Alliance or no alliance-Bargaining power in competing reverse supply chains

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Alliance or no alliance—Bargaining power in competing reverse supply

chains

Jiuh-Biing Sheu

a,⇑

_{, Xiao-Qin Gao}

b

a

Department of Business Administration, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, ROC

b

Institute of Trafﬁc and Transportation, National Chiao Tung University, 4F, 118 Chung Hsiao W. Road, Sec. 1, Taipei 10012, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Available online 26 September 2013 Keywords:

Supply chain management Environment

Strategic alliance Bargaining power

a b s t r a c t

This work investigates how bargaining power affects negotiations between manufacturers and reverse logistics providers in reverse supply chains under government intervention using a novel three-stage reverse supply chain model for two scenarios, a reverse logistics provider alliance and no reverse logistics provider alliance. Utilizing the asymmetric Nash bargaining game, this work seeks equilibrium negotia-tion solunegotia-tions. Analytical results indicate that the reverse logistics provider alliance increases the bar-gaining power of reverse logistics providers when negotiating with a manufacturer for a profitable recycled-component supply contract; however, manufacturer profits are often reduced. Particularly in the case of an recycled-component vender-dominated market, a reverse logistics alliance with extreme bargaining power may cause a counter-profit effect that results in the decreases of profits for all players involved, including buyers (i.e., manufacturers) and allied recycled-component venders (i.e., reverse logis-tics providers). Additional managerial insights are provided for discussion.

1. Introduction

As the concept of extended producer responsibility (EPR) has emerged along with government intervention, interactions between manufacturers and reverse logistics (RL) providers are unavoidable in cooperative reverse supply chains. Practical cases in various man-ufacturing industries, such as the high-tech manman-ufacturing, auto-mobile, iron and steel, textile, and garment industries, further demonstrate the increasing importance of cooperating with RL pro-viders in reverse supply chains, particularly under government intervention. For example, China consumes over 200 million tons of steel annually, including 20 million tons of steel made from steel scrap, 26 million tons of iron recycled by society, and 13 million tons from productive and non-productive recycling of steel scrap. Most Chinese iron and steel manufacturers rely on RL providers to recycle iron and steel scrap at low operational costs and with high efﬁciency, such that the steel manufacturers can focus on their core businesses. Another example is the electronics manufacturing industry. For in-stance, ASUS, a well-known global branded computer manufacturer, has recently has adopted green practices (e.g., green procurement, green design, and green manufacturing) to carry out its so-called ‘‘Green ASUS’’ strategy. In terms of green procurement, ASUS uses Acrylonitrile–Butadiene-Styrene plastic for the housing of its

note-book computers. Nevertheless, the Regulations on the Administra-tion of the Recovery and Disposal of Waste Electrical and Electronic Products are now enforced in China (Ministry of

Environ-mental Protection, China, 2011), as are the Restriction on Hazardous

Substances (RoHS) and Waste Electrical and Electronic Equipment (WEEE) directives in European Union nations. To comply with these new green regulations, ASUS must increase its purchase of recycled Acrylonitrile–Butadiene-Styrene plastic, which is produced by RL providers through reprocessing shredded transfusion tubes, plastic products, and plastic housings of discarded electronics products. Not surprisingly, as a global manufacturer of green notebook com-puters, ASUS must negotiate with RL providers to procure recycled Acrylonitrile–Butadiene-Styrene plastic.

Typically, via negotiation between a manufacturer and an RL provider, a contract is established for recycled material price and amount. The RL providers include recyclers that provide recycled components by recycling end-of-life products for the production of green products by manufacturers. Such a producer-RL provider negotiation process toward a contractual agreement is indispensi-ble, particularly for those highly proﬁtable recycled-materials, e.g., gold, aluminum, copper, palladium, and other precious metals, that can be reused through recovery and recycling processes from elec-tronic wastes (Chen, Sheu, & Lirn, 2012; Kang & Schoenung, 2005). Thus, RL providers play an important role in cooperative reverse supply chains by providing end-customers with opportunities to return defective products for repair (Tug˘ba, Semih, & Elif, 2008)

and by collecting and recycling end-of-life products for

⇑ Corresponding author. Tel.: +886 2 3366 1069.

E-mail addresses: jbsheu@ntu.edu.tw (J.-B. Sheu), carrollgxq@126.com (X.-Q. Gao).

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manufacturers (Guide, Jayaraman, Srivastava, & Benton, 2000), while conforming with green laws/regulations implemented by governments.

Nevertheless, the cooperative reverse supply chain negotiations cannot ignore the issue of bargaining power (DiMatteo, Prentice,

Morant, & Barnhizer, 2007). Bargaining power has been deﬁned

as the ability of one party to inﬂuence the terms and conditions in a contract or subsequent contracts in its favor due to its posses-sion of unique and valuable resources (Argyres & Liebeskind,

1999). Inderst (2002) claimed that contractual distortions are

caused typically by asymmetric bargaining power during negotia-tion.Crook and Combs (2007)further suggested that bargaining power differs among supply chain members. One notable example is the power-dependence relationship between Wal-Mart and its suppliers, where only large suppliers have an ability to exert coun-tervailing power when facing Wal-Mart’s ‘‘big squeeze’’ (Bloom &

Perry, 2001).

Furthermore, a shift in bargaining power caused by either gov-ernment intervention or an RL alliance may increase the complex-ity of such bilateral negotiations. Based on resource dependence theory (Pfeffer & Salancik, 1978; Ulrich & Barney, 1984), we pro-pose that government intervention can increase the dependence of a manufacturer on an RL provider’s resources to comply with green regulations (e.g., take-back laws). According to Pfeffer and

Salancik (1978), organizations are rarely self-sufﬁcient with

re-spect to their critical resources and, thus, are dependent upon the resources of others for survival in competitive environments. Conversely, we argue that government intervention increases the likelihood of an RL provider exerting countervailing power through an RL alliance to seek a balanced power relationship when negoti-ating with manufacturers. For example, government intervention via green legislation and ﬁnancial incentives has altered the rela-tive power of manufacturers and RL providers during negotiations. This argument is based on evidence from several practical cases in Europe, indicating that recyclers inﬂuence producer market share and costs for WEEE compliance (Clean Production Action. 2003;

Stevels & Huisman, 2005). Particularly, strategic alliances of RL

providers that have relatively less power than manufacturers seek opportunities to gain additional beneﬁts while bargaining with manufacturers. This scenario has been observed increasingly in anecdotal evidence and real-world cases. Moreover, an RL alliance is very likely to facilitate a reduction in RL operational costs by consolidating small volumes of scattered RL tasks with similar attributes into full load tasks to attain economies of scale (Liu &

Zhang, 2008).

Although the number of RL studies has grown steadily, reflect-ing the increasreflect-ing significance of RL in the context of government intervention, these studies primarily provide a strong basis for developing general frameworks and mathematical models for ana-lyzing RL operational performance and practices for the case of no RL alliance.Krumwiedea and Sheu (2002)established an RL deci-sion-making model to guide the process of examining the feasibil-ity of implementing RL for third-party providers such as transportation companies.Kim, Song, Kim, and Jeong (2006) devel-oped a mathematical model that maximizes total cost savings by determining the equilibrium quantity of parts to be processed at each remanufacturing facility and the number of parts that should be purchased from subcontractors. Additionally,Sheu (2007)built a linear multi-objective analytical model to systematically mini-mize total RL operating costs and risks, and developed a prototype green supply chain negotiation model (Sheu, 2011).Du and Evans

(2008) established a bi-objective optimization model that

mini-mizes overall costs and total tardiness in RL cycle time. Kara,

Rugrungruang, and Kaebernick (2007) developed a simulation

model to assess the performance of RL networks in collecting end-of-life appliances in the Sydney Metropolitan Area.Min and

Ko (2008)utilized a mixed-integer programming model and a

ge-netic algorithm to solve an RL problem involving location and allo-cation of repair facilities for third-party logistics providers.Mitra

and Webster (2008)analyzed a two-period model of a

manufac-turer that produces and sells a new product and a remanufacmanufac-turer that competes with the manufacturer during the second period; the effects of governmental subsidies used to promote remanufac-turing activities were examined.Hu, Sheu, and Huang (2002) con-structed a discrete-time linear analytical model that minimizes total RL operating costs, subject to constraints that consider such internal and external factors as business operating strategies and government regulations.Aksen, Aras, and Karaarslan (2009) devel-oped and solved two bi-level programming (BP) models describing a subsidization agreement between a government and a company engaged in end-of-life product collection and recovery. Under the same collection rate and proﬁtability ratio, a government must provide a higher subsidy with the supportive model than with the legislative model.Chen and Sheu (2009)established a differen-tial game model comprising the Vidale–Wolfe equation, which fa-vors product recycling. Despite these advances for cooperative reverse supply chains, the research scope of these studies was lim-ited to the scenario of RL operations without considering RL alli-ances. Conversely, this work, including the proposed model and analyses, applies to both the cases of no RL alliance and an RL alliance.

