PricingDecisionsinaCompetitiveClosed-LoopSupplyChainwith … · 2020. 4. 18. · recycling process...

Research ArticlePricingDecisions inaCompetitiveClosed-LoopSupplyChainwithDuopolistic Recyclers

Doo Ho Lee

Division of Software Media and Industrial Engineering Kangwon National University 346 Joongang-ro Samcheok-siGangwon-do 29513 Republic of Korea

Correspondence should be addressed to Doo Ho Lee enjdhleegmailcom

Received 5 February 2020 Accepted 7 March 2020 Published 18 April 2020

Guest Editor Shib Sankar Sana

Copyright copy 2020 DooHo Leeis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this study we consider a three-echelon closed-loop supply chain consisting of a manufacturer a collector and two duopolisticrecyclers In the supply chain the collector collects end-of-life products from consumers in the market en both recyclerspurchase the recyclable waste from the collector and each recycler turns them into new materials e manufacturer has norecycling facilities therefore the manufacturer only purchases the recycled and new materials for its production from the tworecyclers Under this scenario price competition between recyclers is inevitable With two pricing structures (Nash andStackelberg) of the leaders group and three competition behaviors (Collusion Cournot and Stackelberg) of the followers groupwe suggest six different pricing game models In each of them we establish a pricing game model among the members prove theuniqueness of the equilibrium prices of the supply chain members and discuss the effects of competition on the overall supplychainrsquos profitability Our numerical experiment indicates that as the price competition between recyclers intensifies the supplychain profitability decreases Moreover the greater the recyclability degree of the waste is the higher the profits in the supplychain become

1 Introduction

Over the past few decades profitability improvements andcost leadership have been the main goals of supply chainmanagement However more recently the increasingrates of environmental degradation and resource deple-tion triggered by rapid industrialization have shifted thisfocus to socioenvironmental issues in the context ofsupply chain research this has led to more concern aboutsustainability with the concept of supply chain sustain-ability emerging [1] For many industries supply chainsustainability is one of the most critical tasks of theiroperations and long-term planning In addition to busi-ness performance of the supply chain environmental andsocial effects of the supply chain have been increasinglyperceived as critical aspects of supply chain performanceby shareholders As a result sustainable supply chainmanagement has become one of the main interests ofbusiness managers and stakeholders [2ndash4]

e supply chain is an important branch of operationalmanagement and it has a significant impact on the envi-ronment through hazardous gas emission and pollutionCompanies in various industries are now attempting tominimize their environmental impacts by integrating en-vironmental issues into their supply chain operations eintegration of environmental issues into supply chainmanagement practices is referred to as green supply chainmanagement [5ndash8] Green supply chain has become animportant research topic in academia and industry istopic includes environmental management such as eco-friendly productservice designs green purchasing reuseremanufacturing and recycling [9ndash11] Among these solu-tions recycling and reuse are considered more desirablebecause they require less of a quality-of-life compromise ofthe type closely linked to intensive material consumption[12] Many countries have been promoting the policiesrelated to the economic resource circulation For exampleJapan has been encouraging what is termed a sound

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 5750370 22 pageshttpsdoiorg10115520205750370

material-cycle society by implementing the 3R (reducereuse and recycle) strategy [13] Material and energy flowsmust become part of an increasingly sustainable and circulareconomy a concept introduced by the European Union asfollows In a circular economy the value of products andmaterials is maintained for as long as possible Waste andresource use are minimized and when a product reaches theend of its life it is used again to create further valueis canbring major economic benefits contributing to innovationgrowth and job creation In 2018 Apple announced that the2018 models of its MacBook Air and Mac mini would bothbe manufactured with 100 percent recycled aluminumAdditionally the Mac mini would be constructed from 60percent recycled plastic

Recycling is the process of collecting and processing wastethat would otherwise be thrown away as trash and turning thewaste into new products for environmental protection It alsoincludes the optimal management of waste disposal facilitiesAnother aim of recycling is to encourage ecofriendly man-agement and to manage limited supplies of resources esupply chain term refers to a type of systematic collaborationbetween people processes and information to create tangibleor intangible value and deliver it to consumers e mainpurpose of supply chain management is to facilitate bettermaterial and information flows among stakeholders in thesupply chain is creates a better relationship betweenstakeholders in the supply chain which increases the prof-itability of the entire supply chain [14 15] With the depletionof resources around the world waste from end-of-lifeproducts is becoming an important resource that can bemanaged globally As consumersrsquo interest in environmentalissues has increased along with the amounts of waste in-dustrialists and researchers are now focusing on sustainableproducts Reverse and closed-loop supply chains are welladapted to sustainability goals [16] Generally a reversesupply chain and closed-loop supply chain consist of certainoperations such as collecting recyclable waste transforming itinto new materials and transferring these materials to amanufacturer for remanufacturing A dual channel for col-lection can also be implemented in the supply chainSometimes it is found that dual-channel recycling outper-forms single-channel recycling [17 18]

Recyclability is a characteristic of amaterial that can retainuseful chemical andor physical properties after achievingtheir original purpose thus allowing it to be reused orremanufactured into additional products through a recog-nized process us recyclability must be observed andconsidered as the baseline during design production andwaste management activities With the development of in-formation and communication technology (ICT) the de-mand for electronic products has increased greatly and thishas led to more generation of waste electrical and electronicequipment (WEEE) e disruption of rare-earth metal ex-ports to Japan triggered by the Senkaku Islands dispute in2010 led to confusion not only in Japan but also in the globalmarket paradoxically emphasizing the importance of se-curing resources In 2016 the potential recovery of sevenprecious resources specifically iron copper gold silveraluminum palladium and plastics in WEEE amounts to

approximately 123 million tonnes in Europe [19] In light ofthis fact the recyclability ofWEEE plays a key role not only interms of environmental protection but also with regard to thestable supply and demand for various ICT products

Based on these observations this paper deals with aclosed-loop supply chain in which two recyclers competewith each other More specifically each recycler purchasesrecyclable waste from a collector recycles the waste andfinally sells the recycled materials to a manufacturer In thisprocess the two recyclers compete with regard to the sellingprices of their recycled materials e aim of this study is toinvestigate pricing and ordering decisions during the wasterecycling process in a three-echelon closed-loop supplychain with duopolistic recyclers using a game-theoreticframework Due to the competition between recyclers theprice offered by one recycler affects not only the price of theother recycler but also those of all other members in thesupply chain erefore demand and profit in the supplychain are sensitive in all cases to price competition isstudy proposes several pricing game models based onpricing structures and competitive behavior e main re-search questions for this study are as follows

(i) How can each member in the supply chain increasethe profit

(ii) What are the profits and equilibrium variables of thesupply chain members

(iii) How strong is the effect of the price competitionbetween recyclers in the supply chain

(iv) Does the recyclability degree of wastes have apositive effect on the profit of each member in thesupply chain

(v) Does an imbalance in the market share betweencompetitors affect the profit of the entire supplychain

In order to answer the above questions we revisit Jafariet alrsquos study [20] by considering price competition be-tween recyclers e main contributions of this researchare threefold First the impact of price competition be-tween recyclers with different competitive behaviors onthe sustainability of the supply chain is investigatedSecond our study concerns the economic as well as en-vironmental aspects of the supply chain ird we suggestsix different pricing game models and show the existenceof equilibrium solutions for each game Finally wecompare the results of the six pricing game modelsthrough a numerical example

e rest of this study is organized as follows In Section2 we present a brief overview of the relevant literatureafter which we introduce the six pricing game models andthen review the notations used and assumptions in Sec-tion 3 In Section 4 we conduct a preliminary analysis ofour main results Section 5 deals with the equilibriumquantities for each of the six pricing game models Var-ious numerical experiments are conducted in Section 6 toinvestigate the effects of certain parameters on theequilibrium quantities In Section 6 we give a summary ofthe paper and provide future research topics

2 Mathematical Problems in Engineering

2 Literature Review

In this section we review the relevant literature consideringthe main stream of research studies recycling issues in thesustainable supply chains

e economic and environmental benefits of sustainablesupply chain management have been widely recognized overthe past two decades and the closed-loop supply chain(CLSC) has therefore attracted significant attention fromboth industry and academia A CLSC consists of a forwardand a reverse supply chain e forward supply chain in-volves the movement of products from upstream suppliersto downstream consumers while the reverse supply chaininvolves the movement of used or end-of-life products fromconsumers to upstream suppliers [21] In a CLSC it issuggested that once the products are sold to consumers theresponsibilities of producers for dealing with sustainabilityissues should not end ere should be some accountabilitywith regard to the impacts of the products during theirconsumption and during the postconsumption phase Ac-cordingly waste management programs should be adoptedAs a result the linear paradigm of the supply chain becomescircular Input materials into the CLSC are reduced becausesome of the generated waste is retrieved to be reused asresources Hence the energy and resource dependencies arereduced without affecting economic growth [22] e CLSCstimulates the circulation of resources by slowing nar-rowing intensifying and closing resource loops [23] Fromthis point of view recycling is one of the major avenues usedto improve waste management systems [12] Several studieshave investigated this issue Savaskan et al [24] dealt with aCLSC capable of product collection and recycling and foundthat retailer collection is the most effective means of productcollection activity for the manufacturer Savaskan and VanWassenhove [25] studied the reverse channel design andoptimal pricing decisions of a CLSC in which two competingrecyclers collect used products Chen and Sheu [26] de-veloped a differential gamemodel established in view of salescompetition and recycling dynamics as well as regulation-related profit function Atasu et al [27] investigated theimpact of collection cost structures on optimal reversechannel decisions based on the work of Savaskan et al [24]Hong et al [28] investigated three reverse hybrid collectionchannel structures in a manufacturer-oriented CLSC andfound that the retailerrsquos and manufacturerrsquos hybrid collec-tion channel is the most effective Huang et al [18] studiedthe impacts of recycling competition on pricing and recy-cling strategies ey showed that dual-channel recyclingoutperforms a single-channel recycling A similar problemwith a different end-of-life product collection structure wasstudied byWang et al [29] and Modak et al [30 31] Modaket al proposed a two-echelon duopolistic retailer supplychain model with a recycling facility by considering theCournot and Collusion behaviors of retailers Saha et al [32]considered pricing strategies in a dual-channel CLSC underthree systems for the collection of used products third-partycollection manufacturer collection and retailer collectionLiu et al [33] studied the dual-recycling channel collectionto investigate pricing and best reverse-channel choice

decisions eir work suggested that the retailer dual-col-lecting model was the best channel structure for a CLSC In adual-reverse-supply chain consumer preference was con-sidered by Feng et al [17] who assumed a case in whichconsumers return used products via three different recyclingchannels Jafari et al [20] considered a dual-channel recy-cling structure through a collector or a recycler eyconsidered recycling while assuming a smooth waste col-lection flow ie with no shortcomings occurring on thecollectorrsquos side ey established various Stackelberg gamemodels to determine the equilibrium prices for recyclablewaste recycled materials and finished products By con-sidering a more realistic situation of recycling Giri and Dey[34] extended the model by Jafari et al [20] to a CLSC with asecondary or backup supplier who supplies shortfalls ofmaterials to tackle critical situations and obstacles pre-venting the smooth running of the supply chain Wei et al[35] studied a remanufacturing supply chain with dual-collecting channels under a dynamic setting and establishedthree two-period game models by considering both theprofit discount and competition between the two collectingchannels Jian et al [36] explored collaborative collectioneffort strategies involving a third-party collector and ane-tailer based on the ldquointernet + recyclingrdquo business modelNielsen et al [37] examined the effects of governmentsubsidy policies in a CLSC and suggested that governmentorganizations must inspect carefully the product typespower structures and investment efficiency before imple-menting any subsidy policies Saha et al [38] also dealt with aCLSC under the influence of government incentives eyfound that the greening level and used product return rate ina CLSC are always higher under retailer-led Stackelberggame

