Research on Equilibrium Decision Closed loop Supply Chain

ScientificJournalofEconomicsandManagementResearchVolume1Issue05,2019

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ResearchonEquilibriumDecisionClosed‐loopSupplyChainSuper‐networkConsideringConsumerChannelPreferencesLed

byManufacturersMeiyiSong,YafeiZhao

SchoolofEconomicsandManagement,ChongqingUniversityofPostsandTelecommunications,Chongqing,400065,China

AbstractInordertostudyhowconsumers'preferencesforshoppingthroughonlinechannels,andtheintensityofcompetitionbetweenonlineandtraditionalchannelsaffectthedecision‐making and optimal goals of companies at all levels in a closed loop supply chainnetworkdominatedbymanufacturers,thispaperestablishesaclosed‐loopsupplychainsuper‐network equilibrium model consisting of multiple suppliers, manufacturers,retailers,demandmarketsandrecyclers. In thismodel,companiesatall levelsof thesupplychainaimtomaximizeprofits.Thispaperusesthemethodofequilibriumtheoryandvariationalinequalitytoanalyzethedecision‐makingbehaviorsandoptimaltargetsof enterprises at various levels, and solves them through an improved projectiongradientalgorithm.Finally,thispaperusesnumericalexamplestoanalyzetheimpactofconsumerchannelpreferencesandtheintensityofcompetitionbetweenchannelsonthetransactionvolume,profitsofvariouslayersofenterprises,andthepricesofdemandforproductspurchasedthroughonlineandtraditionalchannels.

KeywordsClosed‐loop supply chain; manufacturer‐led; channel preference; super‐networkequilibrium;variationalinequality.

1. Introduction

With the advancement of the times and the development of the Internet, e‐commercecompaniesinchinahavesprunguprapidly.Manymanufacturershavebrokenthetraditionalbusinessmodel,openeduponlinedirectsaleschannels,andprovidedconsumerswithnew,convenient, and trendy Shopping methods. Therefore, a dual‐channel supply chain withmanufacturersasthemainbodyhasbeenformed.Althoughthisemergingshoppingmethodhas brought different shopping experiences to consumers, brought considerable profits tosomeenterprises,andalsopromotedthedevelopmentofthelogisticsindustry,theoperationofonlinedirectsaleschannelshasbroughtunprecedentedopportunitiestotraditionalchannels.And this shock reduced the sales volume of traditional channels, damaged the interests ofretailers,andwasnotconducive to thestabledevelopmentof theentireclosed‐loopsupplychain. Therefore, how to coordinate the supply chain network to achieve equilibrium hasbecome a very important issue. Regarding the coordination of dual‐channel supply chains,Zhangconsideredtheriskofreturnandpricingdifferencesandstudiedthepricingstrategiesof manufacturers under different market demands (Zhang Xuelong, Wu Doudou,etc,2018)[1].Thispapersolvedtheproblemofsupplychainchanneloperationcombinationinthecaseofproduct experience differences between physical channels and network channels(ZhouJianheng,WangQi,2017)[2].Thepaperstudiedthetwo‐tiersupplychainnetworkcomposedofmanufacturers and retailers, and the impact of retailers opening network channels on thesupply chain (Kong Zaojie and Li Zuyi,2017)[3]. Yu studied the supply chain equilibrium


