Research ArticleProduction Decision and Coordination Mechanism of SociallyResponsible Closed-Loop Supply Chain
Xiaofeng Long 12 Jiali Ge 3 Tong Shu 3 and Chunxia Liu 1
1Department of Business Administration Hunan University of Finance and Economics Changsha Hunan 410205 China2School of Economics and Trade Hunan University Changsha 410082 China3School of Business Administration Hunan University Changsha 410082 China
Correspondence should be addressed to Xiaofeng Long 47387681qqcom and Jiali Ge logjiali163com
Received 21 January 2020 Revised 20 April 2020 Accepted 29 April 2020 Published 23 May 2020
Guest Editor Baogui Xin
Copyright copy 2020 Xiaofeng Long et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Corporate social responsibility (CSR) has a significant impact on the operation of enterprises is study analyzes the productionand coordination decisions of closed-loop supply chain (CLSC) by establishing two assumptions of endogenous and exogenousCSRe results reveal that for ordinary consumers CSR is quantified as the parameter of consumer surplus which has an impacton the patent licensing fee revenue-sharing ratio and so on and which not only increases the sales quantity in CLSC but alsocreates more value for the manufacturer and the retailer Considering endogenous CSR the study found that the manufacturerrsquosCSR level and the manufacturerrsquos and the retailerrsquos profits both increase with the proportion of CSR-sensitive consumers In theendogenous model the manufacturer sets a higher wholesale price and lower patent licensing fee than in the exogenous modelPerfect coordination in the two models can be achieved by setting a revenue-sharing ratio related to wholesale price and patentlicensing fee In practice improving the social responsibility consciousness of consumers and raising enterprisesrsquo CSR level canachieve a win-win situation for revenues and social welfare
1 Introduction
In the new era increasing attention has been paid to en-vironmental sustainability driven by laws regulations en-vironmental pressure and social responsibility which hasbecome an important indicator of supply chainmanagementsuccess [1] Sustainable supply chain management focuseson environmental issues such as closed-loop supply chain(CLSC) and corporate social responsibility (CSR)
CSR is a type of intrinsic motivation [2] which refers toan enterprise not only creating profits for shareholders butalso emphasizing contributions to the environment con-sumers and society Consumers with CSR awareness canobtain utility from the environmental attributes of productssuch as remanufactured products which is an importantmarket driver for environmental sustainability in supplychains According to Cotte and Trudel [3] a total of 70 ofconsumers are willing to pay higher prices for products withldquoresponsiblerdquo attributes Most consumers tend to buy
products that are socially responsible and environmentallyfriendly [4] is depends in part on the CSR level of themanufacturer
Enterprisesrsquo recycling and reuse process is also a meansof strengthening their level of CSR Enterprises can achievethe improvement and coordination of supply chains throughjoint CSR investments [5ndash7] e manufacturerrsquos CSR be-havior is beneficial to increase channel profit and improvethe recovery rate [8] and CSR investment is a feasiblestrategy to enhance enterprisesrsquo sales power [9]
Based on theoretical research this study constructsCLSC production and collaboration optimization modelsconsidering CSR and examines the following questions (1)how does endogenous and exogenous CSR affect pricingrevenue of CLSC members (2) what are the impact andcoordination functions of patent licensing fee on the deci-sion of CLSC (3) what is the influencing mechanism ofdifferent types of consumers on CSR and the profit of themanufacturer and the retailer
HindawiComplexityVolume 2020 Article ID 9095215 10 pageshttpsdoiorg10115520209095215
emain contributions of this study are as follows (1) itbrings CSR behaviors into the classic framework of CLSCmanagement examines its impact on the operation of CLSCand clarifies the value of CSR (2) it considers the issue ofpatent licensing in CLSC and reveals the regulatory role ofpatent licensing and (3) it sets a revenue-sharing ratio re-lated to price and patent licensing fee in the two models tocoordinate the profit of the manufacturer and the retailer
e remainder of this paper is organized as follows therelated research is reviewed in Section 2 Section 3 outlinesthe model setting Section 4 investigates the decision andcoordination in the CLSC of exogenous CSR when there areonly ordinary consumers in the market Section 5 examinesthe decision and coordination in the CLSC of endogenousCSR when there are CSR-sensitive consumers and ordinaryconsumers in the market and concluding remarks arepresented in Section 6
2 Literature Review
ere are three streams of research related with this researchCLSC considering patent licensing CSR activities in supplychain management and supply chain coordination
e first stream mainly focuses on CLSC consideringpatent licensing which can be a strategy when there aremultiple remanufacturing subjects in CLSC Cruz [10]studied the impact of CSR in supply chain managementusing a multicriteria decision-making approach Zhao et al[11] investigated the best patent licensing contracts withnetwork effects and investigated the welfare impact bysetting a Stackelberg model Huang and Wang [12] exam-ined the CLSC model for product recycling and hybridremanufacturing under patent licensing and discussed theimpact of remanufacturing capabilities on supply chainmembers and environmental sustainability Hong et al [13]studied the quantity and collective decisions in the CLSCusing two licensing models fixed fees and unit royalty Haoet al [14] discussed the best game strategies for both partiesunder three different decision structures two competitivemodels (competition with and without remanufacturingpatent licensing) and cooperation models Huang andWang[12 15] studied a CLSC with technology licenses Jin et al[16] considered the two-period game model designed theoptimal patent licensing contract and production out-sourcing strategy and analyzed the value of CSR
e second stream is CSR activities in supply chainmanagement Ni and Li [17] investigated how enterprisesand suppliers interact in CSR behaviors and the impact ofexternal parameters on this interaction Panda [18] foundthat revenue-sharing contracts can maximize CSR retailersrsquowelfare Modak et al [19] analyzed the dual-channel supplychain of CSR and studied its impact on the successful op-eration of the dual channel Panda et al [20] discussed theissue of coordination and profit distribution in the supplychain composed of CSR manufacturer and retailer Pandaand Modak [21] examined the channel coordination andbenefit distribution between CSR manufacturer and retailerthrough subgame perfect equilibrium and negotiationsWhite et al [22] summarized the studies on CSR through
quantitative and qualitative models Modak et al [23]studied CSR practice in a two-echelon CLSC
e third stream is supply chain coordination Panda et al[24] resolved channel conflicts and distributed surplus profitsamong channel members by Nash bargaining contracts Zhangand Ren [25] studied CLSC coordination strategy for the re-manufacture of patented products Panda et al [8] discussedthe channel coordination issue of CLSC by setting a revenue-sharing contract Seyedhosseini et al [26] proposed a two-parttariff contract to provide a win-win situation for all supplychain members Hosseini-Motlagh [27 28] studied CLSCcoordination of CSR considering different demand conditionsLi and Gong [29] constructed a CLSC model and designed acost-sharing contract to achieve supply chain coordination
e related literature mainly examines the impact of CSRon supply chain performance decisions and coordinationese studies reveal that environmental improvement can beobtained through supply chain management e currentstudy focuses on the production decision and coordinationmechanism of CLSC with patent licensing from the per-spective of CSR In addition this study considers twomodelsof endogenous and exogenous CSR and types of customersin the market to better grasp the value of CSR Our studydiffers from the existing literature in that enterprisesrsquo CSRand the social responsibility awareness of consumers areinvolved in the model e related theoretical and numericalanalysis reveal how the endogenous and exogenous CSRinfluence production decisions and coordination
3 Model Setting
We establish a CLSC composed of a manufacturer and a re-tailer in which the manufacturer sells new products throughthe retailer and the retailer recycles used products fromconsumers reselling them to consumers after remanufacturingere are two types of consumers in the market CSR-sensitiveconsumers (C-type consumers) which account for a ratio of ρto market capacity and ordinary consumers (N-type con-sumers) which account for a ratio of 1 minus ρ to market capacitye characteristic of C-type consumers is that they can obtainadditional utilities by choosing products produced by a CSRmanufacturer e utility C-type consumers can obtain frombuying a unit of CSR-type products is UC v minus pc + KymN-type consumers are only sensitive to product price and theutility they can obtain from buying a unit of ordinary productsis UN v minus pn Conditions for C-type consumers purchasingCSR products is UC gt 0 andUC geUN Conditions for N-typeconsumers purchasing ordinary products is UN gt 0and UN gtUC in which v sim U[0 1] rough calculation wefind the following
(1) When v minus pc + Kym ge v minus pn the market demand forCSR-type products is qc aρ(1 minus pc + Kym) and themarket demand for ordinary products isqn a(1 minus ρ)(1 minus pn)
(2) When v minus pc + Kym lt v minus pn consumers will notbuy CSR products and all consumers will buy or-dinary products At this time the market demand forCSR-type products is qc 0 and the market demand
2 Complexity
for ordinary products is qn a(1 minus pn) Model pa-rameter settings are presented in Table 1
4 Production Decision and CoordinationMechanismofCLSCBasedonExogenousCSR
is section does not distinguish between consumer groupsmeaning that consumers do not know whether the enterprisehas social responsibility In addition this section explores theimpact of CSR on patent licensing recycling rates and profitse CSR manufacturer will encourage the retailer to recycleproduce or sell more remanufactured products while in-creasing the revenues of all parties [8] We use θ isin [0 1] torepresent the CSR factor of the manufacturer θ 0 is therevenue maximization of the manufacturer and θ 1 is thewelfare maximization of the manufacturer