More recently many studies of corporate social re-sponsibility (CSR) in a CLSC have been carried out due togrowing consumer interest in environmental protectionModak et al [39] investigated a socially responsible supplychain with duopolistic retailers using Cournot and Collu-sion games to demonstrate that a manufacturerrsquos CSR has asignificant effect on wholesale prices because intensive CSRpractice can result in negative wholesale prices Panda et al[40] developed a socially responsible CLSC with recyclingey insisted that the channelrsquos nonprofit maximizingmotive through corporate social responsibility practicesgenerated a higher profit margin than the profit maximizingobjective and that there must be a recycling limit for theoptimal benefit of the channel Modak et al [41] examinedthe influence of a manufacturerrsquos social responsibility on thecollection activity of a third party in a CLSC and showed thatproduct recycling is directly affected by the manufacturerrsquoscorporate social responsibility concerns and that there mustbe a recycling threshold for the optimal benefit Modak andKelle [42] suggested social work donation (SWD) as a tool ofCSR in a CLSC considering carbon taxes and demanduncertainty ey revealed that SWD is beneficial when usedas an investment in CSR activity if the demand has a higherSWD elasticity parameter than the price sensitivity pa-rameter Dual-channel CLSC coordination under SWD wasalso analyzed by Modak et al [43] who asserted that if a

Mathematical Problems in Engineering 3

channel recycles used products and has socially concernedconsumers then consumers have the power to accelerateSWD and recycling simultaneously An excellent survey onreverse logistics and CLSC management studies can befound in Kazemi et al [44] and the references therein

Although comprehensive research has been conductedon recycling and pricing issues in various sustainable supplychains few studies have investigated price competitionbetween recyclers in the recycling market In this work weconsider forward and reverse supply chains where recyclablewaste recycled materials and finished goods flow From ourpricing decision models we investigate the effects of pricecompetition between recyclers on the profits of the membersin the supply chain and on the total profit of the supplychain is work also discusses how an imbalance in themarket share between recyclers affects the profit of the entiresupply chain

3 Model Description and Assumptions

31 Notations To model the investigated supply chain thefollowing notations are used throughout the paper

Index

i recyclers (i 1 2)

Decision variables

Pm selling price of the finished product offered by themanufacturerPri selling price of the recycled material offered by therecycler i

Pc selling price of the recyclable wastes offered by thecollector

Parameters

Cp unit production cost of the finished product to themanufacturerCri unit recycling cost of the recyclable wastes to therecycler i

Cc unit collection cost of the end-of-life product tothe collectorc quantity of the recycled materials required toproduce one unit of the finished product (cgt 1)

θ recyclability degree of the wastes (0lt θlt 1)

α potential market demand for the finished productβm consumerrsquos price sensitivity for the finishedproductβr manufacturerrsquos price sensitivity for the recycledmaterialω cross-price sensitivity for the recycled material(ωlt βr)

δi market share of the recycler i (0lt δi lt 1 and1113936iδi 1)

Functions

D demand faced by the manufacturerDmi quantity ordered by the manufacturer to therecycler i

Dri quantity ordered by the recycler i to the collector

Πm manufacturerrsquos profitΠc collectorrsquos profitΠri recycler irsquos profit

32 Assumptions In this study pricing and ordering de-cisions are investigated on the waste recycling process of athree-echelon CLSC e proposed CLSC consists of onemonopolistic manufacturer one monopolistic collector andtwo duopolistic recyclers Figure 1 depicts the overallconfiguration and the material and cash flows of the in-vestigated supply chain

e manufacturer produces finished products which aremade mainly from recycled wastes In other words themanufacturer uses the recycled (raw) materials to producethe product is assumption is reasonable because inpractice 100 recycled products are now being sold in themarket For example Applersquos MacBook Air is made with100 recycled aluminum Seventh Generation releasedpaper towels made from 100 recycled paper In addition100 recycled products are found in many remanufacturingindustries such as footwear (Allbirds) plastic bottle(Rothyrsquos) watches (Wewood) and clothing and accessories(Cotopaxi Recover Brands and Looptworks) [45] It wasreported that Looptworks significantly reduces the amountof garbage in the region and minimizes carbon emissions byworking with those who gather manufacturing materialsfrom landfills

e manufacturer purchases the recycled materials onlyfrom the recyclers Unlike Jafari et al [20] and Giri and Dey[34] we assume that the manufacturer is not in charge ofrecycling the wastes Hence the manufacturer can obtain therecycled materials directly from the recyclers and thenproduce the finished product Under the considered supplychain the market demand for the finished product is de-termined based on the final price charged by the manu-facturer to consumers in the market We assume that themarket demand D for the finished product is a linearfunction of the selling price Pm set by themanufacturerWetake D α minus βmPm where α and βm indicate the potentialmarket demand and the price sensitivity of the finishedproduct respectively We assume that α βm gt 0 and Dgt 0

e recyclerrsquos main activities are to purchase the recy-clable waste from the collector and provide themanufacturerwith the recycled materials We assume that there are twocompeting recyclers operating their own recycling facilitiese two recyclers sell identical recycled materials to themanufacturer We equivalently index the two recyclers byi 1 2 Each recycler is assumed to employ a uniformpricing strategy to attract the manufacturer us the de-mand of the recycled materials is price-dependent and isassumed to be a decreasing linear function of the price LetDmi denote the demand function of recycler i en Dmi hasthe form of

Dmi δic D minus βrPri + ωPrj gt 0 i 1 2 j 3 minus i (1)

where δi c and Pri indicate recycler irsquos market share ofrecycling the quantity of recycled materials required toproduce one unit of the finished product and the price


offered by recycler i respectively In equation (1) βr repre-sents the manufacturerrsquos price sensitivity with regard to therecycled materials e term ω is the cross-price sensitivitywhich reflects the degree of cannibalization between the twocompeting recyclers In other words ω represents the leakage

of the demand from one recycler to the other recyclererefore the term ω is a competition parameter between thetwo recyclers As ω increases the price competition betweenthe two recyclers in the supply chain becomes more intenseroughout the paper it is assumed that βr gtω e lineartype of the demand function considering the price compe-tition is assumed in most studies [20 34 39 46 47]

e collector is responsible for collecting waste in theform of end-of-life products from consumers e collectedwaste can be classified as either recyclable or nonrecyclableand the collector transfers the recyclable waste to the re-cyclers In this study the recyclability degree of the waste isalso considered ie it is assumed that only a constant shareof the waste remains after the recycling process operated bythe recyclers Let Dri denote the ordering quantity of recycleri for the recyclable waste to the collector en Dri is simplygiven by Dri (1θ)Dmi gt 0 for i 1 2 where the term θindicates the recyclability degree of the waste erefore thefunction of the collectorrsquos total demand becomes 1113936iDri gt 0

Based on the demand functions of the participants in theCLSC considered here the profit function of each partici-pant is obtained by the following equation

Πm Pm minus Cp1113872 1113873D minus 1113944i

PriDmi

Πri PriDmi minus Pc + Cri( 1113857Dri i 1 2

Πc 1113944i

Pc minus Cc( 1113857Dri

(2)

where Πm Πri and Πc denote the profits of the manufac-turer the recycler i and the collector respectively Note thatit is useless to study pricing decisions with no positive profitsof participants in practice therefore the following as-sumption must be made Πm gt 0 Πri gt 0 and Πc gt 0

33 Decision-Making Structure is study utilizes gametheory to model the problem of determining the equilibriumprices of the participants in the investigated CLSC eplayers participating in the six pricing game models (whichare described in the next section) are the manufacturer thecollector recycler 1 and recycler 2 ese four players aredivided into two groups the leaders group and the followersgroup We assume that the manufacturer and the collectorbelong to the leaders group and that the two recyclers belongto the followers group e basic structure of the pricinggame model is as follows e leaders group initially de-termines the prices devised by the collector and the man-ufacturer after which the followers group determines thosedevised by the two recyclers is assumption is reasonablebecause in our setting there exists price competition be-tween the two recyclers and they are under pressure fromthe collector and manufacturer with regard to the demandfor recyclable waste and the supply of recycled materialsrespectively erefore the decision power of the leadersgroup is greater than that of the followers group

In the leaders group we deal with two pricing structuretypes Stackelberg and Nash In the Stackelberg pricingstructure the manufacturer acts as the Stackelberg game leaderand the collector reacts as the follower [48] In the Stackelbergpricing structure the manufacturer initializes the selling pricefor the finished product and the collector then decides on theselling price for the recyclable waste based on the manufac-turerrsquos price In the game theory literature a Nash game is asimultaneous-move game in which the manufacturer and thecollector make their decisions simultaneously [49] In thefollowers group we deal with three types of competition be-havior Collusion Cournot and StackelbergWhen engaging inCollusion behavior the recyclers cooperatively decide on theirselling prices while their selling prices are set competitivelywhen displaying Cournot behavior [50] When using Stack-elberg behavior the leader of the two recyclers initially sets theprice after which the follower determines its own price basedon the leaderrsquos price Without a loss of generality we assumethat recycler 1 (recycler 2) is a leader (follower) throughout thepaper erefore with the two aforementioned pricingstructures in the leaders group and the three types of com-petition behavior in the followers group six combinations ofdifferent pricing game models can be investigated (i) Nash-Collusion (ii) Nash-Cournot (iii) Nash-Stackelberg (iv)Stackelberg-Collusion (v) Stackelberg-Cournot and (vi)Stackelberg-Stackelberg Figure 2 illustrates the six different