The emergence of research in diverse public goods games used to address issues of resource sustainability in the area of evolution-ary games is also noteworthy (Anderson, Goeree, & Holt, 1998; Andreoni, 1988; Hauert, De Monte, Hofbauer, & Sigmund, 2002; Helbing, Szolnoki, Perc, & Szabo, 2010; Semmann, Krambeck, &

Milinski, 2003). Stemming from repeated mix-motive games,

pub-lic goods games aim at the social dilemma in which individual ac-tions enhancing personal prosperity harm the others within groups

(Macy & Flache, 2002). Therein, group members are classiﬁed into

different categories, e.g., cooperators and defectors, interacting with each other, thus contributing to different outcomes desig-nated with respective payoffs. Speciﬁcally, public goods games consider reward and punishment effects on the dynamics and dilemmas of collective actions of game players when moving equi-librium conditions (Helbing et al., 2010; Perc, 2012; Perc &

Szoln-oki, 2012; Szolnoki & Perc, 2010). Similarly, this work treats

government intervention as a form of political power characterized by regulatory and ﬁnancial instruments, which are embedded in the proposed three-stage game-theoretic model. Drawing from the theory of environmental economics (Dobbs, 1991; Polack &

Heertje, 2000; Walls & Palmer, 2001), the ideas of external beneﬁt

and external cost are conceptualized in a social welfare objective function embedded in the first-stage game dominated by the gov-ernment. Furthermore, this work considers the influences of green taxation and subsidization, mimicking the effects of punishment and reward effects in public goods games, on the decisions of pro-ducers and RL providers in negotiations and market competition, thus formulating the follow-up bargaining and market competition problems in the second- and third-stage using asymmetric Nash bargaining game. Relative to public goods games, the distinctive feature of the proposed model is noticeable in its capability of characterizing the relative bargaining power of game players (i.e., competing manufacturers relative to either RL providers or RL-alli-ance) and its influence in the decision outcomes of game players when moving toward equilibrium conditions (e.g., cooperative agreements).

Furthermore, scholars have made notable advances in address-ing supply chain cooperation issues (e.g.,Cachon & Lariviere, 2005;

Koulamas, 2006; Pasternack, 1985); however, literature is

gener-ally limited to vertical coordination of chain members, and does not discuss the phenomenon of bargaining power alteration in

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the case of horizontal cooperation (e.g., strategic alliance of RL pro-viders), and its effect on cooperative reverse supply chains. For in-stance, the closest studies to this work are those byNagarajan and

Bassok (2008) and Sheu (2011).Nagarajan and Bassok (2008)

ad-dressed the assembler-suppliers bargaining problem in a

decen-tralized supply chain, where a single assembler buys

complementary components from allied suppliers. Conversely, this work considers the threats and bidding effect from competitors, thus generating a relatively more comprehensive bargaining framework containing two competing manufacturers and allied suppliers to investigate supply chain cooperation issues. By con-trast, Sheu’s bargaining model (2011) is limited to one-to-one bilateral negotiation and does not consider the RL provider alli-ances. These shortcomings leave room for this work.

The primary objective of this work is to investigate how a man-ufacturer interacts with RL providers for the cases without and with RL-provider alliance under government intervention. Speciﬁ-cally, this work addresses the following research questions.

1. How do an alliance and no alliance among RL providers inﬂu-ence the bargaining power in manufacturer and RL provider negotiation?

2. How does a shift in bargaining power influence the profits of manufacturers and allied RL providers, and how should manu-facturers and RL providers deal with such influence?

3. What solutions exist for decisions of all players, including gov-ernments and cooperative reverse supply chain members, under an equilibrium condition.

Noticeably, this work adds to literature on green supply chain management (GSCM) in the following two ways. First, this work addresses the interplay between competing manufacturers and RL providers in cases with and without an RL alliance under gov-ernmental intervention of tack-back legislation and financial mea-sures. We hypothesize that the altered relative bargaining power of manufacturers and RL providers due to an RL provider alliance will influence the equilibrium solutions of these green supply chain members for cooperative agreements. Thus, this work conceptual-izes the influence of such a shift in bargaining power in the pro-posed manufacturer and RL supplier interplay model for an alliance and no alliance cases. Such a bargaining conceptualization and equilibrium solutions are rarely investigated in literature. Sec-ond, given an RL provider alliance, heterogeneity in the bargaining power of competitive manufacturers relative to that of an RL pro-vider alliance is considered. Under the condition of competing manufacturers seeking the same RL provider alliance as a chain partner, manufacturers encounter threats from competitors and increasing breakdown risks resulting from altered bargaining power when negotiating with an RL provider alliance. The pro-posed model solves the specified manufacturers and RL provider alliance interplay problem by characterizing heterogeneity in com-petitors’ bargaining power in a two-to-allied one bargaining frame-work. To the best of our knowledge, the investigation of such a bargaining framework characterizing the antecedents and out-comes of negotiations between two competing manufacturers and one RL provider alliance is limited to the works byNagarajan

and Bassok (2008) and Sheu (2011).

Additionally, although EPR systems vary worldwide (Kahhat

et al., 2008), this work concentrates on individual EPR systems that

regulate manufacturers as entirely responsible for, but allow them to contact RL providers individually for end-of-life product collec-tion, recycling, and disposal. Such an individual-based EPR system is particularly common in the consumer electronics product man-ufacturing industry. Under either challenges of global green orga-nizations or the spontaneous green branding strategies of enterprises, an increasing number of consumer electronics product

manufacturers (e.g., Apple, ASUS, ACER, and SONY) have incorpo-rated green design into green manufacturing to improve product recyclability. One striking example is the Guide to Greener Elec-tronics, a quarterly publication issued by Greenpeace International, which ranks the top 18 global brands of personal computers, mo-bile phones, televisions, and games consoles based on their policies for toxic chemicals, recycling, and climate change (Greenpeace

International., 2010). This ranking has pressured top

manufactur-ers to be responsible for the entire lifecycle of their products, including electronic waste generated and energy used. Therefore, global consumer electronics brands (e.g., ASUS and ACER) prefer to control and manage their collection and recycling systems.

Brieﬂy, this work aims at the issue of power shifting and restructuring in green supply chain negotiation and collaboration under socio-political power intervention. Such an issue, differing from typical supply chain management issues, requires interdisci-plinary research for investigation. Speciﬁcally, we have extended the research aim and scope from the ‘‘power shifts’’ in supplier– buyer to supplier alliance-buyer negotiations of green supply chains under the third-party power intervention, which has never been addressed in either supply chain management or green sup-ply chain management.

