthewholesaleprice.Thehighwholesalepricechargedinthe“purchasing”regimeleadstothelowquantity;iii)thequantityofFirm2deliveredtothemarketinthe“purchasing”regimeishigherthanthatinthe“no-purchasing”regimewhenFirm2’sdisruptionrateislowerwhileitislowerwhenthedisruptionrateishigher.Thisisbecausebothquantitiesasshownin(24)and(38)decreaseinthedisruptionrate,respectively.However,thequantityin(38)decreasesmorethanin(24).Therefore,thequantityoffirm2ishigherinthe“purchasing”atthelowersideofthedisruptionrateregimewhileitisloweratthehighersideofdisruptionrate.

Supply Chain StructureIntheprevioussections,theoutcomesshowthatFirm1willalwaysinduceFirm2topurchasetheproductsatthetimeofsupplydisruptiontohedgeagainstitssupplyshortagewhetherFirm1choosescentral decision making or decentralized decision making. In this subsection, we would like toanswerthequestion:1)howdoesFirm1behaveinitsretailmarket?2)DoesFirm1choosecentraldecisionmakingordecentralizeddecisionmakingwhenitsrivalhasapotentialsupplydisruptionandpurchasesproductsfromitatthetimeofexperiencingsupplydisruption?TheresultsaresummarizedinLemma3andProposition5.


15

LEMMA 3: Seebelow:(i) q qp

Rdp

1* *>

(ii) a q q wp pdp− − <

1 2* * *

Lemma3showsthati)Firm1’squantityintheretailmarketishigherinthecentraldecisionmakingthaninthedecentralizeddecisionmaking.Thisresultisduetothedoublemarginalizationinthedecentralizeddecisionmaking;ii)ThemarginprofitforFirm1toearnintheretailmarketislowerinthecentraldecisionmakingduetotheaggressiveencroachmentintheretailmarket.

PROPOSITION 5:Firm1willchoosecentralizeddecisionmakingandsellsitsproductsthroughitscentralizedsupplychain.

Proposition5showsthatFirm1’scentralizedsupplychainispreferred.Thisresultprovidesanewinsightforthesuppliertoprovidetheproducttothefirmsinthecommonmarket,comparedtotheresultfromArya,MittendorfandYoon(2008)whoshowedthattheVIPprofitisalwayshigherunderdecentralizationthanundercentralizationwhentherivalis100%dependsonthepurchasefromthemanufacturingcompany.Ourresultsshowthatiftherivalonlypurchasestheproductunderherdisruption,themanufacturingcompany’scentralizedsupplychainispreferred.

CONCLUSION

Outsourcingtheproductstotherivalpartyinthecommonmarkethasgarneredmuchattentioninoperationsmanagement.Theconventionalviewpositsthatmonopolizationispreferredwhentherivalexperiencesdisruptionandshortagesinthemarket.Thispaperdemonstratesthatitmaynotbethecasewhenbothpartiesselltheproductsinthecommonmarket.Insuchacase,onepartywouldinducetherivalpartyintheeventofdisruptiontopurchasetheproductsfromitwhichactuallycanearnahigherprofitcomparedtomonopolizationregardlessofthedisruptionrate.Accordingly,therivalpartydoesnotloseitspresenceonthemarketwhenitexperiencesthedisruptionandfinallyearnsahigherprofittoo.

Centraldecisionmakingeliminatesdoublemarginalization,whichincreasesthequantitydeliveredtothemarket.However,thefirmisabletocommittoaggressiveencroachmentinthemarket,whichinturnmayleadtoalowermarginprofit.Thispaper’sresultsdemonstratethatajudiciousstructurebestbalancesprofitability.Giventheprevalenceofcircumstanceswhereintherivalexperiencesdisruption,theresultsshedsomelightonefficacyofchainforms.Thatis,thecentraldecisionmakingispreferred.

Giventheresultsdemonstratedinthispaper,wehopethatthisstudywillserveasasteppingstoneforfutureresearchtoexplorethewaystomitigatethesupplydisruptionriskincludinginthesituationthatfirmsmayhavedifferentriskattitudes.


16

ReFeReNCeS

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Demirel,S.,Kapuscinski,R.,&Yu,M.(2018).Strategicbehaviorofsuppliersinthefaceofproductiondisruptions.Management Science,64(2),533–551.

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Qin,Z.(2013).Theeffectof“make”or“buy”onthetimingofcapacityinvestmentbymanufacturersinnewmarkets.International Journal of Applied Management Science,5(4),377–396.

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http://www.gottabemobile.com/2013/05/22/why-apple-cant-escape-samsung-globalization/

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http://papers.ssrn.com/sol3/papers.cfm?abstractnid=1616949


17

eNDNOTeS

1 Sincefirm2stillmaintainsherpresenceonthemarketwhensheexperiencesthesupplydisruption,shewouldchoosetopurchaseproductsfromfirm1tohedgeagainstsupplyshortageeventheprofitsintheregimeofnopurchasingandpurchasingarethesame.

ZhaoqiongQinisanassistantprofessorinUniversityofCentralOklahoma.Herresearchinterestsfocusonbehaviorinteractionsamongpartiesinsupplychainmanagement,operationsresearch,optimizationanddecisionsciences.HerseminalworkispublishedinOperationsResearch,InternationalJournalofLogistics:ResearchandApplicationandInternationalJournalofAppliedManagementScience.