Collector

Recycler 1 Recycler 2

Manufacturer

Market

MaterialCash

Figure 1 Material and cash flow diagram in the closed-loop supplychain with duopolistic recyclers


pricing game models In the next sections we develop themathematical programming and prove the uniqueness of thefour playersrsquo prices for each pricing game model

4 Preliminaries Pricing Behaviors in theFollowers Group

In this section we discuss the three competition behaviors ofthe recyclers in the followers group and obtain the pre-liminary results for the next section

41 Collusion Behavior in the Followers Group In the Col-lusion behavior the recyclers collude with each other to settheir prices for recycled materials More specifically theCollusion behavior is similar to the case in which the tworecyclers recognize their interdependence and agree to act inunion in order to maximize the total profit of the recyclingmarket Note that the two recyclers cooperate in pricing butstill compete in selling e total profit of the recyclers Πrtin the Collusion behavior can be formulated as followsΠrt Πr1 + Πr2 Hence the recyclersrsquo pricing problem RPCL

in the Collusion behavior can be formulated as followsRPCL max

Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i

PriDmi( 1113857 minus Pc + Cri( 1113857Dri

st Πrt Pr1 Pr2( 1113857gt 0

(3)

For the recyclersrsquo equilibrium prices we have the fol-lowing proposition

Proposition 1 Given the values of the manufacturerrsquos pricePm and the collectorrsquos price Pc in the Collusion behavior thereexists a unique equilibrium under the recycler irsquos price PCL

ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873

2θ β2r minus ω21113872 1113873 for i 1 2 j 3 minus i

(4)where K cθ(α minus βmPm)

Proof We consider the following Hessian matrix of theobjective function in RPCL

HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)

We define ΔCLk as the leading principal minor of order k

in HCLr We then find that ΔCL

1 minus 2βr lt 0 and ΔSCL2 4β2r minus

ω2 gt 0 because we assume that βr gtω erefore HCLr is

negatively definite implying that Πrt is strictly concave inthe feasible region and that the stationary point of Πrt

becomes the global maximizer of RPCL Consequently given

Stackelberg

The manufacturer is a leader and itinitially sets its selling price

The collector is a follower Based onthe manufacturerrsquos price the

collector determines its selling price

Nash

Themanufactureroptimizes its

selling price tomaximize its

profit

The collectoroptimizes its


profit

Leaders group

Collusion

Recycler 1 and 2 collude with eachother to determine their selling prices

based on the selling prices of theleaders group

Cournot

Recycler 1 iscompeting for

price withRecycler 2

They decidethe prices

independently




independently

Followers group

Stackelberg

Recycler 1 is a leader and it initiallysets its selling price

Recycler 2 is a follower Based onrecycler 1rsquos price recycler 2determines its selling price

Figure 2 Conceptual framework of pricing game models in the dual-channel recycling supply chain


the competitorrsquos price each recycler can find its own pricingstrategy by setting zΠrtzPri 0 for i 1 2

Pr1 βr Pc + Cr1( 1113857 minus ω Pc + Cr2( 1113857 + 2θωPr2 + Kδ1

2βrθ


2βrθ

(6)

Solving the equations system in equation (6) leads toequation (4) is completes the proof

42 Cournot Behavior in the Followers Group e Cournotbehavior forces the recyclers to decide on their prices si-multaneously In other words each recycler independentlysets its price by assuming its competitorrsquos selling price as aparameter Hence recycler irsquos pricing problem RPCT

i considering price competition is modeled as follows

RPCTi max

PriisinR+

Πri Pri( 1113857 PriDmi minus Pc + Cri( 1113857Dri

st Πri Pri( 1113857gt 0

(7)


Proposition 2 Given the values of Pm and Pc in theCournot behavior there exists a unique equilibrium under therecycler irsquos price PCT

ri

PCTri

K 2βrδi + ωδj1113872 1113873 + βr 2βr Pc + Cri( 1113857 + ω Pc + Crj1113872 11138731113960 1113961

θ 4β2r minus ω21113872 1113873

for i 1 2 j 3 minus i

(8)

Proof e second-order derivative of the objective functionin RPCT

i is given by z2ΠrizP2ri minus 2βr lt 0 for i 1 2 Hence

each recyclerrsquos profit function is strictly concave on its owndecision and there exists a unique equilibrium price for eachrecycler Consequently given the competitorrsquos price eachrecycler can find its own pricing strategy by settingzΠrizPri 0 for i 1 2

Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)


43 Stackelberg Behavior in the Followers Group In theStackelberg behavior also known as a sequential game theleader of the game initially sets the price and the followerthen determines its own price based on the leaderrsquos price Asnoted in Section 3 we assume that recycler 1 acts as theStackelberg leader while recycler 2 acts as the Stackelberg

follower With this assumption recycler 1rsquos decision powerand market share are greater than those of recycler 2 Ac-cordingly it is natural to assume that δ1 ge δ2 en recyclerirsquos pricing model RPSTi in the Stackelberg behavior ismodeled as follows

RPST2 max

Pr2isinR+

Πr2 Pr2( 1113857 Pr2Dm2 minus Pc + Cr2( 1113857Dr2

st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+


stPr2 isin argmaxΠr2 Pr2( 1113857

Πr1 Pr1( 1113857gt 0

(10)

For the sequential game above we have the followingproposition

Proposition 3 Given the values of Pm and Pc in theStackelberg behavior there exists a unique equilibrium underrecycler irsquos price PST

ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)

Proof e second-order derivative of the objective functionin RPST2 is given by z2Πr2zP2

r2 minus 2βr lt 0 erefore Πr2 isstrictly concave with respect to (wrt) Pr2 and by solvingzΠr2zPr2 0 the global maximizer of Πr2 is obtained as

PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)

By integrating PSTr2 in equation (12) into RPST

1 it followsthat z2Πr1zP2

r1 minus (2β2r minus ω2)βr lt 0 Hence Πr1 is alsostrictly concave wrt Pr1 and by solving zΠr1zPr1 0 theequilibrium solution of RPST

1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)

is completes the proof

5 Development of the Six Pricing GameModels

In this section we present the main results of this paper Sixdifferent pricing game models are carefully analyzed one byone

51 Nash Game Structure in the Leaders Group e Nashgame structure is a simultaneous-move game in which themanufacturer and the collector make their decisionssimultaneously

511 Nash-Collusion Model In the Nash-Collusion gamemodel which is denoted by NCL a Nash game is played


between the collector and the manufacturer while the re-cyclers collude with each other to set the prices for recycledmaterials In the first stage of the NCL model the manu-facturer and the collector announce their sales prices si-multaneously Based on this in the second stage therecyclers cooperate in terms of pricing with each other andset their prices to maximize the sum of their profitsAccording to Proposition 1 we know that the total profit ofthe recyclers Πrt is strictly concave with respect to therecyclersrsquo prices Pr1 and Pr2 and the equilibrium price ofrecycler i in the NCL model is expressed as

PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)

With recyclersrsquo prices in equation (14) the collectorrsquos pricingproblem CPNCL and the manufacturerrsquos pricing problemMPNCL are formulated as follows

CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+

Πm Pm( 1113857 Pm minus Cp1113872 1113873D minus 1113944i

PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)

Proposition 4 states the result of the NCL pricing gamemodel

Proposition 4 In the Nash-Collusion pricing game modelthere exists a unique Nash equilibrium under the collectorrsquosprice PNCL

c and the manufacturerrsquos price PNCLm

PNCLc

2Cc minus Cr1 minus Cr2

4+

cθ α minus βmCp1113872 1113873 βr + ω( 1113857

8 β2r minus ω21113872 1113873 + 2c2βm 2ωδ1δ2 + βr1113936iδ2i1113872 1113873

PNCLm

αβm

minus2 α minus βmCp1113872 1113873 β2r minus ω21113872 1113873

4βm β2r minus ω21113872 1113873 + c2β2m 2ωδ1δ2 + βr1113936iδ2i1113872 1113873

(16)

Proof From the objective functions in CPNCL and MPNCLtheir second-order derivatives are given by respectively

z2Πc

zP2c

minus2 βr minus ω( 1113857

θ2lt 0

z2Πm

zP2m

minus βm 2 +c2βm 2ωδ1δ2 + βr1113936iδ

2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)

erefore the collectorrsquos and the manufacturerrsquos profitfunctions are both strictly concave on their own decision var-iables and there exist unique equilibrium prices for the collectorand the manufacturer Consequently the collector and themanufacturer can find their own pricing strategies by solving thefirst-order conditions of zΠczPc 0 and zΠmzPm 0

Pc 2Cc minus Cr1 minus Cr2

4+

K

4 βr minus ω( 1113857

Pm βminus 1m α minus

2 α minus βmCp1113872 1113873 β2r minus ω21113872 1113873

4 β2r minus ω21113872 1113873 + c2βm 2ωδ1δ2 + βr1113936iδ2i1113872 1113873

⎡⎢⎣ ⎤⎥⎦

(18)

Solving equation (18) simultaneously leads to equation(16) is completes the proof

By the backward induction the equilibrium prices of therecyclers in the NCL model are determined as follows

PNCLri

PNCLc + Cri

2θ+

cθ α minus βmPNCLm( 1113857 βrδi + ωδj1113872 1113873

2θ β2r minus ω21113872 1113873


(19)

512 Nash-Cournot Model In the Nash-Cournot gamemodel which is denoted by NCT a Nash game is playedbetween the collector and the manufacturer with theCournot behavior displayed by the two recyclers In the firststage of the NCTmodel the manufacturer and the collectorannounce their sales prices simultaneously Based on this inthe second stage the equilibrium prices of the two recyclersare simultaneously and independently obtained Accordingto Proposition 2 the equilibrium price of recycler i in theNCT model is expressed as

PNCTri


θ 4β2r minus ω21113872 1113873


(20)

With the recyclersrsquo equilibrium prices in equation (20) thecollectorrsquos and the manufacturerrsquos pricing games are for-mulated as follows respectively

CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)

e following proposition pertains to the results of theNCT model

Proposition 5 In the Nash-Cournot pricing game modelthere exists a unique Nash equilibrium under the collectorrsquosprice PNCT

c and the manufacturerrsquos price PNCTm


Proof From the objective functions in CPNCT and MPNCTtheir second-order derivatives are given respectively by

z2Πc

zP2c

minus4βr βr minus ω( 1113857

θ2 2βr minus ω( 1113857lt 0

z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where

X1 c2βmβr 8ωβrδ1δ2 + 4β2r minus ω21113872 11138731113936iδ

2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)