2. Model framework and assumptions

The focal story in this work is the interplay of reverse supply chain members under government intervention; two scenarios are considered—an RL alliance and no alliance. Motivated by ad-vances in literature, this work proposes a three-stage reverse sup-ply chain bargaining model for these two scenarios to analyze the effects of bargaining power on the interplay between manufactur-ers and RL providmanufactur-ers as they negotiate toward cooperative agree-ments under government intervention. Speciﬁcally, this work focuses on symmetric Cournot’s duopoly competition, which as-sumes ﬁrms are as similar as possible in all economic aspects and compete for the same buyers in an industry producing a stor-able, homogeneous product. Symmetric competition posits that competitors have the same production and inventory costs, charge the same price, and face symmetric demand functions (

Schemalen-see, 1976). Therefore, we assume all comparable parameters are

equal and ﬁrms have similar market share. In numerous economic studies, competition results in a symmetric oligopoly, and duopoly competition from Cournot models have been proven to be the same under equilibrium conditions (Kreps & Sheinkman, 1983;

Schemalensee, 1976).

2.1. Framework

Negotiation between a manufacturer and an RL provider is pri-mary focus in this work. Subject to government green policies, a transaction concerning the recycled component supply through negotiations over recycled component prices between a manufac-turer and an RL provider is indispensable. Therefore, this work con-ceptualizes the manufacturer and RL provider interplay process as a three-stage game-based framework. The ﬁrst stage (making green policy) conceptualizes the inﬂuence of government interven-tion via take-back legislainterven-tion and economic instruments adopted to increase manufacturer responsibility for collecting and recycling their products (Ongondo, Williams, & Cherrett, 2011; Webster &

Mitra, 2007). According to Khetriwal, Kraeuchi, and Widmer

(2009), the idea of EPR can be implemented via administrative,

economic, and informative instruments. At this stage, this work primarily considers regulatory and economic approaches, which are two most popular measures adopted by governments to

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promote EPR, and are commonly utilized worldwide (Kahhat et al., 2008). Further details about practical cases of government inter-vention to promote EPR are provided in onlineAppendix A (A.1). In the second stage, the negotiation process, the manufacturer and RL provider negotiate an agreement on recycled component supply price and quantity under green policies. Upon negotiation completion, the two parties have identiﬁed the recycled compo-nent supply price and supply quantity. Typically, more than one RL provider may exist in a real situation. A manufacturer may con-sider factors such as breakdown risks from outside options, and thus, negotiate with all RL providers with the intention of purchas-ing recycled components from each provider. The third stage, termed product competition in the market, is used to identify the equilibrium solution with respect to manufacturer production

un-der Cournot competition in the product demand market. Fig. 1

shows the proposed framework.

Furthermore, this work addresses two scenarios for contrast analysis. In Scenario 1, an alliance does not exist and RL provid-ers compete. In Scenario 2, an alliance among RL providprovid-ers ex-ists; these RL providers consider alliances beneﬁcial, as they offer such advantages as a stable and reliable market, and allow RL providers to inﬂuence product pricing and quality (Kannan &

Tan, 2004). Fig. 2 shows the two scenarios for a dual duopoly

competition case. 2.2. Assumptions

This section introduces several assumptions underlying the pro-posed model.

Assumption 1. Competitive markets in which both producers and RL providers are active are characterized by dual duopoly compe-tition, where two duopolistic manufacturers compete in manufac-turing homogeneous green products. Another two duopolistic RL providers collect end-of-life products and then sell the recycled components back to the manufacturers.

Assumption 2. The costs of producing green products, including unit collection and recycling costs, are the same for all manufactur-ers. Unit recycling cost is the cost of recycling a unit recycled com-ponent after collecting and disassembling end-of-life products. Assumption 3. This work only considers the reverse supply chain case for manufacturing new products, where a unit of product is composed of recycled components and virgin components. Therein, recycled component supply price is determined via man-ufacturer and RL provider negotiations. The virgin component pro-curement cost is included in manufacturing cost for simplicity.

Assumption 4. Final product price (P(Q)) is assumed as a simple Cournot inverse demand (Q) function given by P = a bQ, which

follows the downward-sloping linear demand form bySavaskan,

Bhattacharya, and Van Wassenhove (2004), where Q ¼P2

i¼1qi, qi

is the product quantity sold by manufacturer i, and a and b are two positive parameters characterizing the correlation between the price and demand in the end-customer demand market. Assumption 5. Two competing manufacturers have different bar-gaining power

a

i (i = 1, 2) based on their difference in channel

power in recycled component supply chains and are dependent upon the resources of their partners (Dwyer & Walker, 1981;

Pfef-fer & Salancik, 1978). Therein,

a

irepresents the bargaining power

of manufacturer i relative to any given RL provider. For instance, when manufacturer i negotiates with RL provider j("j), the manu-facturer’s bargaining power is

a

i, and that of RL provider j("j) is

1

a

i. Differing from an operations research perspective, economic

scholars typically utilize simple forms of market competition, e.g., monopoly, duopoly, oligopoly, and perfect competition, to facili-tate analyzing market competition of ﬁrms. As this work assumes the market competition as dual duopoly competition (Assumption 1), the bargaining power characterized in this work aims at two competing manufacturers relative to two competing RL provid-ers/one RL-alliance.

Assumption 6. The RL providers have the same bargaining power. This work treats these RL providers similarly in all economic respects and, thus, their market inﬂuence is similar, particularly when an RL alliance exists. We postulate this assumption to facil-itate analysis.

Assumption 7. The government implements green policies to reg-ulate the recycling rate (rc), environmental pollution fee (f) per unit

levied on manufacturers, and unit subsidy (s) provided to RL pro-viders under the goal of social welfare (SW) maximization. Partic-ularly, our rationales for focusing on such economic instruments are rooted in the global trend of EPR from both theoretical and practical perspectives, which are described in detail in online

Appendix A (A.2).

3. Model and solutions

To approximate equilibrium solutions for the three-stage game-based problem, this work adopts the backward induction approach

(Kreps, 1990). The backward induction approach has been used

extensively to search for equilibrium solutions to sequential game problems. In this work, the backward induction process ﬁrst seeks

Production Competition Government intervention: 1.economic measures 2.green regulations

Manufacturer I Reverse logistics provider I

Manufacturer II

Reverse logistics provider II

Green policy making Bilateral negotiations Product competition in themarket

Stage3 Stage2

Stage1

Fig. 1. Model framework which represents the proposed three-stage game-based manufacturer-RL provider negotiation framework in the context of government intervention.

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tentative equilibrium solutions to the third stage, followed by identifying tentative equilibrium solutions in the second stage using tentative equilibrium solutions from the third stage, and then identifies the equilibrium solutions in the first stage. The ten-tative equilibrium solutions have not yet been finalized, except for those obtained in the first stage, since the tentative equilibrium solutions obtained at lower levels contain decision variables from higher levels. Therefore, the high-level equilibrium solutions should be inputted forward to lower levels to finalize equilibrium solutions. According toRasmusen (2007), backward induction en-sures perfect subgame equilibrium solutions obtained for sequen-tial games.

Notably, the ﬁrst and third stages remain unchanged in Scenar-ios I and II. In the ﬁrst stage, a government implements green pol-icies, which include an environmental pollution fee (f) levied on a manufacturer for producing per unit product, and a subsidy (s) is provided to an RL provider for recycling per unit recycled compo-nent. Another government policy addresses the recycling rate (rc),

which is typically stipulated in take-back laws. In the third stage, the two manufacturers compete for equilibrium output in a Cour-not competition game, where both manufacturers have the same market demand curve (byAssumption 4). By contrast, the second stage models the interplay between the manufacturers and RL pro-viders in negotiation using bargaining game theory. The two man-ufacturers negotiate with the RL providers to identify the recycled component supply price and amounts. The proposed models and applied variables may differ slightly in the two scenarios, which are described in detail in the following subsections.