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betweencompanieswithofflineandonlinesaleschannels(YugangYu,XiaoyaHan,etc,2017)[4].Sunalsoconsideredconsumers'preferences for lowcarbonandchannels,andanalyzedthenumericalexamplestoobtaintheoptimalcarbonemissionboundaryofthesupplychain(SunJiananandXiaoZhongdong,2015)[5].Intheresearchofsupplychainnetworkequilibrium,thepaperconsideredtheimpactofconsumerbehaviorintheonlineshoppingsupplychainsystemontheonlineshoppingsupplychainnetworkequilibriumduringthepromotionofe‐commercecompanies,andconstructedamarketbasedonconsumerbehavior.Finally,thepaperanalyzedthe best decision‐making behavior of decision makers at all levels (Ye Zhou, Jue Zeng,etc,2017)[6]. Hamdouch and others proposed a decentralized closed‐loop supply chainnetworkmodel, assuming that thedemand forproducts and the corresponding returns arerandom and price‐sensitive, and finally analyzed the optimal decision‐making behavior ofenterprisesatalllevels(YounesHamdouch,QiangPatrickQiang,KilaniGhoudi,2017)[7].Thepaperconsideredthelosscausedbytheinterruptionriskbetweentheproducerandtheretailer,and studied the dynamicmanagement of supply chain risk (Ma Jun, Dong Qiong and YangDeli,2015)[8]. As the country strongly advocates saving resources and recycling resources,more and more scholars attach importance to the research of closed‐loop supply chainmanagement. Cao Xiaogang and others constructed a closed‐loop supply chain networkcomposedofmultiplesuppliers,manufacturers,retailers,andconsumermarkets,andanalyzedtheimpactofriskfactorsontheequilibriumresultsofthesupplychainnetwork(CaoXiaogang,ZhenBenrong,etc,2014)[9].Most of the supply chain networks constructed by the above studies are made up ofmanufacturersandretailers,withouttakingintoaccountothermembersofthesupplychain,such as suppliers, demand markets, and recyclers. In addition, although the dual‐channelsupply chain coordination problem is considered, the consideration of consumer channelpreferenceshaslessimpactontheclosed‐loopsupplychain.Inviewoftheaboveissues,thispapertakesaclosed‐loopsupplychainconsistingofmultiplesuppliers,multiplemanufacturers,multiple retailers,multiple demandmarkets, andmultiple recyclers as the research object.Whenmanufacturersopenupnetworkchannels,consideringconsumers'preferenceforusingonlineshopping,aclosed‐loopsupplychainsuper‐networkequilibriummodelwasestablished.Then, a numerical example is conducted to discuss the influence of consumer channelpreferencesandinter‐channelcompetitionintensityfactorsonthetransactionvolume,demandprice, and corporate profits of various layers of companies. Finally, this paper gives somesuggestionsforcoordinatingclosed‐loopsupplychains.

2. ModelConstructionandSymbolDescription

2.1. ModelBuildingWe construct a closed‐loop supply chain model consists of five levels: one supplier, Mmanufacturers,Nretailers,Kdemandmarkets,andRrecyclers.Therearedifferent levelsofverticalcooperationinthisnetworksystem.Theclosed‐loopsupplychainincludesaforwardsupply chain and a reverse supply chain. The recycler is a networknode that connects theforwardandreversesupplychains.Inthisnetwork,suppliersareresponsibleforprovidingrawmaterials to manufacturers; manufacturers are responsible for producing new andremanufacturedproducts,andsendingwastematerialsgeneratedduringproductiontoscrapcenters;retailersareresponsibleforsellingproductsproducedbymanufacturerstoDemandmarkets;recyclersareresponsibleforrecyclingandresellingusedproductstomanufacturers.Duetosomeuncertainfactorsintheclosed‐loopsupplychain,thefollowingassumptionsaremade:1. Allcompaniesarerationalandareseekingtomaximizetheirownprofits;


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2. Consideronlythemanufactureorrecyclingofoneproductorafullysubstitutableproduct,andthereisnoessentialdifferencebetweenaremanufacturedproductandanewproduct;

3. Theclosed‐loopsupplychainisdominatedbymanufacturers,anddecisionmakersatthesamelevelareinanon‐cooperativecompetitionstate;

4. The related cost function and economic function are both continuously differentiableconvexfunctions.

2.2. SymbolDescription

Foreaseofreference,notationsusedinthispaperarelistedbelow:

imq transactionquantitybetweenvendoriandmanufacturem

mnq transactionquantitybetweenmanufacturemandretailern

nkq transactionquantitybetweenretailernanddemandmarketk

rkq transactionquantitybetweendemandmarketkandrecyclerr

mrq transactionquantitybetweenmanufacturemandrecyclerr

imp producttransactionpricebetweenvendoriandmanufacturem

mnp producttransactionpricebetweenmanufacturemandretailern

nkp producttransactionpricebetweenretailernanddemandmarketk

rkp producttransactionpricebetweendemandmarketkandrecyclerr

mrp producttransactionpricebetweenmanufacturemandrecyclerr

kp unitproductdemandpriceindemandmarketk

p unitproductdisposalcost

1 productconversionrateofnewmaterials, 1 (0,1)

2 productconversionrateofoldmaterials, 2 (0,1)

recoveryrateofwasteproductsindemandmarkets, (0,1)

recycler'sconversionrateofwasteproductsintousablematerials

recycler'sconversionrateofwasteproductsintounusablematerials

1 demandintensityfactoroftraditionalchannels

2 demandcompetitionintensityfactorofnetworkchannels

consumer'spreferencefactorforonlinechannelshopping

3. EquilibriumModelofClosed‐LoopSupplyChainSuper‐network

In this section,wewill analyze thebehavioraldecisionsandoptimalgoalsofeachsupplier,manufacturer,retailer,demandmarketandrecycler.