Note that the collectorrsquos and the manufacturerrsquos profitfunctions are both strictly concave on their own decisionvariables us there exist unique Nash equilibrium pricesfor the collector and the manufacturer Consequently bysolving the first-order conditions zΠczPc 0 and

zΠmzPm 0 the collectorrsquos equilibrium price PNCTc and

the manufacturerrsquos equilibrium price PNCTm are obtained


e explicit expressions of PNCTc and PNCT

m are long andcomplicated Instead we present a brief version of thesolving procedure of the NCT model in Appendix A

513 Nash-Stackelberg Model In the Nash-Stackelberggame model which is denoted by NST a Nash game is playedbetween the collector and the manufacturer while a Stack-elberg game is played between the two recyclers In the firststage of the NST model the manufacturer and the collectorannounce their sales prices simultaneously Based on this inthe second stage recycler 1 determines its sales price In thethird stage following recycler 1rsquos price recycler 2 makes afurther pricing decision By considering the Stackelberg be-havior of the recyclers their prices are already known as

PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)

erefore with (23) the collectorrsquos pricing problemCPNST and the manufacturerrsquos pricing problem MPNST areformulated as follows respectively

CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)

Proposition 6 states the result of the NST pricing gamemodel

Proposition 6 In the Nash-Stackelberg pricing game modelthere exists a unique Nash equilibrium under the collectorrsquosprice PNST

c and the manufacturerrsquos price PNSTm

Proof e second-order derivative ofΠc wrt Pc is given by

z2Πc

zP2c

minusβr minus ω( 1113857 8β3r minus ω3 + βrω 4βr minus 3ω( 11138571113960 1113961

2θ2βr 2β2r minus ω21113872 1113873 (26)

From the fact that βr gtω⟹ 8β3r gtω3and 4βr gt 3ω it iseasy to show that z2ΠczP2

c lt 0 erefore Πc is strictlyconcave wrt Pc e second-order derivative of Πm wrtPm is also given by z2ΠmzP2

m minus 2βm(1 + X2) where

X2 c2βm 4β2r δ21 2β2r minus ω21113872 1113873 + δ22 4β2r minus ω21113872 11138731113960 1113961 + 4βrωδ1δ2 8β2r minus ω21113872 1113873 + 8β4rδ

21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)

Upon the assumption that δ1 ge δ2 it follows that8β4rδ

21 minus ω4δ22 ge δ

22(8β

4r minus ω4)gt 0 erefore we have the

following relationship δ1 ge δ2⟹X2 gt 0⟹z2ΠmzP2m lt 0

us Πm is also strictly concave wrt Pm and there existunique Nash equilibrium prices for the collector and themanufacturer Consequently by solving the first-orderconditions zΠczPc 0 and zΠmzPm 0 the collectorrsquos

equilibrium price PNSTc and the manufacturerrsquos equilib-

rium price PNSTm are obtained is completes the

proof

e explicit expressions of PNSTc and PNST

m are long andcomplicated Instead we present a brief version of thesolving procedure of the NST model in Appendix A


52 Stackelberg Game Structure in the Leaders Group In theStackelberg game structure the manufacturer acts as aStackelberg game leader and the collector reacts as the follower

521 Stackelberg-Collusion Model In the Stackelberg-Col-lusion game model which is denoted by SCL a Stackelberggame is played between the collector and the manufacturerwhile the recyclers collude with each other to set the prices ofrecycled materials In the first stage of the SCL model themanufacturer announces the selling price for the finishedproduct Based on this in the second stage of the game thecollector determines its selling price for the recyclable wasteIn the last stage following the collectorrsquos price two recyclersmake a decision on their prices cooperatively According toProposition 1 the recycler irsquos equilibrium price PSCL

ri in theSCL model is given by

PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)

By substituting equation (28) into the collectorrsquos profitfunction the collectorrsquos pricing problem CPSCL regardingthe SCL model can be formulated as follows

CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)

Proposition 7 Given the value of Pm there exists a uniqueequilibrium solution PSCL

c which maximizes the collectorrsquos profit

PSCLc


4+

K

4 βr minus ω( 1113857 (30)

Proof e second-order derivative of Πc wrt Pc can beobtained as z2ΠcP2

c minus 2(βr minus ω)θ2 lt 0 erefore theobjective function Πc in CPSCL is strictly concave and thereexists a unique global maximizer of CPSCL By settingzΠczPc 0 we obtain the equilibrium solution PSCL

c inequation (30) is completes the proof

Accordingly by substituting equations (28) and (30) intothe manufacturerrsquos profit function the manufacturerrsquospricing problem MPSCL regarding the SCL model can beformulated as follows

MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)

Proposition 8 In the Stackelberg-Collusion pricing gamemodel there exists a unique Stackelberg equilibrium underthe manufacturerrsquos price PSCL

m

PSCLm

β2r minus ω21113872 1113873 cβm 2Cc + Cr1 + Cr2( 1113857 minus 16θ α + βmCp1113872 11138731113960 1113961 + αc2θβm 16δ1δ2 βr minus ω( 1113857 minus 7βr + ω1113858 1113859

θβm c2βm 16δ1δ2 βr minus ω( 1113857 minus 7βr + ω1113858 1113859 minus 32 β2r minus ω21113872 11138731113966 1113967 (32)

Proof e second-order derivative of Πm wrt Pm can beobtained as

z2Πm

zP2m

βm

c2βm 16δ1δ2 βr minus ω( 1113857 minus 7βr + ω1113858 1113859

16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)

If the condition z2ΠmzP2m lt 0 is satisfied the objective

function in MPSCL is strictly concave and there exists aunique global maximizer of MPSCL Because 0le δ1 δ2 le 1and δ1 + δ2 1 the maximum value of δ1δ2 must be 025where δ1 δ2 05 e upper bound of z2ΠmzP2

m isobtained as follows

z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm

c2βm 4 βr minus ω( 1113857 minus 7βr + ω1113858 1113859

16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)

erefore it is obvious that z2ΠmzP2m lt 0 From the

first-order condition zΠmzPm 0 we can obtain the


manufacturerrsquos equilibrium solution PSCLm in equation (32)

is completes the proofHence considering the backward induction the equi-

librium prices of the collector and the recyclers in the SCLmodel are determined as follows

PSCLc


4+

cθ α minus βmPSCLm( 1113857

4 βr minus ω( 1113857

PSCLr1

cθ α minus βmPSCLm( 1113857 βrδ1 + ωδ2( 1113857 + β2r minus ω21113872 1113873 PSCL

c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)

522 Stackelberg-Cournot Model In the Stackelberg-Cournot game model which is denoted by SCT a Stack-elberg game is played between the collector and the man-ufacturer with the Cournot behavior following the tworecyclers In the first stage of the SCT model the manu-facturer announces the selling price for the finished productBased on this in the second stage game the collector de-termines its selling price for the recyclable waste In the laststage following the collectorrsquos price each recycler reaches aprice decision independently According to Proposition 2recycler irsquos equilibrium price PSCT

ri in the SCTmodel is givenby

PSCTri


θ 4β2r minus ω21113872 1113873


(36)

en by replacing equation (36) into the collectorrsquosprofit function the collectorrsquos pricing problem CPSCT re-garding the SCT model can be formulated as follows

CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)

Proposition 9 Given the value of Pm there exists a uniqueequilibrium solution PSCT

c which maximizes the collectorrsquosprofit

PSCTc


4+

K

4 βr minus ω( 1113857 (38)

Proof e second-order derivative of Πc wrt Pc can beobtained as z2ΠczP2

c minus 4βr(βr minus ω)θ2(2βr minus ω)lt 0erefore the objective function Πc in CPSCT is strictlyconcave and there exists a unique global maximizer of

CPSCT By setting zΠczPc 0 we obtain the equilibriumsolution PSCT

c in equation (38) is completes the proofUltimately by integrating equations (36) and (38) into

the manufacturerrsquos profit function the manufacturerrsquospricing problem MPSCT in the SCT model can be for-mulated as follows

MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)

Proposition 10 In the Stackelberg-Cournot pricing gamemodel there exists a unique Stackelberg equilibrium underthe manufacturerrsquos price PSCT

m By solving the first-ordercondition PSCT

m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3

4 βr minus ω( 1113857 4β2r minus ω21113872 11138732 minus 2⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦

(40)

where X3 6ω3 minus 15ω2βr + 28ωβ2r minus 28β3r If the conditionz2ΠmzP2

m lt 0 is satisfied the objective function in MPSCT isstrictly concave and there exists a unique global maximizerof MPSCT Like the proof of Proposition 8 the upper boundof z2ΠmzP2

m is obtained as follows

z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm

c2βmβr 3βr minus 2ω( 1113857

4 βr minus ω( 1113857 2βr minus ω( 11138572 + 2⎡⎣ ⎤⎦

(41)

Here it is true that 3βr gt 2ω because we assume thatβr gtω is implies that

3βr gt 2ω⟹c2βmβr 3βr minus 2ω( 1113857

4 βr minus ω( 1113857 2βr minus ω( 11138572 gt 0⟹

z2Πm

zP2m

lt 0 (42)

Hence from the first-order condition zΠmzPm 0 wecan obtain the manufacturerrsquos equilibrium solution PSCT

m is completes the proof

e explicit expression of PSCTm is long and complicated

Instead we present a brief version of the solving procedurein Appendix B

523 Stackelberg-Stackelberg Model In the Stackelberg-Stackelberg game model which is denoted by SST only one


Stackelberg game is played throughout the investigatedsupply chain is Stackelberg game consists of four stagesIn the first stage the manufacturer announces the sellingprice of the finished product Based on this in the secondstage of the game the collector determines its selling pricefor the recyclable waste In the third stage following thecollectorrsquos selling price recycler 1 sets the selling price forthe recycled materials Finally in the last stage recycler 2makes a decision on its selling price based on the infor-mation on other playersrsquo prices By considering the Stack-elberg behavior of the recyclers their prices are alreadyknown as

PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)

en by substituting equation (43) into the collectorrsquosprofit function the collectorrsquos pricing problem CPSST re-garding the SST model can be formulated as follows

CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)

Proposition 11 Given the value of Pm there exists a uniqueequilibrium solution PSST