In the manufacturerrsquos revenue function the manufac-turerrsquos CSR is quantified as the proportion of consumersurplus (CS) which refers to the difference between themaximum price a consumer is willing to pay and the actualtotal price to pay When the demand function is thelinear function D a(1 minus p) CS is CS 1113938
a
(aminus D)a (aminus
ap)dp (D22a) [8] Some of the assumptions used hereinare as follows
Assumption 1 the manufacturer is the leader of theStackelberg gameAssumption 2 remanufactured products are used asproducts recycled from consumers by the retailer Toensure the remanufacturing activities of the retailer thesaving value of remanufactured products is Δgt 0Assumption 3 remanufactured products have no dif-ference in quality and use function compared with newproducts produced by the manufacturer consumersvalue both products in the same way and they are soldat the same price in the market
e recycling quantity of used products increases withthe increase in recovery price [30] the recycling quantity ofused products G is a function of the recovery price r G α + βlowast r where α represents the quantity of usedproducts that consumers voluntarily return and β indicatesconsumersrsquo degree of sensitivity to recovery prices
41 Analysis of Decentralized Decision Model e manu-facturer authorizes the retailer to remanufacture charging acertain patent licensing fee In addition the manufacturermay not recycle or remanufacture products for the sake ofrecovery costs or branding e retailer recycles usedproducts from remanufacturing activities and sells new andremanufactured products together to consumers afterobtaining a patent technical license
e decision turn of the Stackelberg game is as follows(1) as the game leader the manufacturer first sets thewholesale price w and patent licensing fee f (2) afterobtaining the manufacturerrsquos patent licensing the retailerdetermines the sale price of the product p and recovery pricer When CSR is not considered the manufacturerrsquos revenuefunction is
maxw f
πM w minus cn( 1113857(a minus alowastp minus α minus βlowast r) + flowast(α + βlowast r)
(1)
and the retailerrsquos revenue function is
maxp r
πR (p minus w)(a minus alowastp minus α minus βlowast r)
+ p minus cn + Δ( 1113857(α + βlowast r) minus (f + r)(α + βlowast r)
(2)
When CSR is considered the manufacturerrsquos revenuefunction is
maxwf
vM w minus cn( 1113857(a minus alowastp minus α minus βlowast r)
+ flowast(α + βlowast r) + θ lowastD2
2a
(3)
Proposition 1 can be obtained by the backward induc-tion solution
Proposition 1 e revenue functions of the manufacturerand the retailer under decentralized decisions are nonconvexe optimal wholesale price can be obtained as followswlowast ((2 minus θ + 2cn)(4 minus θ)) the optimal retail price isplowast ((3 minus θ + cn)(4 minus θ)) the optimal recovery price isrlowast ((βΔ minus 3α)4β) and the optimal patent licensing feeis flowast ((4β + 4α minus 2βθ minus αθ minus 4βcn + 4βΔ + 2βcnθ minus βθΔ)(2β(4 minus θ)))
By Proposition 1 the maximum revenue of the manu-facturer considering CSR is
vlowastM
aα2 + 2aαβΔ minus 4βα2
8+β2Δ2
aβminus a
2βcn +ac2n
2(4 minus θ)
(4)
e maximum revenue of the retailer is
π lowastR (βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2 (5)
e total revenue of the supply chain is
vlowast
(βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2+
aα2 + 2αaβΔ minus 4βα2
8
+β2Δ2
aβminus βa
2cn +
ac2n2(4 minus θ)
(6)
e CS is
CS a 1 minus cn( 1113857
2
2(4 minus θ)2 (7)
Conclusion 1 (1) As the cost of new products increases bothwholesale and retail prices increase the optimal patent li-censing fee charged by the manufacturer decreases therevenue of the manufacturer and the retailer decreases andthe revenue of the supply chain decreases (2) As the
Complexity 3
remanufacturing saving cost increases the recovery priceand recycling quantity of used products both increase thepatent licensing fee charged increases and the profits of themanufacturer the retailer and the supply chain all increase(3) When the manufacturer shows stronger CSR thewholesale and the retail prices of products are lower emanufacturerrsquos revenue is higher the patent licensing fee islower the retailerrsquos revenue increases and CS increases
42 Analysis of Centralized Decision Model In the central-ized decision model the revenue function of the entiresupply chain is
maxpcrc
πc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α + βlowast rc( 1113857 (8)
When the manufacturerrsquo CSR is considered the revenuefunction of the entire supply chain is
maxpcrc
vc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α+βlowastrc( 1113857 +θlowastD2
2a
(9)
Take the partial derivatives of formula (8) with respect topc and rc (zvczpc) 0 (zvczrc) 0 and obtain the bestsolution plowastc and vlowastc e corresponding Hessian matrix is
Hc
z2vc
zp2c
z2vc
zpczrc
z2vc
zrczpc
z2vc
zr2c
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
minus 2β minus 2β
0 aθ minus 2a
⎛⎝ ⎞⎠ (10)
When Hessian matrix Hc gt 0 2 minus θgt 0 that is thecentralized revenue function is nonconvex we can obtainProposition 2
Proposition 2 e revenue function of the entire supplychain under centralized decisions with respect to pc and rc isnonconvex and the optimal solution (plowastc rlowastc ) is(((1 minus θ + cn)(2 minus θ)) ((βΔ minus α)2β)) e revenue of theentire supply chain under centralized decisions is
vlowastc
2aβ + 2α2 + 2aβc2n + 2β2Δ2 minus βα2 minus θβ2Δ2 minus 4βcn + 4αβΔ minus 2αβΔθ4β(2 minus θ)
(11)
43 Revenue-Sharing Coordination Mechanism Tradition-ally the manufacturer and the retailer act independently andmaximize their own respective revenues However an ef-fective supply chain network requires a cooperative rela-tionship erefore a coordination mechanism is needed tocoordinate the manufacturer and the retailer Under arevenue-sharing (RS) contract the manufacturer offers awholesale price and requires a small portion of the revenuefrom the retailer e RS contract sets the revenue-sharingparameter as λ isin (0 1) and the manufacturer receives (1 minus
λ) of the revenue
Proposition 3 Under the RS contract the revenue functionexpressions of the manufacturer and the retailer are re-spectively as follows
πM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)
vM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)θ(a minus ap)2
2a
(12)
When the RS contract the manufacturer provided to theretailer is
Table 1 Model parameter settings
Parameter Representsp Retail price per unit of product set by the retailerw Unit wholesale price given by the manufacturerr Recovery price for used productscn Production cost of new productsΔ Production cost saved by the retailer from remanufactured productsK Impact factors of social responsibility level on consumersrsquo willingness to payf Patent licensing fee for manufacturer-licensed remanufacturingym Manufacturerrsquos level of CSRρ Ratio of CSR-sensitive consumersa Market capacityπj
i e profit function of the enterprise i parameter i isin M R where M represents the manufacturer and R represents the retailer
4 Complexity
wco
fco
( 1113857 2cn minus θ2 minus θ
λ2cn minus θ2 minus θ
λ minus cn1113888 1113889 (13)the RS proportion λ should meet λ1 lt λlt λ2 in which when
λ1 (2 minus θ)2(16 a minus acn( 1113857
2minus 3a(4 minus θ)2(α + βΔ)2
16β(4 minus θ)2 a minus acn( 11138572
λ2 minus1 minus cn( 1113857
2
2(θ minus 2)+4β 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a minus acn( 11138572
(14)
the CLSC can be coordinated by the RS contract (seeAppendix A)
Proposition 4 Under the RS contract it satisfies the fol-lowing relationships pco ltplowast wco ltwlowast fco ltflowast rco gt rlowastπcoR gt π lowastR and vcoM gt vlowastM
Proposition 4shows that when an RS contract is adoptedthe manufacturer pays more attention to CSR and reduces itswholesale price and the product patent licensing fee thus in-creasing the sales volume of products Product sales are directlyproportional to the CSR level of the manufacturer In additionthe recycling intensity of the retailer increases and in responseto the manufacturerrsquos strategies the retailer reduces their saleprices to encourage customers to buy more products and putsmore efforts into collecting used products from customers emanufacturerrsquos CSR therefore influences the retailerrsquos decisionsand further influences their decisions in the reverse supply chainthrough influencing prices In centralized decisions when CSRincreases the manufacturer reduces the wholesale price ofproducts and the sale price under the centralized decision islower than that under the decentralized decision As a resultthere is a higher demand for products of centralized decisionsObviously the retailer will make more efforts to collect usedproducts under centralization e manufacturer the retailerand the entire supply chain have higher revenues under thecentralized model than that under decentralized model thusthe entire CLSC achieves coordination
At the same time consumers can buy new products at alower price and sell used products at a higher price whichgreatly improves consumersrsquo utilities and achieves a win-winsituation for enterprises and consumers
44NumericalExamplesandSensitivityAnalysis Numericalcalculations are made based on the above conclusionsParameter values refer to assumptions of Bakal and Akcali[30] the market demand function of products isD(p) 100(1 minus p) the supply function of old products isG(r) 08 + 10r and the production cost of new products isCn 05 e decision results of different CLSC systems areillustrated in Tables 2 and 3
As can be seen from Table 2 under decentralized decisionswith the increasing awareness of the manufacturerrsquos CSR therevenues of both the manufacturer and the retailer increase themanufacturer reduces the patent licensing fee and lowers the
wholesale prices so that the retailer sets retail prices lower andthe consumer purchase quantity increases With the increase inremanufacturing saving cost the retailerrsquos recycling prices risee manufacturer charges more patent licensing fees and boththe manufacturerrsquos and the retailerrsquos revenues increase FromTable 3 as the RS proportion increases the manufacturerrsquoswholesale price increases the patent licensing fee decreases theretailerrsquos revenue increases and the manufacturerrsquos revenuedecreases
Sensitivity analysis is conducted on the key parameters(Cn and θ) to examine the proposed modelsrsquo performance eeffects of Cn on the w p andf are shown in Figure 1 Byincreasing Cn both wholesale prices w and retail prices p