3.1. SupplierBehavioralDecisionandOptimalGoalThe revenue of the supplier i is im imp q , the transaction cost between the supplier i and the

manufacturerm is ( )im imC q , and the supplier's procurement cost is1

( )M

i imm

f q . The supplier i

pursuesmaximizing profit. This paper uses a standardweight function of 1. The objectivefunctionofthesupplieriis:


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1 1 1

max ( ) ( )M M M

i im im i im im imm m m

U p q f q C q

(1)

Assumingthatthefunctionsinformula(1)areallcontinuouslydifferentiableconvexfunctions,the optimal solution of the supplier i is *

imq . This formula satisfies the following variationalinequality:

* ** *

1 1

( ) ( )[ ] ( ) 0

I Mi im im im

im im imi m im im

f q C qp q q

q q

*( , 0, , )im imq p i m (2)

3.2. ManufacturerBehavioralDecisionandOptimalGoalTheprofitobtainedbymanufacturermfromsellingtheproducttoretailernis mn mnp q ,andthe

profitobtainedbymanufacturermthroughthenetworkchannelis mk mkp q .Thetransactioncostsofmanufacturermandsupplieri,retailern,demandmarketk,andrecyclerrarerespectively

( )im imC q , ( )mn mnC q , ( )mk mkC q , ( )mr mrC q .Manufacturer'snewandoldmaterialsproductioncosts

are 11

( , )I

m imi

f q , 2

1

( , )R

m mrr

f q .Sameasmethod3.1,theobjectivefunctionofmanufacturerm

is:

1 21 1 1 1 1

1 1 1 1 1 1

1 21 1

max ( , ) ( , ) ( )

( ) ( ) ( ) ( )

[(1 ) (1 ) ]

N I R N I

m mn mn m im m mr mn mn im imn i r n i

K K K I R R

mk mk mk mk m mk im im mr mr mr mrk k k i r r

I R

im mri r

U p q f q f q C q p q

p q C q C q C q p q C q

p q q

(3)

. .s t1 2

1 1 1 1

N K I R

mn mk im mrn k i r

q q q q

Assumingthatthefunctionsinequation(3)areallcontinuouslydifferentiableconvexfunctions,theoptimalsolutionofthemanufacturermis( *

imq , *mnq , *

mkq , *mrq , *

1 ).Thentheformulasatisfiesthefollowingvariationalinequality:

* ** * *

11 1 1 1

* *1

* * *1 11

1 1

( ) ( )[ ] ( ) [

( ) ( , )] ( ) [

M N M Kmn mn mk mk

mn mn mnm n m Kmn mk

K I

m mk m imI Mk i

mk mk mki mmk im

C q C qp q q

q q

C q f qp q q

q q

** 2

* * * 11 1 1

1 1

** * * * *

2 2 1 1 21 1 1

* * *1 1

1 1

( , )( )

(1 ) ] ( ) [

( )(1 ) ] ( ) (

) ( ) 0

R

m mrM Rim r

im im imm rim mr

M I Rmr mr

mr mr mr im mrm i rmr

N K

mn mkn k

f qC q

p p q qq q

C qp p q q q q

q

q q

(4)


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* * * *1( , , , , , , , 0, , , , , )im mn mr mk im mn mk mrq q q q p p p p i m n k r

1 istheLagrangecoefficientthatguaranteesthatthevariationalinequality(4)holds.

3.3. RetailerBehavioralDecisionandOptimalGoalRetailernearns nk nkp q ,Thetransactioncostsofretailernwithmanufacturermanddemand

marketkare ( )mn mnC q , ( )nk nkC q .Retailer'sproductstoragefeeis1

( )M

n mnm

C q .Sameas3.1method,

theobjectivefunctionofretailernis:

1 1 1 1 1

max ( ) ( ) ( )K M K M M

n nk nk mn mn nk nk mn mn n mnk m k m m

U p q p q C q C q C q

(5)

. .s t 1 1

K M

nk mnk m

q q

Assumingthatthefunctionsinequation(5)areallcontinuouslydifferentiableconvexfunctions,the optimal solution for retailer n is( *

mnq , *nkq , *

2 ). This equation satisfies the followingvariationalinequality:`

** *

* * * 12

1 1 1 1

* * * * * *2 2 2

1 1 1

( )( ) ( )