3.1. Scenario I: No alliance exists between the two RL providers Consider a dual duopoly competition condition in which two competing manufacturers (denoted by i; i = 1, 2) procure recycled components from two competing RL providers (denoted by j; j = 1, 2), where recycled component supply prices and amounts are determined through negotiations. One can then identify the relationship between recycled component amounts required and product production associated with manufacturer i by

yi1þ yi2¼ qik ð

8

iÞ ð1Þ

where k is the recycled component amount required by a unit prod-uct, and yijis the recycled component amount required by

manufac-turer i and supplied by RL provider j. Suppose these two RL providers have the same bargaining power when negotiating with the two manufacturers; thus,

yi1¼ yi2¼

qik

2 ð

8

iÞ ð2Þ

Under government intervention via green policies, the proﬁt function (

p

i) of manufacturer i can then be expressed as

p

i¼ ðP cm f Þqi

qik

2 ðpi1þ pi2Þ ð

8

iÞ ð3Þ

where cmis the cost of manufacturing a unit product, including

in-put cost of virgin components; pijand yijrepresent recycled

compo-nent supply price (including take-back cost associated with a unit of a recycled component) and the amount associated with manufac-turer i and RL provider j, respectively.

For a given RL provider j, the total recycled component amount supplied to manufacturers isP8iyij, and thus, the required amount

of collected end-of-life products isP₈_iy_ij=rc, where rcis the

recy-cling rate, which can be regulated by green policies, as mentioned. Thus, the proﬁt function (nj) of RLs provider j ("j) can be expressed

as nj¼ X 8i pijyijþ s cr ccol rc _X 8i yij ð

8

jÞ ð4Þ

where ccolis the cost of collecting one end-of-life product unit, and

cris the cost for recycling one recycled component unit.

3.1.1. Solution for stage 3

To ensure the existence of equilibrium solutions of qi("i), let

the ﬁrst-order condition of Eq. (3) with respect to qi ("i) be @pi

@qi¼ 0ð8iÞ. Furthermore,

@2pi

@2qi<0ð8iÞ can be derived to prove that tentative equilibrium solutions exist for manufacturers with re-spect to production ðq

i;i ¼ 1; 2Þ, and are given by

q 1¼ 2ða cm f Þ þ ðp21þ p22 2p11 2p12Þk 6b ð5Þ q 2¼ 2ða cm f Þ þ ðp11þ p12 2p21 2p22Þk 6b ð6Þ

Observed from Eqs.(5) and (6), the equilibrium solution of a man-ufacturer i’s production ðq

i;i ¼ 1; 2Þ has positive associations with

the recycled component supply prices ðpi0_jÞ achieved by its compet-itor (i0_–_{i) with RL providers (j = 1, 2); and however, negative}

asso-ciations with cm, f, and the supply prices achieved by itself with RL

providers (j = 1, 2), in conformity with our expectation.

Based onAssumption 4 regarding the linear product demand

form, tentative equilibrium solutions of product price (P⁄_{) and total}

production (Q⁄_{) can be derived by}

P ¼ a 4ða cm f Þ ðp11þ p12þ p21þ p22Þk 6 ð7Þ ManufacturerI RL provider I Manufacturer II -RL provider II ManufacturerI Alliance between RL providers I and II Manufacturer II Scenario I Government Green policy Scenario II Production competition I Production competition II

Fig. 2. Framework of scenarios which presents the framework in which manufacturers bargain with RL providers in two scenarios: non-alliance (Scenario I) and RL provider alliance (Scenario II).

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Q

¼4ða cm f Þ ðp11þ p12þ p21þ p22Þk

6b ð8Þ

Observed from Eqs. (7) and (8), Q⁄ _{has properties similar to}

q

iðqi;i ¼ 1; 2Þ; and however, a negative association with P ⁄

. Notably, although tentative equilibrium solutions, such as q

iði ¼ 1; 2Þ, P

⁄_{, and Q}⁄_{, are derived, the recycled component supply}

prices pij(i = 1, 2; j = 1, 2) in Eqs.(5)–(8), which are determined in

practice through negotiations between manufacturers and RL pro-viders, have not yet been derived. The next step is to input these tentative equilibrium solutions into the second stage (i.e., the negotiation process) to determine tentative equilibrium solutions of pij(i = 1, 2; j = 1, 2).

Stage 2 deals with the negotiation problem between two competing manufacturers and two competing RL providers. Spe-ciﬁcally, this work utilizes the asymmetric Nash bargaining game to derive the tentative equilibrium solutions of the recycled component supply prices and amounts (i.e., p

ij and yij;8i; jÞ. The

basic concept of the asymmetric Nash bargaining game, particu-larly the components of a generalized form of the asymmetric Nash bargaining objective function, is described in online

Appen-dix B.

Utilizing the asymmetric Nash bargaining game (Muthoo,

1999), this work formulates the pairwise manufacturer and RL pro-vider negotiation problem as an asymmetric Nash bargaining game in which expected proﬁt obtained from cooperation with another partner is considered. The recycled component amount required by a manufacturer can be provided by any one of the two RL pro-viders; thus, remuneration for negotiation breakdown between manufacturer i and RL provider j is the proﬁt from cooperation with another RL provider, provider j0_(j0_–_{j). Let}

_p

ij0 and n

i0j be the resulting proﬁts of manufacturer i and RL provider j in the case

of negotiation breakdown, where

p

ij0 ðP c_m f Þ

y_ij0 k

p_ij0y_ij0ðj0–jÞ and n

i0j p_i0jy_i0jþ ðs crcrcolcÞyi0jði0–iÞ. According to

Muthoo (1999), the proposed asymmetric Nash bargaining

objec-tive function (Ci,j) associated with manufacturer i and RL provider

j ("i, j) can then be expressed as

C

i;j¼ Maxpijð

p

i

p

ij0Þ

ai_ðn

j ni0_jÞ1ai;

8

i; j ð9Þ

where i0_–_{i; j}0_–_{j. The equilibrium solutions of proﬁts (}

_p

i and n

j)

gained by manufacturer i and RL provider j ("i, j) in the asymmetri-cal Nash bargaining game have the following properties (Eqs.(10)

and (11)).

p

i ¼

p

ij0þ

a

_i ð

p

iþ n j

p

ij0 n_i0_jÞ;

8

i ð10Þ nj ¼ ni0jþ ð1

a

iÞ ð

p

i þ n j

p

ij0 n 0 ijÞ;

8

j ð11Þ

Notably, P⁄_(Eq.₍₇₎_{) and Q}⁄_(Eq.₍₈₎_{) obtained from stage 3 are input}

into Eqs.(10) and (11). After taking the ﬁrst-order differential of

Eqs.(10) and (11)with respect to pij("i, j), the tentative equilibrium

solutions of recycled component supply prices p

ijð8i; jÞ can be de-rived as p ij¼ 2

X

ð1

a

iÞð8

a

i0Þ

K

k 16 þ 26

a

_iþ 12

a

_i0 5 Y 8i

a

i ! 32 þ 10X 8i

a

i 3 Y 8i

a

i ! k ð

8

i; jÞ ð12Þ whereX a cm f, andK s crcrcolc for simplifying the repre-sentation of Eq.(12). The tentative equilibrium solutions p

ij("i, j)

derived above can be used to solve for stage 3 output; thus,

q i ¼ ð2 þ 5

a

iÞð8

a

i0Þð

X

þ

K

kÞ 3b 32 þ 10X 8i

a

i 3 Y 8i

a

i ! ;

8

i ð13Þ

Using Eqs.(2) and (13), the tentative equilibrium solutions of recy-cled component supply amounts y

ijð8i; jÞ for output of stage 2 (i.e.,

the negotiation process) can be derived as y ij¼ ð2 þ 5

a

iÞð8

a

i0Þð

X

þ

K

kÞk 6b 32 þ 10X 8i

a

i 3 Y 8i

a

i ! ð

8

i; jÞ ð14Þ

It is worth mentioning that the above tentative equilibrium solu-tions (i.e., p

ij and yij) yielded at stage 2 are determined

collec-tively by k,

a

i, X, and K. Speciﬁcally, X and K can be regarded

as two profit-oriented constructs containing key factors that influence the profits of manufacturers and RL providers, respec-tively. Therein,Xis positively associated with p

ijand yij,

indicat-ing that the increase inXfacilitates a manufacturer’s willingness to pay and intention of procuring more recycled components when bargaining with an RL provider. By contrast,Kis positively associated with y

ij; and however, has negative association with

p

ij, indicating that the increase in K facilitates an RL provider’s

willingness of increasing recycled-component supply amount with a lower supply price when negotiating with a manufacturer.