increase and the optimal patent licensing fee f decreasesWhen the production cost of new products Cn is higher themanufacturer reduces the patent licensing fee to encourage theretailer to produce and recycle more used products and in-crease the revenue Figure 2 illustrates the effects of θ on thew p andf by increasing θ and the decreases in wholesaleprices w retail prices p and patent licensing fee f When themanufacturerrsquos CSR θ is stronger the price of products is lowere sales volume is higher and the profits of both the man-ufacturer and the retailer increase e manufacturer will re-duce the patent licensing fee encouraging the retailer to recycleand remanufacture erefore patent licensing fee is an im-portant adjustment tool for the manufacturer
From Figure 3 the entire CLSC profit is improved under RScontracts the profit of the manufacturer and the retailer isimproved compared to the decentralized model (πcoR gt π lowastR andvcoM gt vlowastM) and the compensation-based whole price mechanismcanmotivate the retailer to take part in the centralized decisions
5 Production Decision and CoordinationMechanism of CLSC of Endogenous CSR
is section divides consumers into CSR-sensitive and or-dinary types constructs the CLSC model considering en-dogenous CSR and mainly examines the impact of theproportion of CSR-sensitive consumers on CSR level theprofits of CLSC members and RS contracts e specificparameter settings are shown in Table 1
51 Analysis of Decentralized Decision Model When CSR isendogenous there are CSR-sensitive consumers and
Complexity 5
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
emain contributions of this study are as follows (1) itbrings CSR behaviors into the classic framework of CLSCmanagement examines its impact on the operation of CLSCand clarifies the value of CSR (2) it considers the issue ofpatent licensing in CLSC and reveals the regulatory role ofpatent licensing and (3) it sets a revenue-sharing ratio re-lated to price and patent licensing fee in the two models tocoordinate the profit of the manufacturer and the retailer
e remainder of this paper is organized as follows therelated research is reviewed in Section 2 Section 3 outlinesthe model setting Section 4 investigates the decision andcoordination in the CLSC of exogenous CSR when there areonly ordinary consumers in the market Section 5 examinesthe decision and coordination in the CLSC of endogenousCSR when there are CSR-sensitive consumers and ordinaryconsumers in the market and concluding remarks arepresented in Section 6
2 Literature Review
ere are three streams of research related with this researchCLSC considering patent licensing CSR activities in supplychain management and supply chain coordination
e first stream mainly focuses on CLSC consideringpatent licensing which can be a strategy when there aremultiple remanufacturing subjects in CLSC Cruz [10]studied the impact of CSR in supply chain managementusing a multicriteria decision-making approach Zhao et al[11] investigated the best patent licensing contracts withnetwork effects and investigated the welfare impact bysetting a Stackelberg model Huang and Wang [12] exam-ined the CLSC model for product recycling and hybridremanufacturing under patent licensing and discussed theimpact of remanufacturing capabilities on supply chainmembers and environmental sustainability Hong et al [13]studied the quantity and collective decisions in the CLSCusing two licensing models fixed fees and unit royalty Haoet al [14] discussed the best game strategies for both partiesunder three different decision structures two competitivemodels (competition with and without remanufacturingpatent licensing) and cooperation models Huang andWang[12 15] studied a CLSC with technology licenses Jin et al[16] considered the two-period game model designed theoptimal patent licensing contract and production out-sourcing strategy and analyzed the value of CSR
e second stream is CSR activities in supply chainmanagement Ni and Li [17] investigated how enterprisesand suppliers interact in CSR behaviors and the impact ofexternal parameters on this interaction Panda [18] foundthat revenue-sharing contracts can maximize CSR retailersrsquowelfare Modak et al [19] analyzed the dual-channel supplychain of CSR and studied its impact on the successful op-eration of the dual channel Panda et al [20] discussed theissue of coordination and profit distribution in the supplychain composed of CSR manufacturer and retailer Pandaand Modak [21] examined the channel coordination andbenefit distribution between CSR manufacturer and retailerthrough subgame perfect equilibrium and negotiationsWhite et al [22] summarized the studies on CSR through
quantitative and qualitative models Modak et al [23]studied CSR practice in a two-echelon CLSC
e third stream is supply chain coordination Panda et al[24] resolved channel conflicts and distributed surplus profitsamong channel members by Nash bargaining contracts Zhangand Ren [25] studied CLSC coordination strategy for the re-manufacture of patented products Panda et al [8] discussedthe channel coordination issue of CLSC by setting a revenue-sharing contract Seyedhosseini et al [26] proposed a two-parttariff contract to provide a win-win situation for all supplychain members Hosseini-Motlagh [27 28] studied CLSCcoordination of CSR considering different demand conditionsLi and Gong [29] constructed a CLSC model and designed acost-sharing contract to achieve supply chain coordination
e related literature mainly examines the impact of CSRon supply chain performance decisions and coordinationese studies reveal that environmental improvement can beobtained through supply chain management e currentstudy focuses on the production decision and coordinationmechanism of CLSC with patent licensing from the per-spective of CSR In addition this study considers twomodelsof endogenous and exogenous CSR and types of customersin the market to better grasp the value of CSR Our studydiffers from the existing literature in that enterprisesrsquo CSRand the social responsibility awareness of consumers areinvolved in the model e related theoretical and numericalanalysis reveal how the endogenous and exogenous CSRinfluence production decisions and coordination
3 Model Setting
We establish a CLSC composed of a manufacturer and a re-tailer in which the manufacturer sells new products throughthe retailer and the retailer recycles used products fromconsumers reselling them to consumers after remanufacturingere are two types of consumers in the market CSR-sensitiveconsumers (C-type consumers) which account for a ratio of ρto market capacity and ordinary consumers (N-type con-sumers) which account for a ratio of 1 minus ρ to market capacitye characteristic of C-type consumers is that they can obtainadditional utilities by choosing products produced by a CSRmanufacturer e utility C-type consumers can obtain frombuying a unit of CSR-type products is UC v minus pc + KymN-type consumers are only sensitive to product price and theutility they can obtain from buying a unit of ordinary productsis UN v minus pn Conditions for C-type consumers purchasingCSR products is UC gt 0 andUC geUN Conditions for N-typeconsumers purchasing ordinary products is UN gt 0and UN gtUC in which v sim U[0 1] rough calculation wefind the following
(1) When v minus pc + Kym ge v minus pn the market demand forCSR-type products is qc aρ(1 minus pc + Kym) and themarket demand for ordinary products isqn a(1 minus ρ)(1 minus pn)
(2) When v minus pc + Kym lt v minus pn consumers will notbuy CSR products and all consumers will buy or-dinary products At this time the market demand forCSR-type products is qc 0 and the market demand
2 Complexity
for ordinary products is qn a(1 minus pn) Model pa-rameter settings are presented in Table 1
4 Production Decision and CoordinationMechanismofCLSCBasedonExogenousCSR
is section does not distinguish between consumer groupsmeaning that consumers do not know whether the enterprisehas social responsibility In addition this section explores theimpact of CSR on patent licensing recycling rates and profitse CSR manufacturer will encourage the retailer to recycleproduce or sell more remanufactured products while in-creasing the revenues of all parties [8] We use θ isin [0 1] torepresent the CSR factor of the manufacturer θ 0 is therevenue maximization of the manufacturer and θ 1 is thewelfare maximization of the manufacturer
In the manufacturerrsquos revenue function the manufac-turerrsquos CSR is quantified as the proportion of consumersurplus (CS) which refers to the difference between themaximum price a consumer is willing to pay and the actualtotal price to pay When the demand function is thelinear function D a(1 minus p) CS is CS 1113938
a
(aminus D)a (aminus
ap)dp (D22a) [8] Some of the assumptions used hereinare as follows
Assumption 1 the manufacturer is the leader of theStackelberg gameAssumption 2 remanufactured products are used asproducts recycled from consumers by the retailer Toensure the remanufacturing activities of the retailer thesaving value of remanufactured products is Δgt 0Assumption 3 remanufactured products have no dif-ference in quality and use function compared with newproducts produced by the manufacturer consumersvalue both products in the same way and they are soldat the same price in the market
e recycling quantity of used products increases withthe increase in recovery price [30] the recycling quantity ofused products G is a function of the recovery price r G α + βlowast r where α represents the quantity of usedproducts that consumers voluntarily return and β indicatesconsumersrsquo degree of sensitivity to recovery prices
41 Analysis of Decentralized Decision Model e manu-facturer authorizes the retailer to remanufacture charging acertain patent licensing fee In addition the manufacturermay not recycle or remanufacture products for the sake ofrecovery costs or branding e retailer recycles usedproducts from remanufacturing activities and sells new andremanufactured products together to consumers afterobtaining a patent technical license
e decision turn of the Stackelberg game is as follows(1) as the game leader the manufacturer first sets thewholesale price w and patent licensing fee f (2) afterobtaining the manufacturerrsquos patent licensing the retailerdetermines the sale price of the product p and recovery pricer When CSR is not considered the manufacturerrsquos revenuefunction is
maxw f
πM w minus cn( 1113857(a minus alowastp minus α minus βlowast r) + flowast(α + βlowast r)
(1)