[ ] ( ) [

] ( ) ( ) ( ) 0

M

n mnN K M Nnk nk mn mn m

nk nk nkn k m nnk mn mn

N M K

mn mn mn mn nkn m k

C qC q C q

p q qq q q

p q q q q

(6)

* *2( , , , , 0, , , )mn nk mn nkq q p p m n k


3.4. DemandMarketEquilibriumConditionsProductsindemandmarketkareprovidedbytraditionalchannelsandonlinechannels.Thedemand for traditional channels is *

1( , , )k kD p , and the demand of the network channel is*

1( , , )ek kD p .Thentheequilibriumconditionofthedemandmarketkis:

* *

1*1

* *

1

0

( , , )

0

N

nk kn

k k N

nk kn

q ifp

D p

q ifp

，

，

(7)

* *

*

* *

0

0k nk

nk nk

k nk

p ifqp C

p ifq

，

，(8)

* *

1*1

* *

1

, 0

( , , )

, 0

Me

mk kme

k k Me

mk km

q ifp

D p

q ifp

(9)

* **

* *

, 0

, 0

ek mk

mk mk ek mk

p ifqp C

p ifq

(10)


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Formulas(7)and(9)respectivelyindicatethatunderequilibriumconditions,ifconsumersinthedemandmarketarewilling topurchasesuchproducts through traditionalchannelsandonlinechannels,thenthedemandisequaltothesupply;whenthesupplyisgreaterthanthedemand,thedemandpriceofsuchproductsiszero.Formulas(8)and(10)respectivelyindicatethat when the demand market and retailer, the demand market and manufacturer's unitproducttransactionpriceandunittransactioncostdonotexceedtheunitdemandpriceoftheproduct,thedemandmarketandtheretailer,manufacturerconducttransactions;otherwise,notransactionoccurs.

* **

* *1

0( )

0

Krk rk

k rkk rk rk

p ifqq

p ifq

，

，(11)

. .s t 1 1 1

( + )R N M

rk nk mkr n m

q q q

ThenegativeutilityfunctioninEquation(11) *

1

( )R

k rkr

q indicatingthatconsumersarewilling

toreturnusedproducts[9].Itisanincreasingfunctionoftherecycler'srecoveryamount,thatis,themorewasteproductsreturnedbyconsumers,themoretroubletheybringtothemselves,so the consumer hopes that the recycler can give more compensation and give a higherrecyclingprice.Equation(11)statesthatwhentheunittransactioncostbetweenthedemandmarketandtherecyclerdoesnotexceedtheunittransactionpriceoftheproduct,thedemandmarketconductstransactionswiththerecycler;otherwise,notransactionoccurs.Constraintsindicatethatthetotalamountofproductsrecycledbytherecyclertothedemandmarketcannotexceedthesupplyinthedemandmarket. istheproductrecoveryrate.Assumingthatthefunctionsin(7),(8),(9),(10),and(11)areallcontinuouslydifferentiableconvex functions, theoptimal solutionof thedemandmarket k is * * * *

3( , , , )nk mk rkq q q , then theformulasatisfiesthefollowingvariationalinequality:

** * * * * *

1 31 1 1 1

** * * *

21 1 1 1

( )[ ( , , )] ( ) [ ]

( )( ) [ ( , , )] ( ) [

K N N Knk nk

nk k k k k nk kk n n k nk

K M M Ke e e mk mk

nk nk mk k k k kk m m k mk

C qq D p p p p p

q

C qq q q D p p p

q

* * * * * * * *3 3

1 1 1

* * * *3 3

1 1 1 1

] ( ) [ ( ) ] ( )

( ) ( ) 0

R K Re

mk k mk mk k rk rk rk rkr k r

K N M R

nk mk rkk n m r

p p q q q p q q

q q q

(12)

* * * *3( , , , , , , , 0, , , , )nk mk rk nk mk rk kq q q p p p p m n k r


3.5. RecyclerBehavioralDecisionandOptimalGoalRecycler earns mr mrp q , the transaction costs between recycler r and demandmarketk, and

manufacturermare ( )rk rkC q , ( )mr mrC q .Recycler'sacquisition,transportation,andstoragecosts

are1

( )K

r rkk

C q [10].Sameasthemethod3.1,theobjectivefunctionoftherecyclerris:

1 1 1 1 1 1

max ( ) ( ) ( )M M K K K K

r mr mr mr mr rk rk rk rk r rk rkm m k k k k

U p q C q p q C q C q p q

(13)