The aforementioned effects of X andK on p

ij and yij, however,

are moderated by bargaining power

a

iwhich remains as a

pri-mary factor inﬂuencing the dyadic members’ decisions in negotiations.

Drawing from the theory of environmental economics (Dobbs,

1991; Walls & Palmer, 2001), SW speciﬁed in this work contains

four elements: (1) consumer surplus (CS); (2) producer surplus (PS); (3) environmental beneﬁts (EB) of green products; and (4) environmental pollution cost (EC) for manufacturing green prod-ucts. According to the classical theory of economics, CS means consumers can purchase a product for a price that is less than the highest price they would be willing to pay. As we assume the product demand function is a linear demand form sloping

downward, one can easily determine that CS ¼1

2bQ 2

. Notably, PS is defined as the benefit amount for producers from selling products at a market price that is higher than the lowest price at which they would be willing to sell a product. In this work, PS is the sum of all profits of chain members (i.e., PS =

p

M1+

p

M2+

p

RS1+

p

RS2). According toDobbs (1991) and Walls and

Pal-mer (2001), external economies mean that the beneﬁt arising

from an economic activity does not accrue to the person or firm controlling the activity, including external benefit and external cost. The discussion of external economies dates back to Marshal, who first introduced the term ‘‘external economies’’ in 1890. Mar-shall’s goal was to explain why the paradigm of a perfect market economy is not destroyed through monopolistic concentrations in an industry, even with increasing returns to scale (downward-slop-ing average cost) (Polack & Heertje, 2000). Therefore, EB and EC are the total environmental benefits for recycling recycled components and total environmental pollution cost for new-product production. The SW function is then derived as SW = CS + PS + EB EC. Accord-ingly, we assert that the government has the goal of SW maximi-zation (MaxSW), which is given by

Max SW ¼ 1 2bQ 2 þ½

p

M1þ

p

M2þ

p

RS1þ

p

RS2 þ d Qk

c

c ½

c

Q ð15Þ where d represents the environmental beneﬁts by recycling one unit of an end-of-life product; and

c

is the environmental pollution cost of manufacturing one green product unit. Based on the value of

(7)

EB EC, the termdk

rc

c

, as in Eq.(15), can be regarded as external proﬁt for recycling each end-of-life product, and must be subject to the conditiondk

rc

c

P0 to ensure that manufacturing recycled components for green production beneﬁts environmental protec-tion. Thus,Corollary 3.1is presented as follows.

Corollary 3.1. Green production using recycled components has a positive effect on the environment only whendk

rc

c

P0 holds.

Suppose the government does not ﬁnancially beneﬁt from the take-back law, then the conditions f = sk and fQ ¼ sP8i

P

8jyijmust

hold in the proposed model. Using the aforementioned conditions yieldsX+Kk = a cm (cr+ ccol/rc)k, which is input back into the

SW objective function (Eq.(15)); thus, Max SW becomes

Max SW ¼2

D

1ð3h1

D

1Þ a cm crþcrcolc k h i2 9bh2 1 þ 2ð3h1

D

1Þ dkrc

c

½a cm ðcrþ ccol=rcÞk 3bh1 ð16Þ where D1¼ 80 þ 11P8i

a

i 4Q8i

a

i; and h1¼ 32 þ 10P8i

a

i 3Q8i

a

i. In Eq.(16), variables f and s no longer exist in the SW function.

Thus, we suggest that a government should determine the unit green tax (f) subject to the condition f = sk, indicating that f must be imposed after the unit green subsidy (s) is determined.

The next step is to solve for the equilibrium solution for recy-cling rate (r

c) by taking the ﬁrst-order condition of Eq. (16) as @SW

@rc ¼ 0. Moreover, the second-order condition

@2SW @2_r

c ¼

/1½/ð3dh12ccolD1Þþ3cccolh14

36bk2_h2

1c3colð3dh1ccolD1Þ <0 can be easily proved, where /1¼ 16 þ 19P8i

a

i 5Q8i

a

ið/1>0Þ and / = a cm f⁄+ (s⁄ cr)k.

One can then easily prove that r

c exists, and is derived by

r c¼

2kccolð3dh1ccolD1Þ

/ð3dh12ccolD1Þþ3cccolh1. The equilibrium solution for SW maximiza-tion (i.e., SW⁄_{) can then be obtained by inputting r}

cinto Eq.(16).

Once the equilibrium solutions r c, f

⁄_{, and s}⁄_{are determined in}

stage 1 for generating green policy, they can be used to derive the equilibrium solutions for recycled components supply prices and amounts (i.e., p

ijand yij, "i, j) discussed in stage 2, and

produc-tion amounts (q

i;"i) derived in stage 3. All equilibrium solutions

obtained in Scenario I (i.e., the case without an alliance between the two RL providers) are summarized in online inAppendix C. 3.2. Scenario II: Alliance between RL providers

In contrast with Scenarios I and II considers an RL provider alli-ance case, where RL providers negotiate as a team when negotiat-ing with manufacturers for recycled component supply prices and amounts. For manufacturer i, the recycled component amount pro-cured from the RL-alliance after negotiation is yiat price pi("i). The

relationship between yiand product production (qi) is as follows:

yi¼ qik;

8

i ð17Þ

The proﬁt function of manufacturer i (

p

i) becomes

p

i¼ ðP cm f Þqi piyi;

8

i ð18Þ

Relative to the manufacturer profit function specified in Sce-nario I (Eq.(3)), the manufacturer profit function (Eq.(18)) defined in Scenario II differs mainly in the characterization of the supply amount (yi) and price (pi) which are dominated by an RL-alliance

in Scenario II.

For the RL-alliance, total recycled component supply amount is P

8iyi; thus, the amount of collected end-of-life products is

P

8iyi

rc , and collection cost is ccol

P

8iyi

rc . Cost of producing recycled

compo-nent is crP8iyiwith subsidy s P8iyi. The proﬁt function of the

RL-alliance, nall, can then be expressed as

nall¼ X 8i piyiþ s cr ccol rc _X 8i yi ð19Þ

Furthermore,

a

i("i) is deﬁned as the bargaining power of

manufac-turer i relative to that of the RL-alliance. As a basic assumption, the bargaining power of the RL-alliance is 1

a

i, relative to that of

manufacturer i.

Based on the ﬁrst-order differential of

p

iwith respect to qi, let

the ﬁrst-order condition @pi

@qi¼ ða cm f Þ 2bqi bqi 0 p_ik ¼ 0ð8iÞ hold. Additionally, one can easily derive@2_p

i

@2_q

i<0ð8iÞ to prove that the tentative equilibrium solutions of production amounts (q

i) associated with these two competing manufacturers exist

("i), and are given by q i ¼ ða cm f Þ þ ðpi0 2p_iÞk 3b ;

8

iði – i 0 Þ ð20Þ

Similar to the equilibrium solution of production derived in Sce-nario I (i.e., Eqs.(5) and (6)), the equilibrium solution of a manufac-turer i’s production ðq

i;i ¼ 1; 2Þ is positively associated with the

supply prices ðpi0Þ achieved by its competitor (i0–i) with the RL-alliance; however, has negative associations with cm, f, and the

sup-ply price achieved by itself with the RL-alliance. Further, the tenta-tive equilibrium solutions of product price (P⁄_{) and total production}

(Q⁄_{) can be derived as} P_¼a þ 2ðcmþ f Þ þ kP8ipi 3 ð21Þ Q ¼2ða cm f Þ k P 8ipi 3b ð22Þ

Therein, P⁄_{and Q}⁄_{derived in Scenario II have the properties the}

same as those gained in Scenario I by comparing Eqs. (21) and

(22)with Eqs.(7) and (8).