and the retailerrsquos revenue function is
maxp r
πR (p minus w)(a minus alowastp minus α minus βlowast r)
+ p minus cn + Δ( 1113857(α + βlowast r) minus (f + r)(α + βlowast r)
(2)
When CSR is considered the manufacturerrsquos revenuefunction is
maxwf
vM w minus cn( 1113857(a minus alowastp minus α minus βlowast r)
+ flowast(α + βlowast r) + θ lowastD2
2a
(3)
Proposition 1 can be obtained by the backward induc-tion solution
Proposition 1 e revenue functions of the manufacturerand the retailer under decentralized decisions are nonconvexe optimal wholesale price can be obtained as followswlowast ((2 minus θ + 2cn)(4 minus θ)) the optimal retail price isplowast ((3 minus θ + cn)(4 minus θ)) the optimal recovery price isrlowast ((βΔ minus 3α)4β) and the optimal patent licensing feeis flowast ((4β + 4α minus 2βθ minus αθ minus 4βcn + 4βΔ + 2βcnθ minus βθΔ)(2β(4 minus θ)))
By Proposition 1 the maximum revenue of the manu-facturer considering CSR is
vlowastM
aα2 + 2aαβΔ minus 4βα2
8+β2Δ2
aβminus a
2βcn +ac2n
2(4 minus θ)
(4)
e maximum revenue of the retailer is
π lowastR (βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2 (5)
e total revenue of the supply chain is
vlowast
(βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2+
aα2 + 2αaβΔ minus 4βα2
8
+β2Δ2
aβminus βa
2cn +
ac2n2(4 minus θ)
(6)
e CS is
CS a 1 minus cn( 1113857
2
2(4 minus θ)2 (7)
Conclusion 1 (1) As the cost of new products increases bothwholesale and retail prices increase the optimal patent li-censing fee charged by the manufacturer decreases therevenue of the manufacturer and the retailer decreases andthe revenue of the supply chain decreases (2) As the
Complexity 3
remanufacturing saving cost increases the recovery priceand recycling quantity of used products both increase thepatent licensing fee charged increases and the profits of themanufacturer the retailer and the supply chain all increase(3) When the manufacturer shows stronger CSR thewholesale and the retail prices of products are lower emanufacturerrsquos revenue is higher the patent licensing fee islower the retailerrsquos revenue increases and CS increases
42 Analysis of Centralized Decision Model In the central-ized decision model the revenue function of the entiresupply chain is
maxpcrc
πc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α + βlowast rc( 1113857 (8)
When the manufacturerrsquo CSR is considered the revenuefunction of the entire supply chain is
maxpcrc
vc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α+βlowastrc( 1113857 +θlowastD2
2a
(9)
Take the partial derivatives of formula (8) with respect topc and rc (zvczpc) 0 (zvczrc) 0 and obtain the bestsolution plowastc and vlowastc e corresponding Hessian matrix is
Hc
z2vc
zp2c
z2vc
zpczrc
z2vc
zrczpc
z2vc
zr2c
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
minus 2β minus 2β
0 aθ minus 2a
⎛⎝ ⎞⎠ (10)
When Hessian matrix Hc gt 0 2 minus θgt 0 that is thecentralized revenue function is nonconvex we can obtainProposition 2
Proposition 2 e revenue function of the entire supplychain under centralized decisions with respect to pc and rc isnonconvex and the optimal solution (plowastc rlowastc ) is(((1 minus θ + cn)(2 minus θ)) ((βΔ minus α)2β)) e revenue of theentire supply chain under centralized decisions is
vlowastc
2aβ + 2α2 + 2aβc2n + 2β2Δ2 minus βα2 minus θβ2Δ2 minus 4βcn + 4αβΔ minus 2αβΔθ4β(2 minus θ)
(11)
43 Revenue-Sharing Coordination Mechanism Tradition-ally the manufacturer and the retailer act independently andmaximize their own respective revenues However an ef-fective supply chain network requires a cooperative rela-tionship erefore a coordination mechanism is needed tocoordinate the manufacturer and the retailer Under arevenue-sharing (RS) contract the manufacturer offers awholesale price and requires a small portion of the revenuefrom the retailer e RS contract sets the revenue-sharingparameter as λ isin (0 1) and the manufacturer receives (1 minus
λ) of the revenue
Proposition 3 Under the RS contract the revenue functionexpressions of the manufacturer and the retailer are re-spectively as follows
πM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)
vM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)θ(a minus ap)2
2a
(12)
When the RS contract the manufacturer provided to theretailer is
Table 1 Model parameter settings
Parameter Representsp Retail price per unit of product set by the retailerw Unit wholesale price given by the manufacturerr Recovery price for used productscn Production cost of new productsΔ Production cost saved by the retailer from remanufactured productsK Impact factors of social responsibility level on consumersrsquo willingness to payf Patent licensing fee for manufacturer-licensed remanufacturingym Manufacturerrsquos level of CSRρ Ratio of CSR-sensitive consumersa Market capacityπj
i e profit function of the enterprise i parameter i isin M R where M represents the manufacturer and R represents the retailer
4 Complexity
wco
fco
( 1113857 2cn minus θ2 minus θ
λ2cn minus θ2 minus θ
λ minus cn1113888 1113889 (13)the RS proportion λ should meet λ1 lt λlt λ2 in which when
λ1 (2 minus θ)2(16 a minus acn( 1113857
2minus 3a(4 minus θ)2(α + βΔ)2
16β(4 minus θ)2 a minus acn( 11138572
λ2 minus1 minus cn( 1113857
2
2(θ minus 2)+4β 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a minus acn( 11138572
(14)
the CLSC can be coordinated by the RS contract (seeAppendix A)
Proposition 4 Under the RS contract it satisfies the fol-lowing relationships pco ltplowast wco ltwlowast fco ltflowast rco gt rlowastπcoR gt π lowastR and vcoM gt vlowastM
Proposition 4shows that when an RS contract is adoptedthe manufacturer pays more attention to CSR and reduces itswholesale price and the product patent licensing fee thus in-creasing the sales volume of products Product sales are directlyproportional to the CSR level of the manufacturer In additionthe recycling intensity of the retailer increases and in responseto the manufacturerrsquos strategies the retailer reduces their saleprices to encourage customers to buy more products and putsmore efforts into collecting used products from customers emanufacturerrsquos CSR therefore influences the retailerrsquos decisionsand further influences their decisions in the reverse supply chainthrough influencing prices In centralized decisions when CSRincreases the manufacturer reduces the wholesale price ofproducts and the sale price under the centralized decision islower than that under the decentralized decision As a resultthere is a higher demand for products of centralized decisionsObviously the retailer will make more efforts to collect usedproducts under centralization e manufacturer the retailerand the entire supply chain have higher revenues under thecentralized model than that under decentralized model thusthe entire CLSC achieves coordination
At the same time consumers can buy new products at alower price and sell used products at a higher price whichgreatly improves consumersrsquo utilities and achieves a win-winsituation for enterprises and consumers
44NumericalExamplesandSensitivityAnalysis Numericalcalculations are made based on the above conclusionsParameter values refer to assumptions of Bakal and Akcali[30] the market demand function of products isD(p) 100(1 minus p) the supply function of old products isG(r) 08 + 10r and the production cost of new products isCn 05 e decision results of different CLSC systems areillustrated in Tables 2 and 3
As can be seen from Table 2 under decentralized decisionswith the increasing awareness of the manufacturerrsquos CSR therevenues of both the manufacturer and the retailer increase themanufacturer reduces the patent licensing fee and lowers the
wholesale prices so that the retailer sets retail prices lower andthe consumer purchase quantity increases With the increase inremanufacturing saving cost the retailerrsquos recycling prices risee manufacturer charges more patent licensing fees and boththe manufacturerrsquos and the retailerrsquos revenues increase FromTable 3 as the RS proportion increases the manufacturerrsquoswholesale price increases the patent licensing fee decreases theretailerrsquos revenue increases and the manufacturerrsquos revenuedecreases
Sensitivity analysis is conducted on the key parameters(Cn and θ) to examine the proposed modelsrsquo performance eeffects of Cn on the w p andf are shown in Figure 1 Byincreasing Cn both wholesale prices w and retail prices p
increase and the optimal patent licensing fee f decreasesWhen the production cost of new products Cn is higher themanufacturer reduces the patent licensing fee to encourage theretailer to produce and recycle more used products and in-crease the revenue Figure 2 illustrates the effects of θ on thew p andf by increasing θ and the decreases in wholesaleprices w retail prices p and patent licensing fee f When themanufacturerrsquos CSR θ is stronger the price of products is lowere sales volume is higher and the profits of both the man-ufacturer and the retailer increase e manufacturer will re-duce the patent licensing fee encouraging the retailer to recycleand remanufacture erefore patent licensing fee is an im-portant adjustment tool for the manufacturer
From Figure 3 the entire CLSC profit is improved under RScontracts the profit of the manufacturer and the retailer isimproved compared to the decentralized model (πcoR gt π lowastR andvcoM gt vlowastM) and the compensation-based whole price mechanismcanmotivate the retailer to take part in the centralized decisions
5 Production Decision and CoordinationMechanism of CLSC of Endogenous CSR
is section divides consumers into CSR-sensitive and or-dinary types constructs the CLSC model considering en-dogenous CSR and mainly examines the impact of theproportion of CSR-sensitive consumers on CSR level theprofits of CLSC members and RS contracts e specificparameter settings are shown in Table 1
51 Analysis of Decentralized Decision Model When CSR isendogenous there are CSR-sensitive consumers and
Complexity 5
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
for ordinary products is qn a(1 minus pn) Model pa-rameter settings are presented in Table 1
4 Production Decision and CoordinationMechanismofCLSCBasedonExogenousCSR
is section does not distinguish between consumer groupsmeaning that consumers do not know whether the enterprisehas social responsibility In addition this section explores theimpact of CSR on patent licensing recycling rates and profitse CSR manufacturer will encourage the retailer to recycleproduce or sell more remanufactured products while in-creasing the revenues of all parties [8] We use θ isin [0 1] torepresent the CSR factor of the manufacturer θ 0 is therevenue maximization of the manufacturer and θ 1 is thewelfare maximization of the manufacturer