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. .s t 1 1

M K

mr rkm k

q q

Assuming that the functions in equation (13) are all continuously differentiable convexfunctions, the optimal solution for the recycler r is * * *

4( , , )mr rkq q ,This formula satisfies thefollowingvariationalinequality:

** *

* * * 14

1 1 1 1

* * * * * *4 4 4

1 1 1

( )( ) ( )

[ ] ( ) [

] ( ) ( ) ( ) 0

K

r rkM R K Rmr mr rk rk k

mr mr mrm r k rmr rk rk

R K M

rk rk rk rk mrr k m

C qC q C q

p q qq q q

p p q q q q

(14)

* *4( , , , , 0, , , )mr rk mr rkq q p p k r m


3.6. ModelDynamicEquilibriumConditionAnalysisAccording to the above formula, the only solution for the dynamic equilibrium state of theclosed‐loopsupplychainsuper‐networkmodelis:

* * * * * * * * * * * *1 2 3 4( , , , , , , , , , , , 0, , , , , )e

im mn nk mk rk mr k kq q q q q q p p i m n k r ,

andmeetthefollowingconditions:

* ** *1

*1 11 1 1

1 1

** *

* * * *11 2

1 1

*

( ) ( , )( ) ( )

[ (1 ) ]

( )( ) ( )

( ) [ ] ( )

( )+ [

M I

i im m imM Im i im im im im

m i im im im im

M

n mnM Nmn mn mn mn m

im im mn mnm n mn mn mn

mk mk

f q f qC q C q

pq q q q

C qC q C q

q q q qq q q

C q

**

* * * *11 3

1 1

* ** * * * *

2 31 1 1 1 1

( )( )

] ( )

( ) ( )[ ] ( ) [ ( )

K

m mkM Kemk mk kk mk mk

m k mk mk mk

K N R K Rnk nk nk nk

k nk nk k rkk n r k rnk nk

C qC q

p q qq q q

C q C qp q q q

q q

(15)

* ** 2

* * *1 13 4

1 1

* ** * * * *

2 4 2 1 11 1

* *

( ) ( , )( )

] ( ) [

( ) ( )(1 ) ] ( ) [ ( , , )]

( ) [ (

K R

r rk m mrM Rk rk rk r

rk rkm rrk rk mr

K Nmr mr mr mr

mr mr nk k kk nmr mr

k k mk k

C q f qC q

p q qq q q

C q C qp q q q D p

q q

p p q D

* * * * *2 1 2

1 1 1 1 1 1

* * * * * * * *1 1 2 2

1 1 1 1 1 1 1 1

* * *3 3

1 1

, , )] ( ) (

) ( ) ( ) ( ) ( )

( ) ( )

K M M I R Ne e ek k k im mr mn

k m m i r n

K N M K K N M R

mk mn nk nk mk rkk n m k k n m r

K M

rk mrr k m

p p p q q q

q q q q q q

q q

*4 4

1

( ) 0R


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Proof:Addingtheaboveformulas(2),(4),(6),(12),and(14)tosimplyobtainformula(15).Ifweadd * *

im imp p tothefirstbracket,add * *mn mnp p tothesecondbracket,add * *

mk mkp p tothe

thirdbracket,add * *nk nkp p tothefourthbracket,add * *

rk rkp p tothefifthbracket,andadd* *mr mrp p tothesixthbracketinformula(15),itwillnotaffectthesolutiontoformula(15).

Therefore,thesolutionofformula(15)isthesumofformula(2),(4),(6),(12),and(14).Finally,thegradientprojectionalgorithmisusedtosolvethevariationalinequalityofthecontinuousconvexfunction.

4. NumericalExamples

Assume that the network consists of two suppliers, twomanufacturers, two retailers, twodemandmarkets and two recyclers. Assume that 1 =0.4, 2 =0.6, =0.8, p =2, =0.4, =0.6.Thepurchasingcostofsuppliersisgivenby:

2 2 2 2 22

1 1 1 1 1

( ) ( ) 0.5( )( )+2i im im im im imm m m m m

f q q q q q

i=1,2

Themanufacturers’productioncostofnewmaterialisgivenby:2 2 2 2

2

1 1 1 1

(0.4, ) 1.5[0.4( ) ] 2( )( ) 5m im im im imi i i i

f q q q q

m=1,2

Themanufacturers’productioncostofoldmaterialisgivenby:2 2 2

2

1 1 1

(0.6, ) 0.5[0.6( ) ] 0.6( )+2m mr mr mrr r r

f q q q

m=1,2

Theproductionstoragecostofretailersisgivenby:2 2

2

1 1

( ) 0.5( )n mn mnm m

C q q

n=1,2

Theproductacquisition,shippingandstoragecostsofrecyclersisgivenby:2 2 2 2

2

1 1 1 1

( ) ( ) 3( )( ) 2r mr mr mr mrk k k k

C q q q q

m,r=1,2

The transaction cost between suppliers and manufacturers, the transaction cost betweenmanufacturersandretailers,thetransactioncostbetweenretaileranddemandmarkets,thetransaction between demand markets and recyclers, the transaction cost betweenmanufacturersandrecyclersaregivenby:

2( ) 0.5im im im imC q q q 2( ) 0.5mn mn mnC q q 2( ) 0.5 0.5mk mk mk mkC q q q 2( ) 0.5 0.5rk rk rk rkC q q q 2( ) 0.5 0.5mr mr mr mrC q q q i,m,n,k,r=1,2

Thecostofmanufacturersoperatingonlinechannelsisgivenby:2 2

1 1

( )m mk mkk k

C q q

m=1,2

Negativeutilityfunctionofconsumerswillingtosellusedproductstorecyclersisgivenby:2 2 2

1 1 1

( ) 0.5( ) 5k rk rkr k r

q q

k=1,2

Theproductdemandfunctionoftraditionalchannelsisgivenby:

1 3 1 3( , , ) 1.5 2 ( ) 825(1 )e ek k k k k kD P p p p p

Theproductdemandfunctionofnetworkchannelsisgivenby:


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2 3 2 3( , , ) 0.5 0.8 ( ) 800e e ek k k k k kD p p p p p

4.1. EquilibriumResultsundertheInfluenceofTraditionalChannelCompetitionIntensityFactors

Undertheseperceivedproductioncostfunctionandeconomicfunction,usingMatlabR2016asoftwareforprogrammingandsimulationexperimentsandsettingthestepsizeoftheiterationto 0.01 and the calculation accuracy to 0.001. The test results of the equilibriummodel ofclosed‐loopsupplychainsuper‐networkaresummarizedinTable1.AndUmeansprofit.

Table1:Closed‐loopsupplychainsuper‐networkequilibriumresults

variable 1 0 1 0.02 1 0.04 1 0.06 1 0.08 1 0.1

( , 1,2)imq i m 5.5569 5.5902 5.6237 5.6574 5.6913 5.7253

( , 1,2)mnq m n 0.7980 0.9948 1.1927 1.3921 1.5928 1.7948

( , 1,2)mkq m k 2.5757 2.3961 2.2148 2.0328 1.8496 1.6653

( , 1,2)nkq n k 1.0225 1.2198 1.4180 1.6179 1.8191 2.0216

( , 1,2)rkq r k 3.0870 3.1013 3.1147 3.1291 3.1436 3.1583

( , 1,2)mrq m r 1.4963 1.5023 1.5075 1.5153 1.5195 1.5256

( 1,2)kp k 176.1935 178.1090 180.0372 181.9776 183.9307 185.8965

( 1, 2)ekp k 176.9254 177.4962 178.0716 178.6498 179.2318 179.8176

( 1,2)iU i 41.3732 51.5106 61.7598 72.1255 82.5965 93.1917

( 1,2)mU m 70.7453 75.8240 77.1626 80.7659 81.3095 85.9306

( 1,2)nU n 59.9759 61.7824 63.2392 64.4789 65.3799 65.9571

( 1,2)rU r 4.3410 7.6843 11.0433 12.5438 13.5813 14.4799

Table1showsthatwiththeincreaseofthetraditionalchannelcompetitionintensityfactor,thetransaction volume on traditional channels has increased, that is, the transaction volumebetweenmanufacturersandretailers, retailersanddemandmarketshas increased.And thetransaction volume of network channels has decreased, that is, the transaction volume ofmanufacturersanddemandmarketshasdecreased.Thisisbecauseasthecompetitionintensityfactoroftraditionalchannelsincreases,thecompetitivenessoftraditionalchannelsincreases,andtheproductssoldthroughtraditionalchannelsincrease.Incontrast,thecompetitiveness


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of network channels weakens. In addition, with the increase in the intensity of traditionalchannel competition factors, the profits of suppliers,manufacturers, retailers and recyclershaveincreased,whichindicatesthattheenhancedcompetitivenessoftraditionalchannelshaspositivefeedbackonalllayersofcompaniesintheclosed‐loopsupplychaineffect.