PSSTc

14

2Cc minus Cr1 minus Cr2 +K

βr minus ω+ω2 K δ2 minus δ1( 1113857 + βr + ω( 1113857 Cr1 minus Cr2( 11138571113858 1113859

8β3r minus ω3 + βrω 4βr minus 3ω( 11138571113896 1113897 (45)

Proof e second-order derivative of Πc wrt Pc can beobtained as

z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)

erefore the objective function Πc in CPSCT is strictlyconcave and there exists a unique global maximizer ofCPSCS By setting zΠczPc 0 we obtain the equilibriumsolution PSCT

c in equation (45) is completes the proofUltimately by integrating equations (43) and (45) into the

manufacturerrsquos profit function the manufacturerrsquos pricingproblemMPSST in the SSTmodel can be formulated as follows

MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

For the uniqueness of the manufacturerrsquos equilibriumprice we introduce the following conjecture

Conjecture 1 gte objective function Πm in MPSST isstrictly concave wrt the manufacturerrsquos price Pm

Because the second-order derivative of the manufac-turerrsquos profit function has a highly complicated form interms of input parameters it is difficult to prove the con-cavity of the manufacturerrsquos profit function Instead wepresent a simple numerical example to show that Conjecture1 is reasonable We set the parameters as follows α 500βm 4 βr 10 ω 5 δ1 07 c 8 θ 05 Cp 1

Cr1 Cr2 05 and Cc 02 In Figure 3 we can observethat Πm is strictly concave wrt Pm and the maximum isobtained at Pm 115946

Proposition 12 Assuming that Conjecture 1 is true in theStackelberg-Stackelberg pricing game model there exists aunique Stackelberg equilibrium under the manufacturerrsquos pricePSST

m By solving the first-order condition PSSTm is obtained

Proof If Conjecture 1 is true there exists a unique globalmaximizer of MPSST By setting zΠmzPm 0 we obtain theequilibrium solution PSST


e explicit expression of PSSTm is long and complicated


6 Numerical Examples

is section numerically investigates the effects of param-eters on the optimal equilibrium quantities e maindataset used for the analysis is as follows α 500 βm 4βr 10 ω 5 δ1 06 c 8 θ 05 Cp 1Cr1 Cr2 05 and Cc 02 For this dataset we obtain theequilibrium price and profit for each player in the developedpricing game models in the next sections

61 Effect of ω onEquilibriumQuantities Parameter ω in therecyclersrsquo demand functions indicates the competition in-tensity between the two recyclers We are interested in aninvestigation of the effects of the competition intensity onequilibrium prices and profits To do this we consider the


main dataset and vary ω from 0 to 8 e equilibriumquantities of the decision variables and the obtained profitsfor different values of ω are plotted in Figure 4 As the valueof ω increases we observe the following

(i) e manufacturerrsquos and the collectorrsquos prices in-crease in each of the six pricing game models

(ii) In the NCL and the SCL models recycler 1rsquos priceincreases while in the remaining four models re-cycler 1rsquos price decreases

(iii) In the NCL and the SCL models recycler 2rsquos priceincreases In the remaining four models recycler 2rsquosprice initially increases to a certain level ie it has amaximum and then decreases

(iv) e profit of all members except recycler 2 decreasesin each of the six pricing game models

(v) Recycler 2rsquos profit initially increases to a certainlevel ie it has a maximum and then decreases ineach of the six pricing game models is is aninteresting phenomenon by which a recycler withsmaller market share will benefit from limitedcompetition

From the facts observed above we suggest the followingmanagerial insight

Insight 1 As the competition between the two recyclersintensifies the profit of all members except recycler 2decreases is leads to lower total profit of the supplychain In other words competition has a negative effecton the profits of not only the supply chain but also itsmembers Note that the competition intensity ω is thekey parameter for raising the prices of supply chainmembers when the recyclers collude with each other

62 Effect of βr on Equilibrium Quantities Parameter βr inthe recyclersrsquo demand functions indicates the manufac-turerrsquos price sensitivity with regard to the recycled materialsTo investigate the effects of the manufacturerrsquos price sen-sitivity on equilibrium prices and profits we consider themain dataset and vary βr from 55 to 10 Figure 5 shows thetrends of the equilibrium quantities of the decision variables

and the obtained profits for different values of βr As thevalue of βr increases we observe the following

(i) e manufacturerrsquos and the collectorrsquos prices de-crease in each of the six pricing game models

(ii) In the NCL and SCL models recycler 1rsquos and re-cycler 2rsquos prices decrease while in the remainingfour models their prices increase

(iii) e profits of all members in the supply chain in-crease in each of the six pricing game modelserefore the total profit of the supply chain alsoincreases


Insight 2 We can infer that the demand for the finishedproduct is an increasing function of βr is is becausethat as the value of βr increases the manufacturerrsquosprice decreases while the manufacturerrsquos profit in-creases In other words increasing βr boosts the de-mands of all the members in the supply chain eseboosted demands then cause the profits of all membersin the supply chain to increase Consequently the totalprofit of the supply chain also increases Note that themanufacturerrsquos price sensitivity βr is the key parameterfor lowering the prices of supply chain members whenthe recyclers collude with each other

63 Effect of δ1 on Equilibrium Quantities Parameter δi inthe recyclersrsquo demand functions indicates the recycler irsquosmarket share In this section we conduct a sensitivityanalysis of the market share on the equilibrium prices andprofits Varying δ1 from 05 to 07 Figure 6 records thetrends of the equilibrium quantities of the decision variablesand the obtained profits for different values of δ1 As thevalue of δ1 increases (ie recycler 1rsquos market share grows)we observe the following

(i) e manufacturerrsquos and recycler 1rsquos prices increasein each of the six pricing game models

(ii) e collectorrsquos and recycler 2rsquos prices decrease ineach of the six pricing game models

110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit

Figure 3 Concavity of the manufacturerrsquos profit in the SST model


0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)

Figure 4 Effect of ω on equilibrium prices and profits

NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)

Figure 5 Effect of βr on equilibrium prices and profits

NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued


(iii) e profit decreases for all members except forrecycler 1 in each of the six pricing game modelsOnly recycler 1rsquos profit increases


Insight 3 An increase in δ1 means that the imbalance inthe market share is intensifying in the recycling marketAs δ1 increases only the recycler 1rsquos profit increaseswhereas the profits of the other members decreaseiscauses the total profit of the supply chain to decreaseSummarizing the above the imbalance in the marketshare has a negative effect on the profit of the supplychain

64 Effect of θ on EquilibriumQuantities Parameter θ in thecollectorrsquos demand indicates the recyclability of the wastethat can be recovered and turned into raw materials issection investigates the effects of the recyclability degree onthe equilibrium prices and profits Varying θ from 01 to 09Figure 7 records the trends of the equilibrium quantities ofthe decision variables and the obtained profits for differentvalues of θ As the value of θ increases we observe thefollowing

In the Stackelberg game structure of the leaders groupthemanufacturerrsquos price increases However in the NCTandthe NSTmodels the manufacturerrsquos price decreases Finallyin the NCLmodel the manufacturerrsquos price is not affected bythe recyclability

(i) e collectorrsquos price increases in each of the sixpricing game models

(ii) Recycler 1rsquos and recycler 2rsquos prices both decrease ineach of the six pricing game models

(iii) e profit increases for all members except for themanufacturer Only the manufacturerrsquos profitdecreases


Insight 4 As θ increases the profit increases for allmembers except for the manufacturer causing the total

profit of the supply chain to increase e greater therecyclability degree of the waste is the higher the profitsfor all the members involved in the recycling processbecome In other words recyclability has a positiveimpact on the total profit of the supply chain Note thatθ raises the price of the collector while it lowers theprice of both retailers in all game models

65 Effect of c on EquilibriumQuantities Parameter c in therecyclersrsquo demand functions indicates the quantity of therecycled materials required to produce one unit of thefinished product is section investigates the effects of the c

on the equilibrium prices and profits Varying c from 4 to 12Figure 8 records the trends of the equilibrium quantities ofthe decision variables and the obtained profits for differentvalues of c As the value of c increases we observe thefollowing

(i) e price decreases for all members except for themanufacturer in each of the six pricing gamemodelsOnly the manufacturerrsquos price increases

(ii) e profit decreases for all members in each of thesix pricing game models


Insight 5 It is observed that a higher value of c leads tolowering the profits of all members As c increases thequantity of the recycled materials needed to meet thecustomerrsquos demand increases Moreover the collectormust collect more waste leading to higher costs As aresult the profit of the supply chain graduallydecreases

66 Effect of βm on Equilibrium Quantities Parameter βm inthe manufacturerrsquos demand functions indicates the con-sumerrsquos price sensitivity with regard to the finished productWe are interested in an investigation of the effects of βm onequilibrium of prices and profits To do this we consider themain dataset and vary βm from 1 to 7 Figure 9 records thetrends of the equilibrium quantities of the decision variables

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)

Figure 6 Effect of δ1 on equilibrium prices and profits


NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)

Figure 7 Effect of θ on equilibrium prices and profits

NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)

Figure 8 Effect of c on equilibrium prices and profits

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued


and the obtained profits for different values of βm As thevalue of βm increases we observe the following

(i) Prices decrease for all members in each of the sixpricing game models

(ii) Profits decrease for all members in each of the sixpricing game models


Insight 6 It is obvious that as βm increases the demandfor the finished product decreases resulting in loweringthe demands for the recyclable waste and the recycledmaterials respectively As a result the profit for eachmember decreases Note that in all game models βm

lowers the prices of all supply chain members as well astheir profits

67 Comparison among Six Pricing Game Models FromFigures 4ndash9 we can find the following

(i) In the case of the Nash game structure of theleaders group the manufacturerrsquos price is higherthan that of the Stackelberg game structurePNCL

m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm

(ii) In the case of the Stackelberg game structure of theleaders group the collectorrsquos price is higher thanthat of the Nash game structure PNCL

c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST

c (iii) In the case of the Stackelberg game structure of the

leaders group recycler 1rsquos price is higher than thatof the Nash game structure PNCL

r1 ltPSCLr1

PNCTr1 ltPSCT

r1 and PNSTr1 ltPSST

r1 (iv) In the case of the Stackelberg game structure of the


r2 ltPSCLr2

PNCTr2 ltPSCT


r2 (v) In the case of the Stackelberg game structure of the

leaders group the manufacturerrsquos profit is higherthan that of the Nash game structureΠNCLm ltΠ