In the manufacturerrsquos revenue function the manufac-turerrsquos CSR is quantified as the proportion of consumersurplus (CS) which refers to the difference between themaximum price a consumer is willing to pay and the actualtotal price to pay When the demand function is thelinear function D a(1 minus p) CS is CS 1113938
a
(aminus D)a (aminus
ap)dp (D22a) [8] Some of the assumptions used hereinare as follows
Assumption 1 the manufacturer is the leader of theStackelberg gameAssumption 2 remanufactured products are used asproducts recycled from consumers by the retailer Toensure the remanufacturing activities of the retailer thesaving value of remanufactured products is Δgt 0Assumption 3 remanufactured products have no dif-ference in quality and use function compared with newproducts produced by the manufacturer consumersvalue both products in the same way and they are soldat the same price in the market
e recycling quantity of used products increases withthe increase in recovery price [30] the recycling quantity ofused products G is a function of the recovery price r G α + βlowast r where α represents the quantity of usedproducts that consumers voluntarily return and β indicatesconsumersrsquo degree of sensitivity to recovery prices
41 Analysis of Decentralized Decision Model e manu-facturer authorizes the retailer to remanufacture charging acertain patent licensing fee In addition the manufacturermay not recycle or remanufacture products for the sake ofrecovery costs or branding e retailer recycles usedproducts from remanufacturing activities and sells new andremanufactured products together to consumers afterobtaining a patent technical license
e decision turn of the Stackelberg game is as follows(1) as the game leader the manufacturer first sets thewholesale price w and patent licensing fee f (2) afterobtaining the manufacturerrsquos patent licensing the retailerdetermines the sale price of the product p and recovery pricer When CSR is not considered the manufacturerrsquos revenuefunction is
maxw f
πM w minus cn( 1113857(a minus alowastp minus α minus βlowast r) + flowast(α + βlowast r)
(1)
and the retailerrsquos revenue function is
maxp r
πR (p minus w)(a minus alowastp minus α minus βlowast r)
+ p minus cn + Δ( 1113857(α + βlowast r) minus (f + r)(α + βlowast r)
(2)
When CSR is considered the manufacturerrsquos revenuefunction is
maxwf
vM w minus cn( 1113857(a minus alowastp minus α minus βlowast r)
+ flowast(α + βlowast r) + θ lowastD2
2a
(3)
Proposition 1 can be obtained by the backward induc-tion solution
Proposition 1 e revenue functions of the manufacturerand the retailer under decentralized decisions are nonconvexe optimal wholesale price can be obtained as followswlowast ((2 minus θ + 2cn)(4 minus θ)) the optimal retail price isplowast ((3 minus θ + cn)(4 minus θ)) the optimal recovery price isrlowast ((βΔ minus 3α)4β) and the optimal patent licensing feeis flowast ((4β + 4α minus 2βθ minus αθ minus 4βcn + 4βΔ + 2βcnθ minus βθΔ)(2β(4 minus θ)))
By Proposition 1 the maximum revenue of the manu-facturer considering CSR is
vlowastM
aα2 + 2aαβΔ minus 4βα2
8+β2Δ2
aβminus a
2βcn +ac2n
2(4 minus θ)
(4)
e maximum revenue of the retailer is
π lowastR (βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2 (5)
e total revenue of the supply chain is
vlowast
(βΔ + α)2
16β+α2 minus 2a2cn + a2c2n
a(4 minus θ)2+
aα2 + 2αaβΔ minus 4βα2
8
+β2Δ2
aβminus βa
2cn +
ac2n2(4 minus θ)
(6)
e CS is
CS a 1 minus cn( 1113857
2
2(4 minus θ)2 (7)
Conclusion 1 (1) As the cost of new products increases bothwholesale and retail prices increase the optimal patent li-censing fee charged by the manufacturer decreases therevenue of the manufacturer and the retailer decreases andthe revenue of the supply chain decreases (2) As the
Complexity 3
remanufacturing saving cost increases the recovery priceand recycling quantity of used products both increase thepatent licensing fee charged increases and the profits of themanufacturer the retailer and the supply chain all increase(3) When the manufacturer shows stronger CSR thewholesale and the retail prices of products are lower emanufacturerrsquos revenue is higher the patent licensing fee islower the retailerrsquos revenue increases and CS increases
42 Analysis of Centralized Decision Model In the central-ized decision model the revenue function of the entiresupply chain is
maxpcrc
πc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α + βlowast rc( 1113857 (8)
When the manufacturerrsquo CSR is considered the revenuefunction of the entire supply chain is
maxpcrc
vc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α+βlowastrc( 1113857 +θlowastD2
2a
(9)
Take the partial derivatives of formula (8) with respect topc and rc (zvczpc) 0 (zvczrc) 0 and obtain the bestsolution plowastc and vlowastc e corresponding Hessian matrix is
Hc
z2vc
zp2c
z2vc
zpczrc
z2vc
zrczpc
z2vc
zr2c
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
minus 2β minus 2β
0 aθ minus 2a
⎛⎝ ⎞⎠ (10)
When Hessian matrix Hc gt 0 2 minus θgt 0 that is thecentralized revenue function is nonconvex we can obtainProposition 2
Proposition 2 e revenue function of the entire supplychain under centralized decisions with respect to pc and rc isnonconvex and the optimal solution (plowastc rlowastc ) is(((1 minus θ + cn)(2 minus θ)) ((βΔ minus α)2β)) e revenue of theentire supply chain under centralized decisions is
vlowastc
2aβ + 2α2 + 2aβc2n + 2β2Δ2 minus βα2 minus θβ2Δ2 minus 4βcn + 4αβΔ minus 2αβΔθ4β(2 minus θ)
(11)
43 Revenue-Sharing Coordination Mechanism Tradition-ally the manufacturer and the retailer act independently andmaximize their own respective revenues However an ef-fective supply chain network requires a cooperative rela-tionship erefore a coordination mechanism is needed tocoordinate the manufacturer and the retailer Under arevenue-sharing (RS) contract the manufacturer offers awholesale price and requires a small portion of the revenuefrom the retailer e RS contract sets the revenue-sharingparameter as λ isin (0 1) and the manufacturer receives (1 minus
λ) of the revenue
Proposition 3 Under the RS contract the revenue functionexpressions of the manufacturer and the retailer are re-spectively as follows
πM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)
vM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)θ(a minus ap)2
2a
(12)
When the RS contract the manufacturer provided to theretailer is
Table 1 Model parameter settings
Parameter Representsp Retail price per unit of product set by the retailerw Unit wholesale price given by the manufacturerr Recovery price for used productscn Production cost of new productsΔ Production cost saved by the retailer from remanufactured productsK Impact factors of social responsibility level on consumersrsquo willingness to payf Patent licensing fee for manufacturer-licensed remanufacturingym Manufacturerrsquos level of CSRρ Ratio of CSR-sensitive consumersa Market capacityπj
i e profit function of the enterprise i parameter i isin M R where M represents the manufacturer and R represents the retailer
4 Complexity
wco
fco
( 1113857 2cn minus θ2 minus θ
λ2cn minus θ2 minus θ
λ minus cn1113888 1113889 (13)the RS proportion λ should meet λ1 lt λlt λ2 in which when
λ1 (2 minus θ)2(16 a minus acn( 1113857
2minus 3a(4 minus θ)2(α + βΔ)2
16β(4 minus θ)2 a minus acn( 11138572
λ2 minus1 minus cn( 1113857
2
2(θ minus 2)+4β 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a minus acn( 11138572
(14)
the CLSC can be coordinated by the RS contract (seeAppendix A)
Proposition 4 Under the RS contract it satisfies the fol-lowing relationships pco ltplowast wco ltwlowast fco ltflowast rco gt rlowastπcoR gt π lowastR and vcoM gt vlowastM
Proposition 4shows that when an RS contract is adoptedthe manufacturer pays more attention to CSR and reduces itswholesale price and the product patent licensing fee thus in-creasing the sales volume of products Product sales are directlyproportional to the CSR level of the manufacturer In additionthe recycling intensity of the retailer increases and in responseto the manufacturerrsquos strategies the retailer reduces their saleprices to encourage customers to buy more products and putsmore efforts into collecting used products from customers emanufacturerrsquos CSR therefore influences the retailerrsquos decisionsand further influences their decisions in the reverse supply chainthrough influencing prices In centralized decisions when CSRincreases the manufacturer reduces the wholesale price ofproducts and the sale price under the centralized decision islower than that under the decentralized decision As a resultthere is a higher demand for products of centralized decisionsObviously the retailer will make more efforts to collect usedproducts under centralization e manufacturer the retailerand the entire supply chain have higher revenues under thecentralized model than that under decentralized model thusthe entire CLSC achieves coordination
At the same time consumers can buy new products at alower price and sell used products at a higher price whichgreatly improves consumersrsquo utilities and achieves a win-winsituation for enterprises and consumers
44NumericalExamplesandSensitivityAnalysis Numericalcalculations are made based on the above conclusionsParameter values refer to assumptions of Bakal and Akcali[30] the market demand function of products isD(p) 100(1 minus p) the supply function of old products isG(r) 08 + 10r and the production cost of new products isCn 05 e decision results of different CLSC systems areillustrated in Tables 2 and 3
As can be seen from Table 2 under decentralized decisionswith the increasing awareness of the manufacturerrsquos CSR therevenues of both the manufacturer and the retailer increase themanufacturer reduces the patent licensing fee and lowers the
wholesale prices so that the retailer sets retail prices lower andthe consumer purchase quantity increases With the increase inremanufacturing saving cost the retailerrsquos recycling prices risee manufacturer charges more patent licensing fees and boththe manufacturerrsquos and the retailerrsquos revenues increase FromTable 3 as the RS proportion increases the manufacturerrsquoswholesale price increases the patent licensing fee decreases theretailerrsquos revenue increases and the manufacturerrsquos revenuedecreases
Sensitivity analysis is conducted on the key parameters(Cn and θ) to examine the proposed modelsrsquo performance eeffects of Cn on the w p andf are shown in Figure 1 Byincreasing Cn both wholesale prices w and retail prices p