Then, the computational results derived above are used as the input to stage 2 to derive the equilibrium solutions for recycled component supply prices and amounts.

Similarly, this work utilizes the asymmetric Nash bargaining game to derive the tentative equilibrium solutions of recycled component supply prices (p

i;8i) and amounts ðyi;8iÞ provided

by the RL-alliance to manufacturers. Differing from the non-zero remuneration characterized in Scenario I, in this scenario remu-neration after negotiation breakdown is zero for any

manufac-turer as recycled component amounts required by

manufacturer i can only be provided by the RLs-alliance. Con-versely, the RL-alliance can retain trading proﬁts when

negotia-tions break down. Thus, in Scenario II the proposed

asymmetric Nash bargaining objective function (Ci) associated

with any given pair of manufacturer i ("i) and the RL-alliance is given by

C

i¼ Max pi f

p

i 0gai nj pi0y_i0þ s c_rccol rc yi0 1ai ;

8

i ð23Þ Inputting product production (Eqs.(20) and (22)) and the product price (Eq.(21)) obtained from stage 3 into Eq.(23)yields

C

i¼ Max pi Xþkðpiþpi0Þ 3 Xþkðpi02piÞ 3b pi½Xþkðpi02piÞk 3b n oai pi½Xþkðpi02piÞk 3b þ K½Xþkðp_i02piÞk 3b n o1ai ;

8

iði – i0 Þ ð24Þ

(8)

After taking the ﬁrst-order differential of Eq.(24)with respect to pi

("i), one can derive the tentative equilibrium solutions of recycled component supply prices p

ið8iÞ as p i¼

X

Y 8i

a

i 5 X 8

a

iþ 4

a

i0þ 5 ! þ 2

K

k Y 8i

a

i 3 X 8

a

iþ 2

a

i0 5 ! 15 þX 8i

a

i Y 8i

a

i ! k ;

8

iði – i0Þ ð25Þ

Observed from Eq.(25), the association ofXwith p

i is positive,

the same as that revealed in Scenario I, indicating that the increase inXfacilitates a manufacturer’s willingness to pay when bargain-ing with an RL-alliance. However, the association ofKwith p

i is

positive, differing from that observed in Scenario I. Therefore, we infer that the increase in the proﬁt-oriented construct (K) caused by the RL-alliance stimulates the RL-alliance’s intention of raising the supply price when negotiating with a manufacturer.

Using Eq.(20), one can further derive the tentative solutions ðq

iÞ for manufacturer production by qi ¼

2ð1þaiÞð5ai0ÞðXþKkÞ 3bð15þP 8iai Q 8iaiÞ ð8i; i – i0

Þ. As yi= qik (by Eq.(17)), the tentative solutions yið8iÞ

for recycled component amounts procured by manufacturers can then be determined by y i ¼ 2kð1 þ

a

iÞð5

a

i0Þð

X

þ

K

kÞ 3b 15 þX 8i

a

i Y 8i

a

i ! ;

8

iði – i0Þ ð26Þ

Consistent with that observed in Scenario I, the association of either XorKwith y

i is positive, indicating that the increase in

either the manufacturer’s proﬁt-oriented construct (X) or the RL-alliance’s proﬁt-oriented construct (K) facilitates the achieve-ment of a high level of recycled-component procureachieve-ment amount in the negotiations between manufacturers and an

RL-alliance. Moreover, the aforementioned effects of X and K on

y

ij are moderated by bargaining power

a

i which remains as a

primary factor that inﬂuences a manufacturer’s decisions when negotiating with an RL-alliance.

Before stage 1, one must specify the means for proﬁt sharing be-tween the two RL providers and allocating their recycled compo-nents to manufacturers. The assumptions indicate that the two RL providers have the same operating conditions, including unit collection cost, unit cost of recycled component manufacturing, and subsidy from the government. Therefore, this work regards the two RL providers as having the same bargaining power when negotiating their proﬁt share and recycled component supply amounts. Accordingly, nj ¼ n j0¼ nall 2 ;

8

jðj – j 0 Þ ð27Þ y j ¼ yj0¼ P 8iyi 2 ;

8

jðj – j 0 Þ ð28Þ

Similar to Scenario I, we posit that the government has the goal of SW maximization. Utilizing the generalized form of SW objective function (Eq.(15)) and tentative equilibrium solutions derived in previous stages, we can then establish the corresponding objective function (MaxSW) as Max SW ¼2

D

2ð3h2

D

2Þð

X

þ

K

kÞ 2 9bh22 þ 2ð3h2

D

2Þ dkrc

c

ð

X

þ

K

kÞ 3bh2 ð29Þ

whereD2¼ 35 P8i

a

iQ8

a

i, and h2¼ 15 þP8i

a

iQ8i

a

ifor

sim-plicity. Similarly, the government does not beneﬁt ﬁnancially from this policy and, thus, conditions f = sk and fQ ¼ sP8iyi hold in this

scenario. Let the ﬁrst-order condition of Eq.(29)be @SW

@rc ¼ 0; and

the second-order condition of @2_SW

@2rc ¼

/2½/ð3dh22ccolD2Þþ3cccolh24

36bk2h2

2c3colð3dh2ccolD2Þ <

0 ð3dh2>ccolD2Þ can be proved easily, where

/2¼ 10 þ 4

P

8i

a

i 2Q8i

a

ið/2>0Þ. Thus, the equilibrium solution

of rcðrcÞ is rc¼

2kccolð3dh2ccolD2Þ /ð3dh22ccolD2Þþ3cccolh2. Likewise, equilibrium solutions r

c, f

⁄_{, and s}⁄_{are input into stages}

2 and 3 to derive equilibrium solutions for recycled component supply prices, amounts (i.e., p

i and yi;8i), and production amounts

(q

i;8i), respectively. All equilibrium solutions obtained for

Sce-nario II (i.e., the case with the RL-alliance) are summarized in

on-lineAppendix C.

Notably, the proposed model is also applicable when the govern-ment does not use ﬁnancial instrugovern-ments. The equilibrium solutions for government ﬁnancial instruments are f⁄_{= s}⁄_{k under equilibrium}

conditions (Tables C1 and C2 in on-line Appendix C). Such equilib-rium solutions also apply to the case with ﬁnancial instruments (i.e., f⁄_{= s}⁄_{k = 0). That is, let f = s = 0, which mimics the case without}

government ﬁnancial instruments; model complexity then

decreases, and derived equilibrium solutions remain applicable. 4. Analysis and results

Based on the derived equilibrium solutions, qualitative and quantitative analyses are applied to provide additional insights into the effects of bargaining power on the negotiation between manufacturers and RL providers in reverse supply chains. Analyti-cal results are given in the following two subsections.

4.1. Qualitative analysis

This subsection brieﬂy describes analytical results in terms of the effects of bargaining power on reverse supply chain perfor-mance based on comparative output in Scenarios I (RL-alliance) and II (no RLs-alliance). In the following example, x(I)_{and x}(II)

de-note variables/parameters (x) associated with Scenarios I and II, respectively.

Proposition 4.1 (bargaining power vs. contracted recycled compo-nent supply). Let d P ccol; condition y

ðIÞ i Py ðIIÞ i holds if

a

ðIÞ i P

a

ðIIÞ

i P0:5; moreover, under equilibrium conditions, yðIIÞ

i

yðIÞ_i 6

1

4ð8iÞ.