SCLm

ΠNCTm ltΠSCTm and ΠNSTm ltΠ

SSTm In terms of prof-

itability the SCL (NCT) pricing game model is the

most advantageous (disadvantageous) for themanufacturer

(vi) In the case of the Stackelberg game structure of theleaders group the collectorrsquos profit is higher thanthat of the Nash game structure ΠNCLc ltΠ

SCLc

ΠNCTc ltΠSCTc and ΠNSTc ltΠ

SSTc In terms of prof-

itability the SCL (NCL) pricing game model is themost advantageous (disadvantageous) for thecollector

(vii) In the case of the Stackelberg game structure of theleaders group the recycler 1rsquos profit is higher thanthat of the Nash game structure ΠNCLr1 ltΠ

SCLr1

ΠNCTr1 ltΠSCTr1 and ΠNSTr1 ltΠ

SSTr1 In terms of profit-

ability the SCL (NCT) pricing game model is themost advantageous (disadvantageous) for recycler 1

(viii) In the case of the Stackelberg game structure of theleaders group the recycler 1rsquos profit is higher thanthat of the Nash game structure ΠNCLr2 ltΠ

SCLr2




(ix) In terms of the total profit of the supply chain theStackelberg game structure of the leaders groupoutperforms the Nash game structure In additionthe recyclersrsquo Collusion (Cournot) behavior per-forms the best (the worst)ΠNCTsc ltΠ

NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where

Πsc is the total profit of the supply chain

7 Conclusion

In this work we discussed a topic related to environmentalsustainability through an investigation of the collecting andrecycling processes of recyclable waste in a three-echelonCLSC consisting of onemanufacturer one collector and tworecyclers is study utilized game theory to model theproblem of determining the equilibrium prices of partici-pants in the investigated supply chain considered We as-sumed that the manufacturer and the collector belong to theleaders group and that the two recyclers belong to thefollowers group In the leaders group we dealt with twopricing structure types the Stackelberg and Nash types In

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)

Figure 9 Effect of βm on equilibrium prices and profits


the followers group price competition was assumed to existbetween the two recyclers and we dealt with three types ofcompetition behavior for the recyclers Collusion Cournotand Stackelberg With the two pricing structure types in theleaders group and the three types of competition behavior inthe followers group six different pricing game models weredeveloped For each of the pricing game models theuniqueness of equilibrium and optimal pricing was ana-lytically proved Finally various numerical experimentswere conducted to investigate the effects of the experimentalparameters on the equilibrium prices and profits of thesupply chain members To the best of our knowledge thecurrent paper is the first to consider the concept of sellingprice competition between recyclers in a three-echelonCLSC

In terms of the total profit of this supply chain our mainfindings are as follows

(i) As the price competition intensifies between therecyclers the total profit of the supply chaindecreases

(ii) e higher the manufacturerrsquos price sensitivity forthe recycled materials is the higher the total profitof the supply chain becomes

(iii) As the imbalance in the market share intensifies inthe recycling market the total profit of the supplychain decreases

(iv) e more likely the waste is to be recycled thehigher the total profit of the supply chain

(v) As the quantity of the recycled materials required toproduce a finished product increases the totalprofit of the supply chain decreases

(vi) e Stackelberg game structure of the leaders groupoutperforms the Nash game structure

(vii) e recyclersrsquo Collusion (Cournot) behavior per-forms the best (the worst)

Several future research studies related to this topic arepossible One can modify the model to consider differentcoordination contracts between the players to obtain higherprofits Moreover different demand patterns especially ofthe nonlinear demand of the consumer can be assumedwhen studying similar types of problems Another possi-bility is to consider the price competition between manu-facturers and collectors and to analyze their outcomes

Appendix

A Solving Procedure for the EquilibriumPrices

For all g isin NCTNST

Step 1 set Pri Pgri i 1 2

Step 2 solve the equations system zΠczPc 0 andzΠmzPm 0 wrt Pc and Pm and set the roots to thecollectorrsquos price P

gc and the manufacturerrsquos price P

gm

respectivelyStep 3 calculate P

gri Pri(P

gm P

gc ) i 1 2

B Solving Procedure for the EquilibriumPrices

For all g isin SCT SST

Step 1 set Pc Pgc and Pri P

gri i 1 2

Step 2 solve the equation zΠmzPm 0 wrt Pm andset the root to the manufacturerrsquos price P

gm

Step 3 calculate Pgc Pc(P

gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability

No data were used to support this study

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by Basic Science Research throughthe National Research Foundation of Korea (NRF) fundedby the Ministry of Education (NRF-2018R1D1A3B07040887)

References

[1] F Taghikhah A Voinov and N Shukla ldquoExtending thesupply chain to address sustainabilityrdquo Journal of CleanerProduction vol 229 pp 652ndash666 2019

[2] D OrsquoRourke ldquoe science of sustainable supply chainsrdquoScience vol 344 pp 1124ndash1127 2014

[3] M-L TsengM S Islam N Karia F A Fauzi and S Afrin ldquoAliterature review on green supply chain management trendsand future challengesrdquo Resources Conservation and Recyclingvol 141 pp 145ndash162 2019

[4] M Xu Y Cui M Hu et al ldquoSupply chain sustainability riskand assessmentrdquo Journal of Cleaner Production vol 225pp 857ndash867 2019

[5] A A Hervani M M Helms and J Sarkis ldquoPerformancemeasurement for green supply chain managementrdquo Bench-marking An International Journal vol 12 no 4 pp 330ndash3532005

[6] H Lorentz Y Shi O-P Hilmola J Srai and K Hung LauldquoBenchmarking green logistics performance with a compositeindexrdquo Benchmarking An International Journal vol 18 no 6pp 873ndash896 2011

[7] A Parmigiani R D Klassen and M V Russo ldquoEfficiencymeets accountability performance implications of supplychain configuration control and capabilitiesrdquo Journal ofOperations Management vol 29 no 3 pp 212ndash223 2011

[8] J Sarkis ldquoA boundaries and flows perspective of green supplychain managementrdquo Supply Chain Management An Inter-national Journal vol 17 no 2 pp 202ndash216 2012

[9] M Grimmer and T Bingham ldquoCompany environmentalperformance and consumer purchase intentionsrdquo Journal ofBusiness Research vol 66 no 10 pp 1945ndash1953 2013

[10] M G Luchs R W Naylor J R Irwin and R Raghunathanldquoe sustainability liability potential negative effects of eth-icality on product preferencerdquo Journal of Marketing vol 74no 5 pp 18ndash31 2010


[11] K Salimifard and R Raeesi ldquoA green routing problemoptimising COrdquo International Journal of Advanced Opera-tions Management vol 6 no 1 pp 27ndash57 2014

[12] P C Chen M C Chiu and H W Ma ldquoMeasuring thereduction limit of repeated recycling a case study of the paperflow systemrdquo Journal of Cleaner Production vol 132pp 98ndash107 2016

[13] J M Allwood M F Ashby T G Gutowski and E WorrellldquoMaterial efficiency a white paperrdquo Resources Conservationand Recycling vol 55 pp 362ndash381 2011

[14] A Ashby M Leat and M Hudson-Smith ldquoMaking con-nections a review of supply chain management and sus-tainability literaturerdquo Supply Chain Management AnInternational Journal vol 17 pp 497ndash516 2012

[15] R B Handfield and E L Nichols Supply Chain RedesignTransforming Supply Chains into Integrated Value Systems FTPress Upper Saddle River NJ USA 2002

[16] M Eskandarpour P Dejax J Miemczyk and O PetonldquoSustainable supply chain network design an optimization-oriented reviewrdquo Omega vol 54 pp 11ndash32 2015

[17] L Feng K Govindan and C Li ldquoStrategic planning designand coordination for dual-recycling channel reverse supplychain considering consumer behaviorrdquo European Journal ofOperational Research vol 260 no 2 pp 601ndash612 2017

[18] M Huang M Song L H Lee andW K Ching ldquoAnalysis forstrategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economicsvol 144 no 2 pp 510ndash520 2013

[19] C P Balde V Forti V Gray R Kuehr and P StegmanngteGlobal E-Waste Monitor 2017 httpswwwituintenITU-DClimate-ChangeDocumentsGEM202017Global-E-waste20Monitor20201720pdf

[20] H Jafari S R Hejazi and M Rasti-Barzoki ldquoSustainabledevelopment by waste recycling under a three-echelon supplychain a game-theoretic approachrdquo Journal of Cleaner Pro-duction vol 142 pp 2252ndash2261 2017

[21] A C S Amaro and A P F D Barbosa-Povoa ldquoe effect ofuncertainty on the optimal closed-loop supply chain planningunder different partnerships structurerdquo Computers ampChemical Engineering vol 33 pp 2144ndash2158 2009

[22] M Geissdoerfer S N Morioka M M de Carvalho andS Evans ldquoBusiness models and supply chains for the circulareconomyrdquo Journal of Cleaner Production vol 190 pp 712ndash721 2018

[23] N M Bocken I de Pauw C Bakker and B van der GrintenldquoProduct design and business model strategies for a circulareconomyrdquo Journal of Industrial and Production Engineeringvol 33 pp 308ndash320 2016

[24] R C Savaskan S Bhattacharya and L N Van WassenhoveldquoClosed-loop supply chain models with product remanu-facturingrdquo Management Science vol 50 pp 239ndash252 2004

[25] R C Savaskan and L N Van Wassenhove ldquoReverse channeldesign the case of competing retailersrdquoManagement Sciencevol 52 pp 1ndash14 2006

[26] Y J Chen and J-B Sheu ldquoEnvironmental-regulation pricingstrategies for green supply chain managementrdquo Trans-portation Research Part E Logistics and Transportation Re-view vol 45 no 5 pp 667ndash677 2009

[27] A Atasu L B Toktay and L N Van Wassenhove ldquoHowcollection cost structure drives a manufacturerrsquos reversechannel choicerdquo Production and Operations Managementvol 22 no 4 pp 1089ndash1102 2013

[28] X Hong Z Wang and D Wang ldquoDecision models of closed-loop supply chain with remanufacturing under hybrid dual-

channel collectionrdquo gte International Journal of AdvancedManufacturing Technology vol 68 no 5ndash8 pp 1851ndash18652013

[29] N Wang Q He and B Jiang ldquoHybrid closed-loop supplychains with competition in recycling and product marketsrdquoInternational Journal of Production Economics vol 217pp 246ndash258 In press 2019

[30] N M Modak N Modak S Panda and S S Sana ldquoAnalyzingstructure of two-echelon closed-loop supply chain for pricingquality and recycling managementrdquo Journal of Cleaner Pro-duction vol 171 pp 512ndash528 2018