increase and the optimal patent licensing fee f decreasesWhen the production cost of new products Cn is higher themanufacturer reduces the patent licensing fee to encourage theretailer to produce and recycle more used products and in-crease the revenue Figure 2 illustrates the effects of θ on thew p andf by increasing θ and the decreases in wholesaleprices w retail prices p and patent licensing fee f When themanufacturerrsquos CSR θ is stronger the price of products is lowere sales volume is higher and the profits of both the man-ufacturer and the retailer increase e manufacturer will re-duce the patent licensing fee encouraging the retailer to recycleand remanufacture erefore patent licensing fee is an im-portant adjustment tool for the manufacturer
From Figure 3 the entire CLSC profit is improved under RScontracts the profit of the manufacturer and the retailer isimproved compared to the decentralized model (πcoR gt π lowastR andvcoM gt vlowastM) and the compensation-based whole price mechanismcanmotivate the retailer to take part in the centralized decisions
5 Production Decision and CoordinationMechanism of CLSC of Endogenous CSR
is section divides consumers into CSR-sensitive and or-dinary types constructs the CLSC model considering en-dogenous CSR and mainly examines the impact of theproportion of CSR-sensitive consumers on CSR level theprofits of CLSC members and RS contracts e specificparameter settings are shown in Table 1
51 Analysis of Decentralized Decision Model When CSR isendogenous there are CSR-sensitive consumers and
Complexity 5
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
remanufacturing saving cost increases the recovery priceand recycling quantity of used products both increase thepatent licensing fee charged increases and the profits of themanufacturer the retailer and the supply chain all increase(3) When the manufacturer shows stronger CSR thewholesale and the retail prices of products are lower emanufacturerrsquos revenue is higher the patent licensing fee islower the retailerrsquos revenue increases and CS increases
42 Analysis of Centralized Decision Model In the central-ized decision model the revenue function of the entiresupply chain is
maxpcrc
πc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α + βlowast rc( 1113857 (8)
When the manufacturerrsquo CSR is considered the revenuefunction of the entire supply chain is
maxpcrc
vc pc minus cn( 1113857(a minus alowastp) + Δ minus rc( 1113857 α+βlowastrc( 1113857 +θlowastD2
2a
(9)
Take the partial derivatives of formula (8) with respect topc and rc (zvczpc) 0 (zvczrc) 0 and obtain the bestsolution plowastc and vlowastc e corresponding Hessian matrix is
Hc
z2vc
zp2c
z2vc
zpczrc
z2vc
zrczpc
z2vc
zr2c
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
minus 2β minus 2β
0 aθ minus 2a
⎛⎝ ⎞⎠ (10)
When Hessian matrix Hc gt 0 2 minus θgt 0 that is thecentralized revenue function is nonconvex we can obtainProposition 2
Proposition 2 e revenue function of the entire supplychain under centralized decisions with respect to pc and rc isnonconvex and the optimal solution (plowastc rlowastc ) is(((1 minus θ + cn)(2 minus θ)) ((βΔ minus α)2β)) e revenue of theentire supply chain under centralized decisions is
vlowastc
2aβ + 2α2 + 2aβc2n + 2β2Δ2 minus βα2 minus θβ2Δ2 minus 4βcn + 4αβΔ minus 2αβΔθ4β(2 minus θ)
(11)
43 Revenue-Sharing Coordination Mechanism Tradition-ally the manufacturer and the retailer act independently andmaximize their own respective revenues However an ef-fective supply chain network requires a cooperative rela-tionship erefore a coordination mechanism is needed tocoordinate the manufacturer and the retailer Under arevenue-sharing (RS) contract the manufacturer offers awholesale price and requires a small portion of the revenuefrom the retailer e RS contract sets the revenue-sharingparameter as λ isin (0 1) and the manufacturer receives (1 minus
λ) of the revenue
Proposition 3 Under the RS contract the revenue functionexpressions of the manufacturer and the retailer are re-spectively as follows
πM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)
vM (1 minus λ)p(a minus ap) + w minus cn( 1113857(a minus ap minus α minus βr)
+ f(α + βr)θ(a minus ap)2
2a
(12)
When the RS contract the manufacturer provided to theretailer is
Table 1 Model parameter settings
Parameter Representsp Retail price per unit of product set by the retailerw Unit wholesale price given by the manufacturerr Recovery price for used productscn Production cost of new productsΔ Production cost saved by the retailer from remanufactured productsK Impact factors of social responsibility level on consumersrsquo willingness to payf Patent licensing fee for manufacturer-licensed remanufacturingym Manufacturerrsquos level of CSRρ Ratio of CSR-sensitive consumersa Market capacityπj
i e profit function of the enterprise i parameter i isin M R where M represents the manufacturer and R represents the retailer
4 Complexity
wco
fco
( 1113857 2cn minus θ2 minus θ
λ2cn minus θ2 minus θ
λ minus cn1113888 1113889 (13)the RS proportion λ should meet λ1 lt λlt λ2 in which when
λ1 (2 minus θ)2(16 a minus acn( 1113857
2minus 3a(4 minus θ)2(α + βΔ)2
16β(4 minus θ)2 a minus acn( 11138572
λ2 minus1 minus cn( 1113857
2
2(θ minus 2)+4β 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a minus acn( 11138572
(14)
the CLSC can be coordinated by the RS contract (seeAppendix A)
Proposition 4 Under the RS contract it satisfies the fol-lowing relationships pco ltplowast wco ltwlowast fco ltflowast rco gt rlowastπcoR gt π lowastR and vcoM gt vlowastM
Proposition 4shows that when an RS contract is adoptedthe manufacturer pays more attention to CSR and reduces itswholesale price and the product patent licensing fee thus in-creasing the sales volume of products Product sales are directlyproportional to the CSR level of the manufacturer In additionthe recycling intensity of the retailer increases and in responseto the manufacturerrsquos strategies the retailer reduces their saleprices to encourage customers to buy more products and putsmore efforts into collecting used products from customers emanufacturerrsquos CSR therefore influences the retailerrsquos decisionsand further influences their decisions in the reverse supply chainthrough influencing prices In centralized decisions when CSRincreases the manufacturer reduces the wholesale price ofproducts and the sale price under the centralized decision islower than that under the decentralized decision As a resultthere is a higher demand for products of centralized decisionsObviously the retailer will make more efforts to collect usedproducts under centralization e manufacturer the retailerand the entire supply chain have higher revenues under thecentralized model than that under decentralized model thusthe entire CLSC achieves coordination
At the same time consumers can buy new products at alower price and sell used products at a higher price whichgreatly improves consumersrsquo utilities and achieves a win-winsituation for enterprises and consumers
44NumericalExamplesandSensitivityAnalysis Numericalcalculations are made based on the above conclusionsParameter values refer to assumptions of Bakal and Akcali[30] the market demand function of products isD(p) 100(1 minus p) the supply function of old products isG(r) 08 + 10r and the production cost of new products isCn 05 e decision results of different CLSC systems areillustrated in Tables 2 and 3
As can be seen from Table 2 under decentralized decisionswith the increasing awareness of the manufacturerrsquos CSR therevenues of both the manufacturer and the retailer increase themanufacturer reduces the patent licensing fee and lowers the
wholesale prices so that the retailer sets retail prices lower andthe consumer purchase quantity increases With the increase inremanufacturing saving cost the retailerrsquos recycling prices risee manufacturer charges more patent licensing fees and boththe manufacturerrsquos and the retailerrsquos revenues increase FromTable 3 as the RS proportion increases the manufacturerrsquoswholesale price increases the patent licensing fee decreases theretailerrsquos revenue increases and the manufacturerrsquos revenuedecreases
Sensitivity analysis is conducted on the key parameters(Cn and θ) to examine the proposed modelsrsquo performance eeffects of Cn on the w p andf are shown in Figure 1 Byincreasing Cn both wholesale prices w and retail prices p
increase and the optimal patent licensing fee f decreasesWhen the production cost of new products Cn is higher themanufacturer reduces the patent licensing fee to encourage theretailer to produce and recycle more used products and in-crease the revenue Figure 2 illustrates the effects of θ on thew p andf by increasing θ and the decreases in wholesaleprices w retail prices p and patent licensing fee f When themanufacturerrsquos CSR θ is stronger the price of products is lowere sales volume is higher and the profits of both the man-ufacturer and the retailer increase e manufacturer will re-duce the patent licensing fee encouraging the retailer to recycleand remanufacture erefore patent licensing fee is an im-portant adjustment tool for the manufacturer
From Figure 3 the entire CLSC profit is improved under RScontracts the profit of the manufacturer and the retailer isimproved compared to the decentralized model (πcoR gt π lowastR andvcoM gt vlowastM) and the compensation-based whole price mechanismcanmotivate the retailer to take part in the centralized decisions
5 Production Decision and CoordinationMechanism of CLSC of Endogenous CSR
is section divides consumers into CSR-sensitive and or-dinary types constructs the CLSC model considering en-dogenous CSR and mainly examines the impact of theproportion of CSR-sensitive consumers on CSR level theprofits of CLSC members and RS contracts e specificparameter settings are shown in Table 1
51 Analysis of Decentralized Decision Model When CSR isendogenous there are CSR-sensitive consumers and
Complexity 5
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
wco
fco
( 1113857 2cn minus θ2 minus θ
λ2cn minus θ2 minus θ
λ minus cn1113888 1113889 (13)the RS proportion λ should meet λ1 lt λlt λ2 in which when
λ1 (2 minus θ)2(16 a minus acn( 1113857
2minus 3a(4 minus θ)2(α + βΔ)2
16β(4 minus θ)2 a minus acn( 11138572
λ2 minus1 minus cn( 1113857
2
2(θ minus 2)+4β 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a minus acn( 11138572
(14)
the CLSC can be coordinated by the RS contract (seeAppendix A)
Proposition 4 Under the RS contract it satisfies the fol-lowing relationships pco ltplowast wco ltwlowast fco ltflowast rco gt rlowastπcoR gt π lowastR and vcoM gt vlowastM