4.2. EquilibriumResultsundertheInfluenceofNetworkChannelCompetitionIntensityFactors

Sameas4.1, carryout simulationexperiments.The test resultsof theequilibriummodelofclosed‐loopsupplychainsuper‐networkaresummarizedinTable2.


variable 2 0 2 0.02 2 0.04 2 0.06 2 0.08 2 0.1

( , 1,2)imq i m 5.2797 5.2902 5.3086 5.4748 5.5996 5.7253

( , 1,2)mnq m n 3.5637 3.5688 3.5538 2.9538 2.3763 1.7948

( , 1,2)mkq m k 0 0 0 0.3803 1.0208 1.6653

( , 1,2)nkq n k 3.8873 3.8924 3.8672 3.1799 2.6028 2.0216

( , 1,2)rkq r k 3.3620 3.3660 3.3357 3.0567 3.1076 3.1583

( , 1,2)mrq m r 1.7114 1.7129 1.6953 1.4843 1.5051 1.5256

( 1,2)kp k 183.3393 183.6592 183.9979 184.6877 185.2900 185.8965

( 1, 2)ekp k 153.8462 159.4958 165.1535 170.2445 175.0152 179.8176

( 1,2)iU i 49.4546 59.7483 69.8965 76.7277 80.7160 93.1917

( 1,2)mU m 29.1842 44.3038 56.7022 68.8965 76.7945 85.9306

( 1,2)nU n 107.3242 93.7652 85.3935 76.4592 70.4580 65.9571

( 1,2)rU r 1.4328 3.7607 7.1035 12.3131 13.6072 14.4799

Table 2 shows that the competition intensity factor of network channels increases, thetransactionvolumeonnetworkchannels increases, that is, the transactionvolumebetweenmanufacturersandthedemandmarketincreases;whilethetransactionvolumeontraditionalchannelsdecreases,thatis,thevolumeoftransactionsbetweenmanufacturersandretailers,retailers and demand markets has decreased. Just as during special festivals such as theJingdong 618 Shopping Festival and the Taobao Double 11 Carnival Shopping Festival, the


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online channels will carry out large‐scale promotional activities to stimulate consumers'shoppingneeds.Consumersaremorewillingtobuycost‐effectiveequivalentproductsthantogotophysicalstorestobuysuchproducts.Inaddition,asthecompetitionintensityfactorforonlinechannelsincreases,theprofitsofsuppliers,manufacturersandrecyclersincrease,whilethe profits of retailers decrease. This shows that the increased competitiveness of onlinechannels has caused a certain impact on traditional channels, resulting in damage to theinterestsofretailersanddetrimenttotheoperationofretailers.

4.3. EquilibriumResultsundertheInfluenceofConsumerChannelPreferencesSameas4.1,carryoutsimulationexperiments.Assume 1 0.1 , 2 0.1 , =0.2~0.25 .Thetestresultsoftheequilibriummodelofclosed‐loopsupplychainsuper‐networkaresummarizedinTable3andFigure1toFigure4.


variable α=0.2 α=0.21 α=0.22 α=0.23 α=0.24 α=0.25

( , 1,2)imq i m 5.6621 5.5963 5.5301 5.5056 5.6289 5.7253

( , 1,2)mnq m n 3.7523 3.7207 3.6887 3.5404 2.6551 1.7948

( , 1,2)mkq m k 0 0 0 0 0.7573 1.6653

( , 1,2)nkq n k 4.0775 4.0446 4.0128 3.8194 2.8819 2.0216

( , 1,2)rkq r k 3.5142 3.4878 3.4625 3.2758 3.1202 3.1583

( , 1,2)mrq m r 1.7724 1.7618 1.7519 1.6323 1.5104 1.5256

( 1,2)kp k 194.9715 192.9672 190.9623 189.0534 187.5044 185.8965

( 1, 2)ekp k 153.0652 158.9107 164.7561 170.5961 175.3080 179.8176

AscanbeseenfromTable1above,withtheincreaseofconsumers’preferencefactorsforonlineshopping, the transaction volume of online channels has increased, while the transactionvolume of traditional channels has decreased. This is becausewith the development of theInternetandtheprogressofthetimes,moreandmoreconsumerschooseonlineshopping,andonlineshoppingcanbecompletedonlinewithouttheconsumergoingout,anddeliveryismoreconvenient. Therefore, some consumers Prefer online shopping. When the online channelpreference factor increases, the demand price of products sold through the online channelincreases,whilethedemandpriceofproductssoldthroughthetraditionalchanneldecreases.Thisshowsthatthepreferencefactorofonlinechannelsispositivelyrelatedtochangesinthedemandpriceofonlinechannelproducts,andnegativelyrelatedtochangesinthedemandpriceoftraditionalchannelproducts.