[31] N M Modak S Panda and S S Sana ldquoTwo-echelon supplychain coordination among manufacturer and duopolies re-tailers with recycling facilityrdquo gte International Journal ofAdvanced Manufacturing Technology vol 87 no 5ndash8pp 1531ndash1546 2015

[32] S Saha S P Sarmah and I Moon ldquoDual channel closed-loopsupply chain coordination with a reward-driven remanu-facturing policyrdquo International Journal of Production Re-search vol 54 no 5 pp 1503ndash1517 2016

[33] L Liu ZWang L Xu X Hong and K Govindan ldquoCollectioneffort and reverse channel choices in a closed-loop supplychainrdquo Journal of Cleaner Production vol 144 pp 492ndash5002017

[34] B C Giri and S K Dey ldquoGame theoretic analysis of a closed-loop supply chain with backup supplier under dual channelrecyclingrdquo Computers amp Industrial Engineering vol 129pp 179ndash191 2019

[35] J Wei Y Wang J Zhao and E D R Santibanez GonzalezldquoAnalyzing the performance of a two-period remanufacturingsupply chain with dual collecting channelsrdquo Computers ampIndustrial Engineering vol 135 pp 1188ndash1202 2019

[36] H Jian M Xu and L Zhou ldquoCollaborative collection effortstrategies based on ldquoInternet + recyclingrdquo business modelrdquoJournal of Cleaner Production vol 241 p 118120 2019

[37] I E Nielsen S Majumder and S Saha ldquoGame-theoreticanalysis to examine how government subsidy policies affect aclosed-loop supply chain decisionrdquo Applied Sciences vol 10no 1 p 145 2020

[38] S Saha I E Nielsen and S Majumder ldquoDilemma in twogame structures for a closed-loop supply chain under theinfluence of government incentivesrdquo Journal of IndustrialEngineering International vol 15 no S1 pp 291ndash308 2019

[39] N M Modak S Panda and S X Sana ldquoPricing policy andcoordination for a two-layer supply chain of duopolistic re-tailers and socially responsible manufacturerrdquo InternationalJournal of Logistics Research and Applications vol 19pp 487ndash508 2016

[40] 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 pp 11ndash21 2017

[41] N MModak S Sinha S Panda and N Kazemi ldquoAnalyzing asocially responsible closed-loop distribution channel withrecycling facilityrdquo SN Applied Sciences vol 1 no 10 p 11892019

[42] N M Modak and P Kelle ldquoUsing social work donation as atool of corporate social responsibility in a closed-loop supplychain considering carbon emissions tax and demand uncer-taintyrdquo Journal of the Operational Research Society 2019 Inpress

[43] 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


Responsibility practicerdquo International Journal of ProductionEconomics vol 207 pp 19ndash33 2019

[44] N Kazemi N M Modak and K Govindan ldquoA review ofreverse logistics and closed loop supply chain managementstudies published in IJPR a bibliometric and content anal-ysisrdquo International Journal of Production Research vol 57no 15-16 pp 4937ndash4960 2019

[45] 8 Companies that Only Sell 100 Percent Recycled Productshttpsgreenbusinessbureaucomblog8-companies-that-only-sell-100-percent-recycled-products

[46] M-B Jamali and M Rasti-Barzoki ldquoA game theoretic ap-proach to investigate the effects of third-party logistics in asustainable supply chain by reducing delivery time and carbonemissionsrdquo Journal of Cleaner Production vol 235 pp 636ndash652 2019

[47] W Li and J Chen ldquoBackward integration strategy in a retailerStackelberg supply chainrdquo Omega vol 75 pp 118ndash130 2018

[48] N M Modak S Panda and S S Sana ldquoree-echelon supplychain coordination considering duopolistic retailers withperfect quality productsrdquo International Journal of ProductionEconomics vol 182 pp 564ndash578 2016

[49] T Chakraborty S S Chauhan and N Vidyarthi ldquoCoordi-nation and competition in a common retailer channelwholesale price versus revenue-sharing mechanismsrdquo Inter-national Journal of Production Economics vol 166 pp 103ndash118 2015

[50] 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


material-cycle society by implementing the 3R (reducereuse and recycle) strategy [13] Material and energy flowsmust become part of an increasingly sustainable and circulareconomy a concept introduced by the European Union asfollows In a circular economy the value of products andmaterials is maintained for as long as possible Waste andresource use are minimized and when a product reaches theend of its life it is used again to create further valueis canbring major economic benefits contributing to innovationgrowth and job creation In 2018 Apple announced that the2018 models of its MacBook Air and Mac mini would bothbe manufactured with 100 percent recycled aluminumAdditionally the Mac mini would be constructed from 60percent recycled plastic

Recycling is the process of collecting and processing wastethat would otherwise be thrown away as trash and turning thewaste into new products for environmental protection It alsoincludes the optimal management of waste disposal facilitiesAnother aim of recycling is to encourage ecofriendly man-agement and to manage limited supplies of resources esupply chain term refers to a type of systematic collaborationbetween people processes and information to create tangibleor intangible value and deliver it to consumers e mainpurpose of supply chain management is to facilitate bettermaterial and information flows among stakeholders in thesupply chain is creates a better relationship betweenstakeholders in the supply chain which increases the prof-itability of the entire supply chain [14 15] With the depletionof resources around the world waste from end-of-lifeproducts is becoming an important resource that can bemanaged globally As consumersrsquo interest in environmentalissues has increased along with the amounts of waste in-dustrialists and researchers are now focusing on sustainableproducts Reverse and closed-loop supply chains are welladapted to sustainability goals [16] Generally a reversesupply chain and closed-loop supply chain consist of certainoperations such as collecting recyclable waste transforming itinto new materials and transferring these materials to amanufacturer for remanufacturing A dual channel for col-lection can also be implemented in the supply chainSometimes it is found that dual-channel recycling outper-forms single-channel recycling [17 18]

Recyclability is a characteristic of amaterial that can retainuseful chemical andor physical properties after achievingtheir original purpose thus allowing it to be reused orremanufactured into additional products through a recog-nized process us recyclability must be observed andconsidered as the baseline during design production andwaste management activities With the development of in-formation and communication technology (ICT) the de-mand for electronic products has increased greatly and thishas led to more generation of waste electrical and electronicequipment (WEEE) e disruption of rare-earth metal ex-ports to Japan triggered by the Senkaku Islands dispute in2010 led to confusion not only in Japan but also in the globalmarket paradoxically emphasizing the importance of se-curing resources In 2016 the potential recovery of sevenprecious resources specifically iron copper gold silveraluminum palladium and plastics in WEEE amounts to

approximately 123 million tonnes in Europe [19] In light ofthis fact the recyclability ofWEEE plays a key role not only interms of environmental protection but also with regard to thestable supply and demand for various ICT products

Based on these observations this paper deals with aclosed-loop supply chain in which two recyclers competewith each other More specifically each recycler purchasesrecyclable waste from a collector recycles the waste andfinally sells the recycled materials to a manufacturer In thisprocess the two recyclers compete with regard to the sellingprices of their recycled materials e aim of this study is toinvestigate pricing and ordering decisions during the wasterecycling process in a three-echelon closed-loop supplychain with duopolistic recyclers using a game-theoreticframework Due to the competition between recyclers theprice offered by one recycler affects not only the price of theother recycler but also those of all other members in thesupply chain erefore demand and profit in the supplychain are sensitive in all cases to price competition isstudy proposes several pricing game models based onpricing structures and competitive behavior e main re-search questions for this study are as follows

(i) How can each member in the supply chain increasethe profit

(ii) What are the profits and equilibrium variables of thesupply chain members

(iii) How strong is the effect of the price competitionbetween recyclers in the supply chain

(iv) Does the recyclability degree of wastes have apositive effect on the profit of each member in thesupply chain

(v) Does an imbalance in the market share betweencompetitors affect the profit of the entire supplychain

In order to answer the above questions we revisit Jafariet alrsquos study [20] by considering price competition be-tween recyclers e main contributions of this researchare threefold First the impact of price competition be-tween recyclers with different competitive behaviors onthe sustainability of the supply chain is investigatedSecond our study concerns the economic as well as en-vironmental aspects of the supply chain ird we suggestsix different pricing game models and show the existenceof equilibrium solutions for each game Finally wecompare the results of the six pricing game modelsthrough a numerical example

e rest of this study is organized as follows In Section2 we present a brief overview of the relevant literatureafter which we introduce the six pricing game models andthen review the notations used and assumptions in Sec-tion 3 In Section 4 we conduct a preliminary analysis ofour main results Section 5 deals with the equilibriumquantities for each of the six pricing game models Var-ious numerical experiments are conducted in Section 6 toinvestigate the effects of certain parameters on theequilibrium quantities In Section 6 we give a summary ofthe paper and provide future research topics


2 Literature Review










Index

i recyclers (i 1 2)

Decision variables



Parameters






Functions
















PriDmi


Πc 1113944i


(2)




Collector


Manufacturer

Market

MaterialCash








Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i



(3)



ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873




HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)







Stackelberg




Nash



profit



profit

Leaders group

Collusion



Cournot




independently




independently

Followers group

Stackelberg







2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































2 Literature Review










Index

i recyclers (i 1 2)

Decision variables



Parameters






Functions
















PriDmi


Πc 1113944i


(2)




Collector


Manufacturer

Market

MaterialCash








Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i



(3)



ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873




HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)







Stackelberg




Nash



profit



profit

Leaders group

Collusion



Cournot




independently




independently

Followers group

Stackelberg







2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References




























































Index

i recyclers (i 1 2)

Decision variables



Parameters






Functions
















PriDmi


Πc 1113944i


(2)




Collector


Manufacturer

Market

MaterialCash








Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i



(3)



ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873




HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)







Stackelberg




Nash



profit



profit

Leaders group

Collusion



Cournot




independently




independently

Followers group

Stackelberg







2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References





























































PriDmi


Πc 1113944i


(2)




Collector


Manufacturer

Market

MaterialCash








Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i



(3)



ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873




HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)







Stackelberg




Nash



profit



profit

Leaders group

Collusion



Cournot




independently




independently

Followers group

Stackelberg







2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References





























































Pr1 Pr2( )isinR2+

Πrt Pr1 Pr2( 1113857 1113936i



(3)



ri

PCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873




HCLr

z2Πrt

zP2r1

z2Πrt

zPr1zPr2

z2Πrt

zPr2zPr1

z2Πrt

zP2r2

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

minus 2βr ω

ω minus 2βr

⎡⎢⎢⎢⎢⎣ ⎤⎥⎥⎥⎥⎦ (5)