Proposition 4shows that when an RS contract is adoptedthe manufacturer pays more attention to CSR and reduces itswholesale price and the product patent licensing fee thus in-creasing the sales volume of products Product sales are directlyproportional to the CSR level of the manufacturer In additionthe recycling intensity of the retailer increases and in responseto the manufacturerrsquos strategies the retailer reduces their saleprices to encourage customers to buy more products and putsmore efforts into collecting used products from customers emanufacturerrsquos CSR therefore influences the retailerrsquos decisionsand further influences their decisions in the reverse supply chainthrough influencing prices In centralized decisions when CSRincreases the manufacturer reduces the wholesale price ofproducts and the sale price under the centralized decision islower than that under the decentralized decision As a resultthere is a higher demand for products of centralized decisionsObviously the retailer will make more efforts to collect usedproducts under centralization e manufacturer the retailerand the entire supply chain have higher revenues under thecentralized model than that under decentralized model thusthe entire CLSC achieves coordination
At the same time consumers can buy new products at alower price and sell used products at a higher price whichgreatly improves consumersrsquo utilities and achieves a win-winsituation for enterprises and consumers
44NumericalExamplesandSensitivityAnalysis Numericalcalculations are made based on the above conclusionsParameter values refer to assumptions of Bakal and Akcali[30] the market demand function of products isD(p) 100(1 minus p) the supply function of old products isG(r) 08 + 10r and the production cost of new products isCn 05 e decision results of different CLSC systems areillustrated in Tables 2 and 3
As can be seen from Table 2 under decentralized decisionswith the increasing awareness of the manufacturerrsquos CSR therevenues of both the manufacturer and the retailer increase themanufacturer reduces the patent licensing fee and lowers the
wholesale prices so that the retailer sets retail prices lower andthe consumer purchase quantity increases With the increase inremanufacturing saving cost the retailerrsquos recycling prices risee manufacturer charges more patent licensing fees and boththe manufacturerrsquos and the retailerrsquos revenues increase FromTable 3 as the RS proportion increases the manufacturerrsquoswholesale price increases the patent licensing fee decreases theretailerrsquos revenue increases and the manufacturerrsquos revenuedecreases
Sensitivity analysis is conducted on the key parameters(Cn and θ) to examine the proposed modelsrsquo performance eeffects of Cn on the w p andf are shown in Figure 1 Byincreasing Cn both wholesale prices w and retail prices p
increase and the optimal patent licensing fee f decreasesWhen the production cost of new products Cn is higher themanufacturer reduces the patent licensing fee to encourage theretailer to produce and recycle more used products and in-crease the revenue Figure 2 illustrates the effects of θ on thew p andf by increasing θ and the decreases in wholesaleprices w retail prices p and patent licensing fee f When themanufacturerrsquos CSR θ is stronger the price of products is lowere sales volume is higher and the profits of both the man-ufacturer and the retailer increase e manufacturer will re-duce the patent licensing fee encouraging the retailer to recycleand remanufacture erefore patent licensing fee is an im-portant adjustment tool for the manufacturer
From Figure 3 the entire CLSC profit is improved under RScontracts the profit of the manufacturer and the retailer isimproved compared to the decentralized model (πcoR gt π lowastR andvcoM gt vlowastM) and the compensation-based whole price mechanismcanmotivate the retailer to take part in the centralized decisions
5 Production Decision and CoordinationMechanism of CLSC of Endogenous CSR
is section divides consumers into CSR-sensitive and or-dinary types constructs the CLSC model considering en-dogenous CSR and mainly examines the impact of theproportion of CSR-sensitive consumers on CSR level theprofits of CLSC members and RS contracts e specificparameter settings are shown in Table 1
51 Analysis of Decentralized Decision Model When CSR isendogenous there are CSR-sensitive consumers and
Complexity 5
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
ordinary consumers in the market and the revenue functionof the manufacturer is
maxwcwn fym
πM wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+ f(α + βr) minus y2m
(15)
e revenue function of the retailer is
maxpcpnr
πR pc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ pn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857
+(Δ minus f minus r)(α + βr)
(16)
Proposition 5 can be obtained through the backwardinduction solution
Proposition 5 e revenue functions of the manufacturerand the retailer are nonconvex e optimal wholesale priceof CSR-type products that can be obtained is wc
minus (minus acnρK2 + 4cn + 4)(aρK2 minus 8) the optimal retail price ispc minus ((2cn minus acnρK2 + 6)(aρK2 minus 8)) the optimal whole-sale price of ordinary products is wn ((1 + cn)2) and theoptimal retail price is pn ((3 + cn)4) e optimal recoveryprice is r minus ((3α minus βΔ)4β) the optimal patent licensing feeis f ((α + βΔ)2β) and the manufacturerrsquos optimal CSRlevel is ym minus ((aKρ(1 minus cn))(aK2ρ minus 8)) From pc gt 0ym gt 0 0lt cn lt 1 we can obtain aρK2 lt 8
Conclusion 2
(1) As the cost of products increases the retail price andthe wholesale price of ordinary products increasewhen aρK2 lt 4 the wholesale price of CSR-sensitiveproducts increases When 4lt aρK2 lt 8 the wholesaleprice of CSR-sensitive products decreases When
aρK2 lt 2 the retail price of CSR-sensitive productsincreases When 2lt aρK2 lt 8 the retail price of CSR-sensitive products decreases Optimum patent li-censing fee and recovery prices are not affected by thecost of products and the manufacturerrsquos CSR leveldecreases as the cost of products increases
(2) As the remanufacturing saving cost increases therecovery price and the recycling quantity of usedproducts both increase the patent licensing fee in-creases and the profits of the manufacturer theretailer and the supply chain all increase
(3) With the increase in the proportion of CSR-sensitiveconsumers the wholesale and retail prices of CSR
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
products increase the CSR level of the manufacturerincreases and the profits of both the manufacturerand the retailer increase
(4) wn ltwc pn ltpc the wholesale and selling prices ofsocially responsible products are higher than those ofordinary products
52 Analysis of CentralizedDecisionModel In the centralizeddecisionmodel the revenue function of the entire supply chain is
π aρ pc minus cn( 1113857 1 minus pc + Kym( 1113857 + a pn minus cn( 1113857(1 minus ρ) 1 minus pn( 1113857
+(Δ minus r)(α + βr) minus y2m
(17)
Proposition 6 e revenue function of the entire supplychain under centralized decisions is nonconvex with respect topc pn and r e optimal solution of (plowastc plowastn rlowast) is(minus ((2 minus acρK2 + 2cn)(aρK2 minus 4)) (1 + cn)2 (βΔ minus α)2β)
Proposition 7 is compares the results of decentralizedand centralized decisions pn gtplowastn rlowast lt rlowastc When aρK2 lt 2pc gtplowastc and when 2lt aρK2 lt 8 pc ltplowastc
Conclusion 3 In the centralized decision model (1) with theincrease in remanufacturing cost savings the maximumrevenue of the entire supply chain increases and the recoveryprice of products increases (2) With the increase in theproportion of CSR-sensitive consumers the sale price ofCSR products increases and the overall revenue of thesupply chain increases
53 CoordinationMechanism RS contracts are still adoptedfor coordination here In RS contracts the manufacturer
provides a wholesale price and requires a portion of therevenue from the retailere revenue-sharing parameter setin RS contracts is λ isin (0 1) and the manufacturer receives(1 minus λ) times a portion of the revenue
e revenue function of the manufacturer is
πM (1 minus λ) pcaρ 1 minus pc + Kym( 1113857 + pna(1 minus ρ) 1 minus pn( 1113857( 1113857
+ wc minus cn( 1113857aρ 1 minus pc + Kym( 1113857
+ wn minus cn( 1113857a(1 minus ρ) 1 minus pn( 1113857 + f(α + βr) minus y2m
(18)
e retailerrsquos revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(19)
Proposition 8 When the manufacturer offers the contractwc minus 2λ(((2 + 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α + βΔ)2β) the CLSC can becoordinated See Appendix B
54 Sensitivity Analysis e data are set as in Section 44a 100 G(r) 08 + 10r Cn 05 Δ 03 and k 02Sensitivity analysis is conducted on the key parameter ρ toexamine the proposedmodelrsquos performance in the followingFigure 4 illustrates the effects of ρ on ym and Figure 5 showsthe effects of ρ on the profits of the manufacturer and theretailer under the decentralized and coordinated structuresWith the increase in the proportion of CSR-sensitive con-sumers ρ the CSR level of enterprises ym increases and theprofits of both the manufacturer and the retailer increasewhich are more than those in the decentralized structure
1
2
3
4
5
6
7
8
9
02 04 06 08 10θ
TTRvRco
TTMvMco
Figure 3 Profit comparison between decentralized and centralizeddecisions when θ changes
0
02
04
06
08
1
12
14
16
18
005 01 015 02 025 03 035 040ρ
ymco
ym
Figure 4 Optimal CSR results between decentralized and cen-tralized decisions when ρ changes
Complexity 7
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
e result confirms those of Hosseini-Motlagh et al [28]who used the cost-sharing contract to coordinate the CLSC
Comparing the wholesale price patent licensing fee andprofits in Propositions 1 and 5 we can obtain wlowast ltwn ltwcplowast ltpn ltpc and flowast gtf e price of any product in theendogenous model is higher than that of the exogenousmodel which means that manufacturerrsquos CSR level haseffects on CSR-sensitive consumers and further affectscustomersrsquo price sensitivity But the patent license fee in theendogenous model is lower which is set by themanufacturerto encourage the retailer to recycle and remanufactureHowever the manufacturer and the retailerrsquos profits in theexogenous model are not necessarily more than those inendogenous model
6 Conclusion