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Figure1:Impactofchannelpreferencefactorsonsupplierprofits

Figure2:Impactofchannelpreferencefactorsonmanufacturerprofits

AscanbeseenfromFigure1above,asthenetworkchannelpreferencefactorincreases,thesupplier'sprofitdecreasesfirstandthenincreases.Thisisbecausetheincreaseofthenetworkchannel preference factor causes the transaction volume between the supplier and themanufacturertodecreasefirstandthenincrease,andchangesintradingvolumeaffectprofits.InFigure2above,whentheonlinechannelpreferencefactor increases, themanufacturer ’sprofitdecreasesfirstandthenincreases,becauseinthe0.2‐0.23range,thetransactionvolumebetween the manufacturer and the retailer continues to decrease, while the transactionbetween themanufacturer and thedemandmarket If the quantity is 0, so theprofit of themanufacturer isalsodecreasing. In the rangeof0.23‐0.25,although the transactionvolumebetweenmanufacturersandretailerscontinuestodecrease,thetransactionvolumebetweenmanufacturersanddemandmarketshas increasedrapidly.Theprofitgainedfromproductssold through online channels makes up for the loss of profits from traditional channels.Eventually,manufacturers’profitshaveincreased.


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Figure3:Impactofchannelpreferencefactorsonretailerprofits

Figure4:Impactofchannelpreferencefactorsonrecyclerprofits

AscanbeseenfromFigure3,theretailer'sprofitdecreasesastheonlinechannelpreferencefactorincreases.Whentheonlinechannelpreferencefactorincreases,thetransactionvolumebetweenmanufacturersandretailers,retailersanddemandmarketscontinuetodecrease.Atthis time,moreandmoreconsumersuseonlinechannels for shoppingor someconsumers'preferences for online shopping are deepened, resulting in a decrease in retailer sales andthereforeadecreaseinretailerprofits.ItcanbeseenfromFigure4thattheprofitofrecyclersincreases with the increase of network channel preference factors, indicating a positivecorrelationbetweenthetwo.

5. Conclusion

Inthecasewherethemanufactureropensupthenetworkchannelandformsadualchannel,considering the two factorsof the consumer ’spreference for thenetwork channel and thecompetitionbetweenthetraditionalchannelandthenetworkchannel,thispaperestablishesaclosed‐loopsupplychainsuper‐networkmodel.Andthispaperstudiesthebehavioraldecision‐makingandoptimalgoalsofenterprisesineachlayeroftheclosed‐loopsupplychainnetwork.Finally,theequilibriumpointofthesystemnetworkisobtainedbyusingvariationalinequalitytheoryandgradientprojectionalgorithm.Throughnumericalexampleanalysis,thefollowingconclusionsareobtained:1. When the traditional channel competition intensity factor increases, changes in thetransactionvolumeoftraditionalchannelsintheclosed‐loopsupplychain,theprofitsofvariouslayersofcompanies,andthedemandandpriceofthetwosaleschannelsarepositivelyrelated


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to the competition intensity factor between channels; while the change in the transactionvolume of online channels competition intensity factor between channels is negativelycorrelated.2. When the competition intensity factor of network channels increases, the competitionintensity factor is positively related to changes in transaction volume, demand price, andcorporateprofitsrelatedtonetworkchannels,andnegativelyrelatedtotransactionvolume,demandprice,andcorporateprofitsrelatedtotraditionalchannels.3. As consumers’ preference for online channels increases, the profits of suppliers andmanufacturersfirstdecreaseandthenincrease,theprofitsofretailersdecrease,andtheprofitsofrecyclersincrease.Thisshowsthattheincreaseinthepreferenceofonlinechannelsisverydetrimental to theoperationof retailers.On theonehand, it is recommended that retailersstrengthen their own operational capabilities to attract consumers, such as providingpersonalizedservicesandimprovingthequalityofafter‐salesservices,sothatconsumersareloyal to using traditional channels for shopping; on the other hand, manufacturers shouldcoordinatethecompetitivenessof thetwochannels,andtrytoavoidthenegative impactofonlinechannelsontraditionalchannels.

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Research on Equilibrium Decision Closed loop Supply Chain