18

APPeNDIX

PROOF OF LEMMA 1:IfFirm2canearnahigherprofitbybuyingtheproductsfromFirm1tohedgeagainsttheunexpectedsupplydisruptioncomparedtotheearnedprofitbynotbuyingfrom Firm 1, then Firm 2 will choose to buy. That is ( ) ( )12 6≥ . So only when

w c a c≤ + − −−+

( )

( )

1

2

3 1

2 3λλ

λ λ,Firm2willbuyproductsfromFirm1tohedgeagainstthe

unexpectedsupplydisruption.

PROOF OF PROPOSITION 1: TomakeFirm1’sprofitinFirm2’spurchasingregimeishigherthantheprofitwithoutpurchasing,thefollowingconditionshouldbesatisfied:

c a c w c a c+ − −− −

+

≤ ≤ + −( )

( )( )

1

2

225 90 135

10 3

12

λλ λ

λ λ 22

225 90 135

10 3

2

λλ λ

λ λ+

− −+

( )

ToinduceFirm2topurchasetheproductfromitsrivalFirm1inthecaseofsupplydisruption:

w c a c≤ + − −−+

( )

( )

1

2

3 1

2 3λλ

λ λ

Since:

225 90 135

53 1

2− −> −

λ λλ

c a c c a c+ −− −

+

< + − −( )

( )( )

1

2

225 90 135

10 3

1

2

2

λλ λ

λ λ λ33 1

2 3 2

−+

< +

−λλ λ λ( )

ca c

From(11),itisalsoknownthatFirm1willachievethemaximumprofitatw ca c

= +−2λ

.

ThereforeFirm1willannouncethewholesalepriceat:

w c a c* ( )( )

= + − −−+

1

2

3 1

2 3λλ

λ λ

PROOF OF LEMMA 2:Inthedecentralizeddecisioncase,ifFirm2canearnahigherprofitbybuyingtheproductsfromFirm1tohedgeagainsttheunexpectedsupplydisruptioncomparedtotheearnedprofitbynotbuyingfromFirm1,thenFirm2willchoosetobuy.Thatis( ) ( )3 240 ≥ ,i.e.when:

w c a cdp ≥ + −

+( ) +( )+( )( )

( )

3 1- 5 -4 3

1-2

λ λ λ

λ λ4 3


19

Firm2willpurchasetheproductfromFirm1intheeventofsupplydisruption.

PROOF OF PROPOSITION 3:Seebelow:

(i) Tomake(32)ishigherthan(25),thatis,Firm1willmakeahigherprofitinthepurchasing,then:

( )( )

( )

( )( )( )

(

a c w c a cdp− +

− −+ −+

+ −< − < − +

+ −1

1 13 13

4 11

1 132

2λ

λ λλ

λ λλ

113

4 1

2

2

+ −+

+ −

λ λλ

λ λ

)

( )

Whenλ ≤ 12

,285 734 309 742 03 2− − + >λ λ λ .Therefore:

285 734 309 742 4 63 9 02 4 3 5 6 7λ λ λ λ λ λ λ− − + + + + >

Soitisclearthat:

( )( )

( )

( ) ( )

( )( )( )

1

4 1

3 1 5 4 3

4 3 1 22

+ −

+ −>

− + − ++ −

−λλ λ

λ λ λλ λ

a ca c

Basedonthefirst-orderconditionin(32),whenw ca c

dp − =

+ −

+ −

( )( )

( )

1

4 1 2

λλ λ

,(32)ismaximized.

BasedonLemma2,themaximizerof(32)alsocanguaranteesFirm2purchasesproductsfromFirm1 at the time of supply disruption. Therefore, Firm 1 announces the wholesale price

w ca c

dp* ( )( )

( )= +

+ −

+ −

1

4 12

λλ λ

.

Firm1willannouncew c a cdp* ( )= + −

21

44λtomaximizeitsownprofit.

(ii)Byinsertingwdp* into(32):

πλ

λ λ1

2

2

1

24 1-dp a c=

+( )+( )

−( )2

PROOF OF PROPOSITION 4:Seebelow:(i) When 0 18 0 5. .≤ ≤λ , 2 11 02− − ≤λ λ , ( ) ( )36 < 22 , i.e., q q

dp

df

2 2* *≤ , while when

λ < 0 18. ,2 11 02− − >λ λ ,( ) ( )36 > 22 ,i.e.,q qdp

df

2 2* *> ;

(ii)Since10 13 02 3λ λ λ− − < , 35( ) < ( )21 ,i.e.,q qRdp

Rdf* *< ;

(iii)Sinceλ λ( )( )2 1 0− − <a c ,the 20 33( ) < ( ) ,i.e.,w wdf

dp* *< .


20

PROOF OF PROPOSITION 5:When7 152 47 02λ λ+ − ≤ ,Firm1’sprofitin(38)ishigherthan

orequaltothatin(14),i.e., 0 6105 76

70 3< ≤

−≈λ . ,Firm1’sprofitinthedecentralized

supplychainwillbehigherthanorequaltotheprofitinthecentralizedsupplychain.ThereforeFirm1willchooseadecentralizedsupplychainandsellitsproductsthroughtheretailer.Otherwiseitwillchoosethecentralizedsupplychaintosellitsproducts.

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