Stackelberg




Nash



profit



profit

Leaders group

Collusion



Cournot




independently




independently

Followers group

Stackelberg







2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References


























































2βrθ


2βrθ

(6)




RPCTi max

PriisinR+



(7)



ri

PCTri


θ 4β2r minus ω21113872 1113873


(8)




Pr1 βr Pc + Cr1( 1113857 + θωPr2 + Kδ1

2θβr

Pr2 βr Pc + Cr2( 1113857 + θωPr1 + Kδ2

2θβr

(9)




RPST2 max

Pr2isinR+


st Πr2 Pr2( 1113857gt 0

RPST1 maxPr1isinR+



Πr1 Pr1( 1113857gt 0

(10)



ri

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSTr2

ωPSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(11)



PSTr2

ωPr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(12)




1 is given by

PSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873 (13)








PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References

























































PNCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(14)


CPNCL maxPcisinR+

Πc Pc( 1113857 1113944i


st eq (14)

Πc Pc( 1113857gt 0

MPNCL maxPmisinR+


PriDmi

st eq(14)

Πm Pm( 1113857gt 0

(15)




PNCLc


4+



PNCLm

αβm



(16)


z2Πc

zP2c


θ2lt 0

z2Πm

zP2m


2i1113872 1113873

2 β2r minus ω21113872 1113873⎡⎢⎣ ⎤⎥⎦lt 0

(17)



4+

K

4 βr minus ω( 1113857




⎡⎢⎣ ⎤⎥⎦

(18)



PNCLri

PNCLc + Cri

2θ+


2θ β2r minus ω21113872 1113873


(19)


PNCTri


θ 4β2r minus ω21113872 1113873


(20)


CPNCT maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(20)

Πc Pc( 1113857gt 0

MPNCT maxPmisinR+


PriDmi

st eq(20)

Πm Pm( 1113857gt 0

(21)






z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References

























































z2Πc

zP2c



z2Πm

zP2m

minus 2βm 1 + X1( 1113857lt 0

(22)

where


2i1113960 1113961

4β2r minus ω21113872 11138732 gt 0 (23)








PNSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PNSTr2

ωPNSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(24)


CPNST maxPcisinR+

Πc Pc( 1113857 1113944i


st eq(24)

Πc Pc( 1113857gt 0

MPNST maxPmisinR+


PriDmi

st eq(24)

Πm Pm( 1113857gt 0

(25)





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873 (26)





21 minus ω4δ221113966 1113967

16βr 2β2r minus ω21113872 11138732 (27)



22(8β






proof







PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References



























































PSCLri

Pc + Cri

2θ+

K βrδi + ωδj1113872 1113873


(28)


CPSCL maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(28)

Πc Pc( 1113857gt 0

(29)



PSCLc


4+

K

4 βr minus ω( 1113857 (30)





MPSCL maxPmisinR+


PriDmi

st eqs(28) and (30)

Πm Pm( 1113857gt 0

(31)


m

PSCLm




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

(33)




z2Πm

zP2m

βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

le βm


16 β2r minus ω21113872 1113873minus 2

⎧⎨

⎩

⎫⎬

⎭

minus βm

3c2βm

16 βr minus ω( 1113857+ 21113890 1113891

(34)







PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References



























































PSCLc


4+


4 βr minus ω( 1113857

PSCLr1


c + Cr1( 1113857

2θ β2r minus ω21113872 1113873

PSCLr2


c + Cr2( 1113857

2θ β2r minus ω21113872 1113873

(35)



PSCTri


θ 4β2r minus ω21113872 1113873


(36)


CPSCT maxPcisinR+

Πc Pc( 1113857 1113936i


st eq(36)

Πc Pc( 1113857gt 0

(37)



PSCTc


4+

K

4 βr minus ω( 1113857 (38)






MPSCT maxPmisinR+


PriDmi

st eqs(36) and (38)

Πm Pm( 1113857gt 0

(39)



m is obtained


z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


(40)




z2Πm

zP2m

βm

4c2δ1δ2βmβr

2βr + ω( 11138572 +

c2βmβrX3


le βm

c2βmβr

2βr + ω( 11138572 +

c2βmβrX3


minus βm



(41)




z2Πm

zP2m

lt 0 (42)








PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References

























































PSSTr1

Pc + Cr1

2θ+βrω Pc + Cr2( 1113857 + K 2βrδ1 + ωδ2( 1113857

2θ 2β2r minus ω21113872 1113873

PSSTr2

ωPSSTr1

2βr

+Pc + Cr2

2θ+

Kδ22θβr

(43)


CPSST maxPcisinR+

Πc Pc( 1113857 1113936i


st eq (43)

Πc Pc( 1113857gt 0

(44)



PSSTc

14





z2Πc

zP2c


2θ2βr 2β2r minus ω21113872 1113873lt 0 (46)




MPSST maxPmisinR+


PriDmi

st eqs(43) and (45)

Πm Pm( 1113857gt 0

(47)

































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References










































































110 112 114 116 118 120

1400

1600

1800

2000

2200

PmM

anuf

actu

rerrsquos

pro

fit



0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































0 2 4 6 8

110

115

120

ω

Man

ufac

ture

rrsquos p

rice

NCLNCTNST

SCLSCTSST

(a)

NCLNCTNST

SCLSCTSST

0 2 4 6 8

6

7

8

9

ω

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

0 2 4 6 8ω

Recy

cler

1rsquos

pric

e

1618202224262830

(c)

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

16182022242628

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

1000

2000

3000

4000M

anuf

actu

rerrsquos

pro

fit

(e)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Colle

ctor

rsquos pr

ofit

500

1000

1500

(f )

ω

NCLNCTNST

SCLSCTSST

0 2 4 6 8

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

50

100

150

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

ω0 2 4 6 8

Supp

ly ch

ain

prof

it

200030004000500060007000

(i)


NCLNCTNST

SCLSCTSST

6 7 8 9 10114

116

118

120

122

124

βr

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

6

7

8

9

10

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Recy

cler

1rsquos

pric

e

20

25

30

(c)

Figure 5 Continued


NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































NCLNCTNST

SCLSCTSST

βr

6 7 8 9 1015

20

25

30

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

500

1000

1500

2000

2500

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Colle

ctor

rsquos pr

ofit

200400600800

10001200

(f )

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

100

200

300

400

500

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 100

50

100

150Re

cycl

er 2

rsquos pr

ofit

(h)

NCLNCTNST

SCLSCTSST

βr

6 7 8 9 10

Supp

ly ch

ain

prof

it

1000

2000

3000

4000

(i)


NCLNCTNST

SCLSCTSST

050 055 060 065 070114

115

116

117

δ1

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07055606570758085

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Recy

cler

1rsquos

pric

e

18

20

22

24

26

(c)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 07014161820222426

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

220023002400250026002700

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Colle

ctor

rsquos pr

ofit

800900

1000

1200

1400

(f)

Figure 6 Continued




















NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References










































































NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

200300400500600700

Recy

cler

1rsquos

profi

t

(g)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

50100150200250300350

Recy

cler

2rsquos

profi

t

(h)

NCLNCTNST

SCLSCTSST

δ1

050 055 060 065 070

Supp

ly ch

ain

profi

t

3500

4000

4500

(i)



NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































NCLNCTNST

SCLSCTSST

02 04 06 08

1180

1190

1200

θ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

02 04 06 08

5

10

15

θ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Recy

cler

1rsquos

pric

e

20

25

30

(c)

NCLNCTNST

SCLSCTSST

02 04 06 0815

20

25

30

θ

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

02 04 06 08

140015001600170018001900

θ

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

02 04 06 08θ

Colle

ctor

rsquos pr

ofit

300400500600700800900

(f )

NCLNCTNST

SCLSCTSST

θ02 04 06 08

50100150200250300350

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

20406080

100120

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

θ02 04 06 08

Supp

ly ch

ain

prof

it

1800

2200

2600

3000

(i)


NCLNCTNST

SCLSCTSST

4 6 8 10 12

105

110

115

120

γ

Man

ufac

ture

rrsquos p

rice

(a)

NCLNCTNST

SCLSCTSST

4 6 8 10 124

6

8

10

12

14

γ

Colle

ctor

rsquos pr

ice

(b)

NCLNCTNST

SCLSCTSST

4 6 8 10 12γ

Recy

cler

1rsquos

pric

e

152025303540

(c)

Figure 8 Continued


NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

10152025303540

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

1000

2000

3000

4000

5000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Colle

ctor

rsquos pr

ofit

500

1000

1500

2000

(f )

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

200

400

600

800

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

50100150200250300

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

γ4 6 8 10 12

Supp

ly ch

ain

prof

it

2000

4000

6000

8000

(i)


NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

100150200250300350400

Man

ufac

ture

rrsquos p

rice

βm

(a)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

5

10

15

20

Colle

ctor

rsquos pr

ice

βm

(b)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

Recy

cler

1rsquos

pric

e

βm

10203040506070

(c)

NCLNCTNST

SCLSCTSST

1 2 3 4 5 6 7

102030405060

βm

Recy

cler

2rsquos

pric

e

(d)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

500010000

20000

Man

ufac

ture

rrsquos p

rofit

(e)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 7

Colle

ctor

rsquos pr

ofit

0

2000

4000

6000

8000

10000

(f )

Figure 9 Continued










m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
































































m gtPSCLm PNCT

m gtPSCTm and PNST

m gtPSSTm


c ltPSCLc

PNCTc ltPSCT

c and PNSTc ltPSST



r1 ltPSCLr1

PNCTr1 ltPSCT




r2 ltPSCLr2

PNCTr2 ltPSCT




SCLm






SCLc





SCLr1





SCLr2





NSTsc ltΠ

NCLsc ltΠ

SCTsc ltΠ

SSTsc ltΠ

SCLsc where


7 Conclusion


NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

1000

2000

3000

4000

Recy

cler

1rsquos

prof

it

(g)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

200400600800

10001200

Recy

cler

2rsquos

prof

it

(h)

NCLNCTNST

SCLSCTSST

βm

1 2 3 4 5 6 70

10000

20000

30000

40000

Supp

ly ch

ain

prof

it

(i)













Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References


































































Appendix






gm


gri Pri(P

gm P

gc ) i 1 2




gri i 1 2


gm


gm) and P

gri Pri(P

gm P

gc )

i 1 2

Data Availability




Acknowledgments


References
























































PricingDecisionsinaCompetitiveClosed-LoopSupplyChainwith … · 2020. 4. 18. · recycling process...

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