In contrast with the case without an RL-alliance,Proposition 4.1

indicates that an RL-alliance may decrease recycled component procurement by manufacturers. We infer that in negotiations with manufacturers, an RL-alliance decreases the bargaining power of manufacturers, even when manufacturers still have relatively more power in reverse supply chains. Therefore, the RL-alliance may raise recycled component supply prices in contracts, which would reduce recycled components procurement by manufacturers. Proposition 4.2 (bargaining power vs. manufacturer proﬁts). Let d Pccol; condition

p

ðIÞi >

p

ðIIÞ i holds if

a

ðIÞ i P

a

ðIIÞ i P0:5 under

equilibrium conditions; moreover,p ðIÞ i pðIIÞ i 61 4ð8iÞ.

Combiningpropositions 4.1 and 4.2indicates that even when a manufacturer has relatively more bargaining power than an RL provider after an RL-alliance is formed, the resulting manufacturer proﬁts decrease when compared with those in the case of no RL-alliance. This analytical result is likely when recycled component supply prices increase and the recycled component supply decreases. A further inference is that an RL-alliance may weaken

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manufacturer bargaining power and further decrease proﬁt sharing in a cooperative supply chain. The proofs ofpropositions 4.1 and 4.2are provided in on-lineAppendix D.

Corollary 4.1. According to Proposition 4.2, the proﬁt for a given manufacturer i may decrease by up to 25% (

p

ðIIÞ

i =

p

ðIÞ

i ﬃ 1=4) under a

symmetric power condition (i.e.,

a

ðIIÞ

i ¼ 1

a

ðIIÞ

i ¼ 0:5;8i).

Corollary 4.1 approximates manufacturer proﬁt. Suppose a

manufacturer has the same bargaining power as an RL provider in an RL-alliance. In this speciﬁc condition, the resulting proﬁts of a manufacturer decrease to approximately 75% that in the case without an RL-alliance.

Corollary 4.2 (high asymmetric bargaining power—powerful manu-facturers). If

a

ðIÞ i ¼

a

ðIIÞ i ¼ 1:0ð8iÞ; then

p

ðIÞ i ¼ ½49ðd/cccolÞ2 4bð3dh1ccolD1Þ2 and

p

ðIIÞ i ¼ ½4ðd/cccolÞ2 bð3dh2ccolD2Þ2while n ðIÞ j ¼ n ðIIÞ j ¼ 0.

This corollary presents the case of extreme asymmetric bargain-ing power in which a manufacturer has markedly more bargainbargain-ing power (i.e.,

a

ðIÞ

i ¼

a

ðIIÞ

i ¼ 1:0;8i) in negotiations than either RL

pro-vider or the RL-alliance. In this case, the manufacturer monopolizes the resulting chain-based profits, including profits of its chain part-ners. Thus, an RL provider may not profit when dealing with such an powerful manufacturer.

Theorem 4.1 (Vender-dominated market—extremely powerful RL providers/alliance). If

a

ðIÞ

i ¼

a

ðIIÞ

i ¼ 0ð8iÞ, then (a)

p

ðIÞ

i >

p

ðIIÞ

i >0

and nðIÞ_j >2nðIIÞ_j ð8i; jÞ; and (b) nðIÞ_j ¼ 3

p

ðIÞ

i and n ðIIÞ j ¼ 3 2

p

ðIIÞ i ð8i; jÞ.

This theorem provides several managerial insights into the per-formance of reverse supply chain members in a recycled compo-nent market dominated by RL providers. First, an RL-alliance does not enhance profits of RL providers in a recycled component market dominated by RL providers. AsTheorem 4.1(a) indicates, induced RL provider profits may decrease by more than 50% (i.e., nðIIÞ_j <1=2nðIÞ_j ) when an RL-alliance forms to negotiate with manu-facturers. The resulting inference is that RL providers do not need to form an RL-alliance to negotiate with manufacturers in a recy-cled component vender-dominated market. Specifically, according

toTheorem 4.1(b), RL provider proﬁts (nðIÞ

j ) are three times higher

than manufacturer proﬁts in Scenario I (i.e., no RL-alliance) (

p

ðIÞ i )

but only 1.5 times higher in Scenario II (an RL-alliance exists) (nðIIÞ_j ¼3

2

p

ðIIÞ

i ). From the manufacturer’s perspective, the resulting

manufacturer proﬁts may decrease when negotiating with a pow-erful RL-alliance. However, a manufacturer will still beneﬁt from a cooperative reverse supply chain agreement, even when the recy-cled component market is dominated by RL providers. Since

Theo-rem 4.1 is easily proven using equilibrium solutions by setting

a

ðIÞ i ¼

a

ðIIÞ

i ¼ 0, the corresponding proof is not given.

Theorem 4.2. Let d = ccol;

p

ðIÞi >

p

ðIIÞ

i ð8iÞ then holds

uncondition-ally; however, the relationship between nðIÞ_j and nðIIÞ_j varies ("j).

Theorem 4.2indicates that manufacturer proﬁt when an

RL-alli-ance (Scenario II) exists is unconditionally lower than that without an RL-alliance (Scenario I). This generalization indicates that the coalition of RL providers, which may increase the bargaining power of an RL provider in negotiations with manufacturers, is never favorable for manufacturer proﬁts in the reverse supply chain negotiation framework. For example, let

a

ðIIÞ

i ¼

ea

ðIÞ

i ð0 6

e

61);

inputting this relational function into the manufacturer proﬁt functions

p

ðIÞ

i and

p

ðIIÞ

i for comparison shows that

p

ðIÞ i >

p

ðIIÞ

i ðð8iÞÞ. Conversely, bargaining power has a variable

ef-fect on RL provider proﬁts when RL providers bargain as a coalition. From the perspective of RL providers, an interesting issue exists under the condition in which the RL-alliance obtains a proﬁt in-crease (i.e., nðIÞ

j <n ðIIÞ

j ). To identify the conditions favorable for an

RL-alliance, the values of

a

ðIÞ i ;

a

ðIIÞ i , and

a

ðIÞ i

a

ðIIÞ i are determined

subject to constraint nðIÞ_j <nðIIÞ_j .Fig. 3presents analytical results, which generate three important remarks.

Remark 1. An RL-alliance positively affects RL provider proﬁts when 0:67 6

a

ðIÞ

i <1. In the proposed reverse supply chain negotiation

framework, an RL-alliance increases RL provider proﬁts (i.e.,

nðIIÞ_j >nðIÞ_j ;8j) only when the initial condition for manufacturer

bargaining power, 0:67 6

a

ðIÞ

i <1, holds. For instance, the

RL-alliance contributes to a signiﬁcant decrease in manufacturer bargaining power (from 0.67 to 0.02), which increases RL provider proﬁts.

Remark 2. The RL-alliance is proﬁtable to an RL provider, particularly when negotiating with manufacturers that have extremely high bar-gaining power For instance, given

a

ðIÞ

i ¼ 0:98, a slight decrease in

manufacturer bargaining power (from 0.98 to 0.97) caused by an RL-alliance increases RL provider proﬁts (i.e., nðIIÞ_j >nðIÞ_j ).

Remark 3. The effect of an RL-alliance on bargaining power corre-lates negatively with manufacturer bargaining power For example, given

a

ðIÞ

i ¼ 0:67, the RL-alliance signiﬁcantly decreases

manufac-turer bargaining power (

a

ðIÞ i

a

ðIIÞ

i ¼ 0:62), and this decrease is

much greater than that in the case of

a

ðIÞ i ¼ 0:99.