is study investigates the CLSC production and coordi-nation problem by setting endogenous and exogenous CSRassumptions CSR level can effectively improve the revenuesof the manufacturer and the retailer and patent licensing feehas an important regulatory effect on regulating the man-ufacturerrsquos revenue and encouraging the retailer to re-manufacture CLSC considering CSR is more competitivethan the traditional pure profit maximization supply chainIn practice improving consumersrsquo social responsibilityconsciousness and raising enterprisesrsquo level of CSR canachieve a win-win situation for revenues and social welfareRS contracts coordinate the CLSC of endogenous and ex-ogenous CSR
From the comparisons and discussions of the resultsamong the two models we obtained some managerial in-sights e manufacturerrsquos level of CSR affects the wholesale
price and patent licensing fee and this result is significantlydifferent from the profit maximization of a pure supplychain Improving the social responsibility consciousness ofconsumers and raising the CSR level can achieve a win-winsituation for revenues and social welfare the manufacturerand the retailer should therefore increase the proportion ofsocially responsible consumers through the price mecha-nisme results of sensitivity analysis reveal that the supplychain can be coordinated by using the compensation-basedwholesale price mechanism erefore the mechanism notonly increases the profits of the CLSC and all members butalso increases CSR activities for environmental social andeconomic development
is study has several limitations and future researchopportunitiesis study adopts the linear demand In termsof random demand there remains an issue of how to solvethe model In addition regarding the RS contract coordi-nating the supply chain adopted herein we can try to adoptquantity discount contracts and bargaining models forcoordination
Appendix
A Proof of Proposition 3
Proof of Proposition 3 e retailerrsquos revenue function
πR (λp minus w)(a minus ap) + w minus cn + Δ( 1113857(α + βr)
minus (f + r)(α + βr)(A1)
Take first derivation with respect to p and r and getpco ((λ + w)2λ) and rco ((minus α + β(w + Δ minus fminus cn))2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + w)2λ) ((α minus αθ + acn)(2a minus aθ))((minus α + β(w + Δ minus f minus cn) minus aθ)2β) ((βΔ minus α)2β))
e manufacturerrsquos optimum wholesale price and patentlicensing fee are
wco
2cn minus θ(2 minus θ)
λ
fco
2cn minus θ(2 minus θ)
λ minus cn
(A2)
At this point the revenues of the manufacturer and theretailer are
vcoM
a minus cn( 11138572(θ + 2λ minus 2)
2(2 minus θ)2
πcoR 4aλβ 1 minus cn( 1113857
2+(2 minus θ)2(α + βΔ)2
4β(2 minus θ)2
(A3)
e condition of both parties receiving the contract isvcoM gt vlowastM and obtain λ1 lt λlt λ2
02501 015 02005 03 035 040ρ
TTRco
TTRTTMco
TTM
15
2
25
3
35
4
45
5
55
6
65
Figure 5 Profit comparison between decentralized and centralizeddecisions when ρ changes
8 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
λ1 (2 minus θ)2 16a 1 minus cn( 1113857
2minus 3(4 minus θ)2(α + βΔ)21113872 1113873
16aβ(4 minus θ)2 minus cn( 11138572
λ2 minusa 1 minus cn( 1113857
2
2(θ minus 2)+4aβ 1 minus cn( 1113857
2+(4 minus θ)(α + βΔ)2 minus 3β2Δ2θ
8β(4 minus θ)1113888 1113889
(2 minus θ)2
a 1 minus cn( 11138572
(A4)
B Proof of Proposition 8
Proof of Proposition 8 e retailerrsquo s revenue function is
πR λpc minus wc( 1113857aρ 1 minus pc + Kym( 1113857
+ λpn minus wn( 1113857a(1 minus ρ) 1 minus pn( 1113857 +(Δ minus f minus r)(α + βr)
(B1)
Take the first derivation respects to pc pn and r andobtain pc ((λ + wc + Kλym)2λ) pn ((λ + wn)2λ) andr minus ((α minus βΔ)2β)
Let the profits of the CLSC under the revenue-sharingcontract be the same as that under centralized decisions andit needs to satisfy ((λ + wc + Kλym)2λ) minus ((2 + 2cnminus
acρK2)aρK2 minus 4) and ((λ + wn)2λ) ((1 + cn)2)e optimal wholesale price and the patent licensing fee
of the manufacturer are wc minus 2λ(((2+ 2cn minus acnρK2)(aρK2 minus 4)) + ((λ + Kλym)2λ)) wn λcn and f ((α+
βΔ)2β)e total revenue under the coordinated decision should
be greater than the total revenue under the decentralizeddecision (πM + πR)co gt (πM + πR)lowast and we can obtainλ1 and λ2 satisfying λ1 lt λlt λ2
Data Availability
e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
is study was financially supported by Natural ScienceFoundation of Hunan Province (No 2020JJ5011) ScientificResearch Fund of Hunan Provincial Education Department(No 19C0315) and National Natural Science Foundation ofChina (Nos 71771080 and 71802075)
References
[1] Z Hong and X Guo ldquoGreen product supply chain contractsconsidering environmental responsibilitiesrdquo Omega vol 83pp 155ndash166 2019
[2] KM Amaeshi O K Osuji and P Nnodim ldquoCorporate socialresponsibility in supply chains of global brands a boun-daryless responsibility Clarifications exceptions and impli-cationsrdquo Journal of Business Ethics vol 81 no 1 pp 223ndash2342008
[3] J Cotte and R Trudel ldquoSocially conscious consumerismasystematic review of the body of knowledgerdquo in Network forBusiness Sustainability Knowledge Project Series EconomistBoston University Boston MA USA 2009
[4] J Gaur M Amini and A K Rao ldquoClosed-loop supply chainconfiguration for new and reconditioned products an integratedoptimization modelrdquo Omega vol 66 pp 212ndash223 2017
[5] C-F Hsueh ldquoImproving corporate social responsibility in asupply chain through a new revenue sharing contractrdquo In-ternational Journal of Production Economics vol 151 no 3pp 214ndash222 2014
[6] C-F Hsueh ldquoA bilevel programming model for corporatesocial responsibility collaboration in sustainable supply chainmanagementrdquo Transportation Research Part E Logistics andTransportation Review vol 73 pp 84ndash95 2015
[7] C-HWu ldquoCollaboration and sharingmechanisms in improvingcorporate social responsibilityrdquo Central European Journal ofOperations Research vol 24 no 3 pp 681ndash707 2016
[8] S Panda N M Modak and L E Cardenas-Barron ldquoCo-ordinating a socially responsible closed-loop supply chainwith product recyclingrdquo International Journal of ProductionEconomics vol 188 no 1 pp 11ndash21 2017
[9] S La and B Choi ldquoPerceived justice and CSR after service re-coveryrdquo Journal of ServicesMarketing vol 33 no 2 pp 206ndash2192019
[10] JM Cruz ldquoe impact of corporate social responsibility in supplychain management multicriteria decision-making approachrdquoDecision Support Systems vol 48 no 1 pp 224ndash236 2009
[11] D Zhao H Chen X Hong and J Liu ldquoTechnology licensingcontracts with network effectsrdquo International Journal ofProduction Economics vol 158 pp 136ndash144 2014
[12] Y Huang and Z Wang ldquoClosed-loop supply chain modelswith product take-back and hybrid remanufacturing undertechnology licensingrdquo Journal of Cleaner Production vol 142pp 3917ndash3927 2016
[13] X Hong K Govindan L Xu and P Du ldquoQuantity andcollection decisions in a closed-loop supply chain withtechnology licensingrdquo European Journal of Operational Re-search vol 256 no 3 pp 820ndash829 2017
[14] S Hao Y Jun H Jin-song D A Qing-li andW Kai ldquoResearchon the game strategies for the OEM and the remanufacturerunder different decision structuresrdquo Chinese Journal of Man-agement Science vol 25 no 1 pp 160ndash169 2017
[15] Y Huang and ZWang ldquoInformation sharing in a closed-loopsupply chain with technology licensingrdquo International Journalof Production Economics vol 191 pp 113ndash127 2017
[16] L Jin B Zheng and X Hu ldquoPatent licensing productionoutsourcing and corporate social responsibilityrdquo NankaiBusiness Review vol 22 no 3 pp 40ndash53 2019
[17] D Ni and K W Li ldquoA game-theoretic analysis of social re-sponsibility conduct in two-echelon supply chainsrdquo InternationalJournal of Production Economics vol138 no 2 pp 303ndash313 2012
[18] S Panda ldquoCoordination of a socially responsible supply chainusing revenue sharing contractrdquo Transportation Research Part ELogistics and Transportation Review vol 67 pp 92ndash104 2014
Complexity 9
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
10 Complexity
[19] N M Modak S Panda S S Sana and M Basu ldquoCorporatesocial responsibility coordina tion and profit distribution in adual-channel supply chainrdquo Pacific Science Review vol 16no 4 pp 235ndash249 2015
[20] S Panda N M Modak and D Pradhan ldquoCorporate socialresponsibility channel coordination and profit division in atwo-echelon supply chainrdquo International Journal of Man-agement Science and Engineering Management vol 11 no 1pp 22ndash33 2016
[21] S Panda and N M Modak ldquoExploring the effects of socialresponsibility on coordination and profit division in a supplychainrdquo Journal of Cleaner Production vol 139 pp 25ndash402016
[22] C L White A E Nielsen and C Valentini ldquoCSR research inthe apparel industry a quantitative and qualitative review ofexisting literaturerdquo Corporate Social Responsibility and En-vironmental Management vol 24 no 5 pp 382ndash394 2017
[23] N M Modak N Kazemi and L E Cardenas-Barron ldquoIn-vestigating structure of a two-echelon closed-loop supplychain using social work donation as a corporate social re-sponsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019
[24] S Panda N M Modak M Basu and S K Goyal ldquoChannelcoordination and profit distribution in a social responsiblethree-layer supply chainrdquo International Journal of ProductionEconomics vol 168 pp 224ndash233 2015
[25] C-T Zhang and M Ren ldquoClosed-loop supply chain coor-dination strategy for the remanufacture of patented productsunder competitive demandrdquo Applied Mathematical Model-ling vol 40 no 13-14 pp 6243ndash6255 2016
[26] S M Seyedhosseini S-M Hosseini-Motlagh M Johari andM Jazinaninejad ldquoSocial price-sensitivity of demand forcompetitive supply chain coordinationrdquo Computers amp In-dustrial Engineering vol 135 pp 1103ndash1126 2019
[27] S-M Jazinaninejad M Nouri-Harzvili T-M Choi andS Ebrahimi ldquoReverse supply chain systems optimization withdual channel and demand disruptions sustainability CSRinvestment and pricing coordinationrdquo Information Sciencesvol 503 pp 606ndash634 2019
[28] S-M Hosseini-Motlagh S Ebrahimi andR Zirakpourdehkordi ldquoCoordination of dual-function ac-quisition price and corporate social responsibility in a sus-tainable closed-loop supply chainrdquo Journal of CleanerProduction vol 251 pp 1ndash15 2020
[29] J Li and S Gong ldquoCoordination of closed-loop supply chainwith dual-source supply and low-carbon concernrdquo Com-plexity vol 202014 pages 2020
[30] I S Bakal and E Akcali ldquoEffects of random yield in rema-nufacturing with price-sensitive supply and demandrdquo Pro-duction amp Operations Management vol 15 no 3pp 407ndash420 2006