According to analytical results, the RL-alliance will likely in-crease the bargaining power of an RL provider when negotiating with a manufacturer for a profitable recycled component supply contract; however, this typically decreases manufacturer profit. Particularly in the case of a recycled component vender-dominated market, an RL-alliance may not be a win–win strategy as RL provid-ers may become overly powerful when negotiating with manufac-turers. The resulting counter-profit effect then hurts all players in the reverse supply chain negotiation framework, including RL pro-viders, and decreases aggregate profit in reverse supply chains. 4.2. Numerical analysis

The subsequent quantitative analysis was conducted by adopt-ing the example of China’s notebook computer (NC) manufacturadopt-ing industry. Lenovo, HP, Dell, ASUS and Acer are ﬁrst-tier manufactur-ers in China’s NC market. According to a survey byChina Computer

World (CCW) Research (2008), the top 5 NC manufacturers in

terms of annual sales are Lenovo, HP, Dell, ASUS and Acer. Lenovo (including the Thinkpad) is ranked No. 1 with a market share of 29.1%, followed by HP (16.8%), Dell (11.5%), ASUS (10.9%) and Acer (7.0%). China’s NC market is dominated by these ﬁve NC ﬁrms as they account for over 80% of China’s NC market. In the symmetric Fig. 3. Changes in bargaining power of a manufacturer when bargaining with RL providers without and with RL-alliance (subject to nðIÞ

j <n ðIIÞ

j ) represented bya(I)

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oligopoly market, the competing behaviors of these five companies are characterized by mutual dependence and mutual constraint. In the same economic environment, NC prices of these five manufac-turers are similar because they have similar operational scales and cost structures. Competition among these firms is fierce, particu-larly in terms of output competition for market share. Such com-petitive situations are characterized by features of symmetric Cournot oligopoly/duopoly competition, and conform to the assumptions of this work.

Via preliminary analysis, cost-related parameters for the pro-posed model were then preset using data obtained from semi-structured interviews of 12 managers in the global logistics sectors of NC producers and recyclers in China. These cost-related param-eters are unit manufacturing cost, cm, unit green cost,

c

, beneﬁt, d,

recycled component amount per unit product production, k, unit cost for recycling one recycled component unit, cr, and unit cost

for end-of-life product collection, ccol. Particularly, the necessary

condition (i.e.,dk

rc

c

P0) revealed inCorollary 3.1is utilized to set the values of

c

and d to ensure that the use of recycled compo-nents for green production beneﬁts the environment. Furthermore, we collected information with respect to green taxes and subsidies applied in real cases. In reality, several examples of advanced

recycling fees and similar programs have been applied in the US, California, Canada, Japan, and Taiwan (Gable & Shireman, 2001; Hicks, Dietmar, & Eugster, 2005; Hong & Ke, 2011; Lee, Chang,

Wang, & Wen, 2000; Nixon & Saphores, 2007). For example, an

ad-vanced recycling fee ranging from $6 to $10 on all electronic prod-ucts is adopted in California (Nixon & Saphores, 2007). InHong and

Ke (2011), the unit green subsidy of US$9 is suggested for

collect-ing and recyclcollect-ing per unit end-of-life product in the case of Taiwan. As the case illustrated in this work is China, we thus adopt $5 as the unit green subsidy used for recycling per unit recycled compo-nent in the numerical example for simplicity.Table 1summarizes the key preset parameters in this case study; cost parameters are in US dollars.

In the following numerical analysis, ﬁve levels of manufacturer bargaining power (

a

i, i = 1, 2) relative to that of RL providers in the

reverse supply chain negotiation framework are on a scale of 0–1, where

a

i= 1 and

a

i= 0 represent two extreme power asymmetric

cases, i.e., absolute bargaining power of manufacturers and RL pro-viders, respectively.Figs. 4–8present analytical results.

Fig. 4shows the variation in equilibrium SW (SW⁄_{). In both}

sce-narios, SW⁄_{increases as the bargaining power (}

_a

2) of manufacturer

2 increases. If the bargaining power (

a

1) of manufacturer 1 also

Table 1

Preset values of parameters used for quantitative analysis, where the values of cost-related parameters are determined using data obtained from semi-structured interviews; the values of government-related parameters are determined through reviewing several real cases implemented around the world.

1. Government-related parameters 3. Manufacturer-related parameters

Unit green tax f⁄

30 Unit manufacturing cost Cm 100

Unit green subsidy S⁄ ₅ _{Recycled component amount for unit product production k} ₆

Unit green beneﬁt d 19 4. RL-provider related parameters

Unit green costc 37 Unit cost for recycling one recycled component unit Cr 7

2. Number of competitors Unit cost for end-of-life product collection Ccol 20

Number of competitive manufacturers 2 5. Product demand market P = a bQ

Number of competitive RL-providers 2 a = 600 b = 1

Scenario II Scenario I SW * SW *

Fig. 4. Numerical results with respect to the correlations between bargaining power and social welfare (SW⁄

) obtained in Scenarios I (non-alliance) and II (RL-alliance), where a1anda2represent the bargaining powers of manufacturers 1 and 2 relative to RL-providers, respectively.

P * P * Scenario II Scenario I

Fig. 5. Numerical results with respect to the correlations between bargaining ower and product price (P⁄

) obtained in Scenarios I (non-alliance) and II (RL-alliance), wherea1

(11)

increases, SW⁄_{increases; however, the rate of increase in SW}⁄

de-clines. Therefore, we infer that SW⁄ _{correlates negatively with}

manufacturer bargaining power.

Fig. 5shows the variation in equilibrium product price (P⁄_).

Gi-ven the bargaining power (

a

1) of manufacturer 1, P⁄declines as the

bargaining power (

a

2) of manufacturer 2 increases; however, the

rate of decline in P⁄_{correlates negatively with}

_a

2(Fig. 5). A further

inference is that since a manufacturer with high bargaining power often negotiates a low recycled component supply price from RL providers, it can reduce the prices of its products. This variation in P⁄

is extremely important when the bargaining power of com-petitive manufacturers is highly asymmetric.

Speciﬁcally,Fig. 6indicates that a trade-off exists between vari-ations in equilibrium solutions for disaggregate production amounts (i.e., q

1 and q2) associated with these two competitive

manufacturers. The negatively and positively sloped curves

represent production of manufacturer 1 (q

1) and manufacturer 2

(q

2), respectively. When the bargaining power of manufacturer 2

(

a

2) increases subject to condition

a

2P

a

1, both q2and Q

⁄_increase

because the increase in q

2exceeds the rate of decline in q1. When

a

2<

a

1, the rate of increase in q2caused by the increase in

a

2

be-comes smaller than the rate of decline in, leading to a decline in to-tal production (Q⁄_). _{Fig. 7} _{shows the trade-offs for varying}

manufacturer proﬁts (

p

i) under equilibrium conditions. The curve

with the negative slope is the proﬁt curve (

p

1) for manufacturer 1,

and the curve with the positive slope is the proﬁt curve (

p

2) for

manufacturer 2. Thus, as the bargaining power of manufacturer 2 increases,

p

2 increases and

p

1 decreases. Speciﬁcally, when the

bargaining power of manufacturer 2 (

a

2) increases subject to

con-dition

a

2P

a

1, the incremental increase in proﬁt of manufacturer

II exceeds the decrease in proﬁt of manufacturer 1 (i.e., jD

p

2j > jD

p

1j). Conversely, when

a

2<

a

1, the incremental increase

* i q * i q Scenario II Scenario I q2 q2

Fig. 6. Numerical results with respect to the correlations between bargaining power and manufacturer production (q

i) obtained in Scenarios I (non-alliance) and II

(RL-alliance), wherea1anda2represent the bargaining powers of manufacturers 1 and 2 relative to RL-providers, respectively; negatively-sloped curves for q1; and

positively-sloped curves for q 2. * i π * i π Scenario II Scenario I

Fig. 7. Numerical results with respect to the correlations between bargaining power and manufacturer proﬁt (p

i) obtained in Scenarios I (non-alliance) and II (RL-alliance),

wherea1anda2represent the bargaining powers of manufacturers 1 and 2 relative to RL-providers, respectively; negatively-sloped curves forp1; and positively-sloped

curves forp 2. * all ξ * all ξ Scenario I Scenario II

Fig. 8. Numerical results with respect to the correlations between bargaining power and aggregate proﬁt of RL providers (n

all) obtained in Scenarios I (non-alliance) and II